EP4634797A1

EP4634797A1 - Machine learning models for dental restoration design generation

Info

Publication number: EP4634797A1
Application number: EP23829130.6A
Authority: EP
Inventors: Francis J. T. YATES; Michael Starr; Jonathan D. Gandrud; Seyed Amir Hossein Hosseini; Mariah Sonja Pereira Penha; Richard E Raby
Original assignee: Solventum Intellectual Properties Co
Current assignee: Solventum Intellectual Properties Co
Priority date: 2022-12-14
Filing date: 2023-12-14
Publication date: 2025-10-22
Also published as: WO2024127311A1

Abstract

Systems and methods are disclosed for generating a dental restoration tooth design. The method involves receiving a three-dimensional (3D) pre-restoration tooth representation and providing it as input to a trained encoder of a reconstruction autoencoder. The trained encoder outputs a lower- dimensional latent space representation of the 3D pre-restoration tooth. The latent space representation is then modified, and the modified representation is provided as input to a trained decoder of the reconstruction autoencoder. Using the modified latent space representation, the trained decoder reconstructs a 3D tooth representation that defines a post-restoration version of the 3D pre-restoration tooth. Finally, at least one oral care appliance is generated using the reconstructed 3D tooth representation. These systems and method enable efficient and accurate generation of dental restoration tooth designs, improving the overall oral care process.

Description

MACHINE LEARNING MODELS FOR DENTAL RESTORATION DESIGN GENERATION Related Documents [0001] The entire disclosure of PCT Application No. PCT/IB2022/057373 is incorporated herein by reference. The entire disclosures of each of PCT Applications with Publication Nos. WO2022123402A1, WO2021245480A1, and WO2020026117A1 are incorporated herein by reference. The entire disclosure of each of the following Provisional U.S. Patent Applications is incorporated herein by reference: 63/432,627; 63/366,492; 63/366,495; 63/352,850; 63/366,490; 63/366,494; 63/370,160; 63/366,507; 63/352,877; 63/366,514; 63/366,498; 63/366,514; and 63/264,914. Technical Field [0002] This disclosure relates to configurations and training of machine learning models to improve the accuracy of automatically generated 3D oral care representations (e.g., such as crowns and/or roots) which may be used in dental restoration and orthodontic treatment. Summary [0003] The present disclosure describes systems and techniques for training and using one or more machine learning models, such as neural networks, to generate 3D oral care representations. The techniques may train encoder-decoder structures to perform tooth restoration design generation. In particular, one or more autoencoders of this disclosure may be trained to reconstruct 3D oral care representations. The autoencoder(s) may be trained to reconstruct examples of 3D oral care representations that appear in the training dataset. In some instances, the autoencoder may be trained on examples of 3D triangle meshes (or polylines), and become configured to reconstruct examples of 3D triangles meshes (or polylines) of the type used in training (e.g., restored teeth for use in dental restoration, appliance components – such as for dental restoration, clear tray aligner trimlines, archform polyline or mesh, fixture models, an appliance design for 3D printing - such as an aligner tray design, or the like). [0004] An encoder-decoder structure may comprise at least one encoder or at least one decoder. Non- limiting examples of an encoder-decoder structure include a 3D U-Net, a transformer, a pyramid encoder- decoder or an autoencoder, among others. Non-limiting examples of autoencoders are variational autoencoders, regularized autoencoders, masked autoencoders or capsule autoencoders. [0005] In some implementations, the generative techniques described herein (e.g., which use encoder- decoder structures) may contain elements derived from a denoising diffusion model (e.g., a neural network which may be trained to iteratively denoise one or more point clouds – starting from points which are initialized stochastically or using a Gaussian distribution). In some implementations, the generative techniques described herein (e.g., which use encoder-decoder structures) may generate point clouds, at least in part, using one or more neural networks which are trained to use mathematical operations associated with continuous normalizing flows (e.g., the use of a neural network which may be trained in one form and then be inverted for use in inference). [0006] In some instances, an encoder-decoder structure may be trained on examples of matrices, transforms, or lists of 3D points, and become capable to reconstruct examples of those data types (e.g., coordinate system axes, which may be described using transforms, transformation matrices, transformation vectors, spline control points to describe archforms, and the like). For example, an encoder-decoder structure may be trained on a dataset comprising 3D triangle meshes (or point clouds) of tooth crowns and/or roots. Such an encoder-decoder structure may be trained to convert a tooth crown into a latent form using a 3D encoder (e.g., a latent vector or latent capsule) which may retain aspects of the shape and/or structure of the tooth crown, but in a reduced dimensionality form. This latent form may be reconstructed into a facsimile of the original tooth crown using a 3D decoder, after which point a reconstruction error (e.g., distance between corresponding mesh elements in two corresponding meshes) may be computed to quantify the difference between the original and reconstructed tooth crowns. If the reconstruction error is below a threshold in magnitude, then the reconstructed tooth crown may be considered to be a reasonable reproduction of the original tooth. A low reconstruction error shows that the latent form (e.g., latent vector or latent capsule) describes enough information about the original tooth to enable the tooth to be reconstructed. This latent form may be modified, for example, after a process of experimentation to map out the latent space. A modification to the latent form may result in a reconstructed tooth with desirable aspects, such as a shape which conforms with the distribution of ground truth examples (e.g., which have been approved by clinicians or technicians) of restored teeth in a training dataset. Stated another way, the latent form may be modified to yield a reconstructed tooth design with properties that make the tooth acceptable for use in dental restoration. In some examples, the restored tooth design may be used in the creation of a dental restoration appliance, such as a custom 3D printed matrix which is used to shape dental composite in-place on the patient’s teeth, so that the dental composite may be cured. The appliance may be used to fabricate veneers to be placed on one more teeth of the patient. [0007] More generally, an encoder-decoder structure may be trained to reconstruct examples of 3D oral care representations disclosed herein (e.g., mesh element labels for segmentation or mesh cleanup, transforms, appliance components, IPR cut surfaces, tooth restoration designs, trimlines, archforms, segmentation masks, among others). During inference, a trial 3D oral care representation (of the same variety that was used in training) may be encoded into latent form by the encoder portion of the encoder- decoder structure. That latent form may subsequently undergo intentional modification, and then be reconstructed by the decoder portion of the encoder-decoder structure, to yield an outputted 3D oral care representation with modified shape/structure/properties/aspects. [0008] Techniques of this disclosure may generate 3D representations of oral care data (e.g., tooth designs, appliance components, fixture model components, archforms, or others described herein) using encoder-decoder structures (e.g., reconstruction autonencoders). The encoder structure of a fully trained reconstruction autoencoder may generate a latent space representation of a 3D representation of oral care data (e.g., a tooth restoration design). One or more aspects of the latent representation (e.g., one or more dimensions of a latent vector) may, in some implementations, be modified (e.g., in response to one or more oral care arguments). In some implementations, a latent representation may be modified by a latent representation modification module (LRMM). The decoder structure of the trained reconstruction autoencoder may be used to reconstruct this modified latent vector, resulting in a reconstructed 3D representation of oral care data (e.g., a modified tooth restoration design) which differs from the input 3D representation of oral care data in one or more aspects. For example, a pre-restoration tooth may be provided to the encoder-decoder structure (e.g., where each of the encoder and decoder was fully trained as a part of a reconstruction autoencoder) and be encoded into a latent representation. That latent representation may undergo modification (e.g., using an LRMM) or by other means described herein (e.g., in response to one or more oral care arguments). The modified latent representation may be reconstructed by the decoder portion of the encoder-decoder structure, resulting in a post-restoration tooth design which has a shape and/or structure which is suitable for use in oral care appliance generation. 3D representations of this disclosure may comprise 3D meshes, 3D point clouds, voxelized representations, or the like. A 3D representation of oral care data may contain one or more mesh elements, such as points, vertices, edges, faces, or voxels. In some implementations, such as implementations of a tooth reconstruction autoencoder, a template 3D representation (e.g., a standardized example of a tooth mesh for a particular tooth type) may be used in a correspondence calculation. The mesh elements of the template may be ordered in a manner consistent with an arrangement that was used in training the autoencoder. One or more correspondences may be computed between one or more mesh elements of a 3D pre-restoration tooth representation and a template representation. [0009] In some implementations, the 3D pre-restoration tooth representation and the correspondences may then be provided as the execution-phase input to the trained reconstruction autoencoder. In some implementations, the encoder or the decoder of an encoder-decoder structure may be pretrained, at least in part, using a continuous normalizing flow, according to the descriptions herein. In some implementations, aspects of the style of one or more reference 3D representation of oral care data may be assigned to one or more target 3D representations of oral care data (e.g., one or more restoration tooth designs). Style transfer may assign aspects of the shape, structure and/or color of the reference to the target. The oral care arguments may, in some implementations, specify one or more aspects of an intended shape and/or structure for the reconstructed 3D oral care representation. For example, when a post-restoration tooth design is generated, the oral care arguments may influence the shapes of: the tooth silhouette, one or more mamelon grooves, one or more perikymata, one or more fossae, or one or more vertical striations of the post-restoration tooth design. In some instances, a reconstructed 3D representation of oral care data (e.g., a post-restoration tooth restoration design, an appliance component, a fixture model component, among others described herein) may be used in the generation of an oral care appliance (e.g., an orthodontic aligner tray, a dental restoration appliance, an indirect bonding tray, a veneer – such as a zirconia veneer). The oral care appliance may, in some implementations, be 3D printed. A dental restoration appliance may be used to shape dental composite in the patient’s mouth to form veneers. In some instances, the methods may be deployed at a clinical context, where the methods may be performed in near real-time during an encounter with a patient. Brief Description of Drawings [0010] FIG.1 shows a method of augmenting training data for use in training machine learning (ML) models of this disclosure. [0005] FIG.2 shows a method of training a capsule autoencoder. [0006] FIG.3 shows a method of training a tooth reconstruction autoencoder. [0007] FIG.4 shows a method of using a deployed fully trained tooth reconstruction autoencoder. [0008] FIG.5 shows a reconstructed tooth mesh, which has been reconstructed using a reconstruction autoencoder, according to techniques of this disclosure. [0009] FIG.6 shows a reconstructed tooth mesh, which has been reconstructed using a reconstruction autoencoder, according to techniques of this disclosure. [0010] FIG.7 shows a visualization of reconstruction error for a tooth. [0011] FIG.8 shows reconstruction error values for several tooth reconstructions. [0012] FIG.9 shows method of training a reconstruction autoencoder. [0013] FIG.10 shows non-limiting example code for a reconstruction autoencoder. [0014] FIG.11 shows examples of 3D representations which have been reconstructed, according to techniques of this disclosure. [0015] FIG.12 shows a latent space where loss incorporates reconstruction loss but does not incorporate KL-Divergence loss. [0016] FIG.13 shows a latent space in which the loss includes both reconstruction loss and KL- divergence loss. [0017] FIG.14 shows a method of training a reconstruction autoencoder using a capsule autoencoder. [0018] FIG.15 shows examples of vertical striations and mamelon grooves in teeth (e.g., tooth restoration designs). [0019] FIG.16 shows a method of training a continuous normalizing flows model to generate (or modify) a 3D oral care representation. [0020] FIG.17 shows a method of using a fully trained continuous normalizing flows model to generate (or modify) a 3D oral care representation. [0021] FIG.18 shows a method to extract refined neural network features from a 3D representation for use in style transfer. [0022] FIG.19 shows a method to extract refined neural network features from a 3D representation for use in style transfer (for Spatial, Structural, and/or Color Style Transfer). [0023] FIG.20 shows a pyramid encoder-decoder structure, which may be used to extract hierarchical features from a 3D representation. [0024] FIG.21 shows a U-Net structure, which may be used to extract hierarchical features from a 3D representation. [0025] FIG.22 shows a method of training a latent representation modification module (LRMM). [0026] FIG.23 shows a method of using a fully trained LRMM. Detailed Description [0011] Multiple techniques in digital oral care may benefit from the use of a first module (e.g., an autoencoder neural network) which has been trained to reconstruct a 3D oral care representation (e.g., trained to reconstruct a tooth mesh – comprising crown, root and/or attached articles). A 3D encoder may be trained to convert an oral care mesh into a latent form, and a 3D decoder may be trained to reconstruct that latent form into a facsimile of the received oral care mesh, where techniques disclosed herein may be used to measure the resulting reconstruction error. The first module may create a representation. A second module may use that representation for prediction. There may be one or more instances of the first module, and there may be one or more instances of the second module. [0012] Described herein are techniques which may make use of an autoencoder which has been trained for oral care mesh reconstruction, which provides the advantage of converting a potentially complex oral care mesh into a latent form (e.g., such as a latent vector or latent capsule) which may have reduced dimensionality and may be ingested by an instance of the second module (e.g., a predictive model for mesh cleanup, setups prediction, tooth restoration design generation, classification of 3D representations, validation of 3D representations, or setups comparison) for prediction purposes. While the dimensionality of the latent form may be reduced relative to the received oral care mesh, information about the reconstruction characteristics of the received oral care mesh may be retained. This latent representation of the original oral care mesh may be received as input to the predictive model of the second module, providing the advantage of improving accuracy and data precision in comparison to other techniques. The latent representation may, in some implementations, be modified according to the techniques of this disclosure to enable the predictive model of the second module to customize output data. An advantage of computing reconstruction error on a reconstructed oral care mesh is to allow systems so configured to verify that the reconstructed oral care mesh is a facsimile of the received oral care mesh (e.g., where one or more dimensions or other aspects of the reconstructed oral care mesh are measured to be within a threshold reconstruction error of the received oral care mesh), which is more difficult in the absence of a computed reconstructed error. In some implementations, the first module may also be trained to produce other kinds of representations, such as those generated by neural networks performing convolution and/or pooling operations (e.g., a network with a size 5 convolution kernel which also performs average pooling, or a network such as a U-Net). [0013] Either or both of the first and/or second modules may receive a variety of input data, as described herein, including tooth meshes for one or both arches of the patient. The tooth data may be presented in the form of 3D representations, such as meshes or point clouds. These data may be preprocessed, for example, by arranging the constituent mesh elements into lists and computing an optional mesh element feature vector for each mesh element. Such feature vectors may provide valuable information about the shape and/or structure of an oral care mesh to either or both of the first and/or second modules. For example, the first module, which generates the representations, may receive the vertices of a 3D mesh (or of a 3D point cloud) and compute a mesh element feature vector for each vertex. Such a feature vector may contain the XYZ coordinates of each vertex, in addition to other optional mesh element features described herein. Additional inputs may be received at the ingress point(s) of either or both of the first and/or second modules, such as one or more oral care metrics. Oral care metrics may be used for measuring one or more physical aspects of an oral care mesh (e.g., physical relationships within a tooth or between teeth). In some instances, an oral care metric may be computed for either or both of a malocclusion oral care mesh example and aground oral care mesh example which is then used in the training of either or both of the first and second modules. The metric value may be received as input of either or both of the first and second modules, as a way of training the underlying model of that particular module to encode a distribution of such a metric over the several examples of the training dataset. During training, the network may then receive this metric value as an input, to assist in training the network to link that inputted metric value to the physical aspects of the ground truth oral care mesh which is used in loss calculation. Such a loss calculation may quantify the difference between a prediction and a ground truth example (e.g., between a predicted oral care mesh and a ground truth oral care mesh). By providing the network data describing a metric value, the techniques of this disclosure may, through the course of loss calculation and subsequent backpropagation, train the network to encode a distribution of a given metric. In deployment, one or more oral care parameters (procedure parameters or restoration design parameters) may be defined to specify one or more aspects of an intended oral care mesh, which is to be generated using either or both of the first and/or second modules which has been trained for that purpose. In some implementations, an oral care parameter may be defined which corresponds to an oral care metric, which may be received as input to either or both of a deployed first module and/or a deployed second module and be taken as an instruction to that module to generate an oral care mesh with the specified customization. This interplay between oral care metrics and oral care parameters may also apply to the training and deployment of other predictive models in oral care as well. [0014] The predictive models of the present disclosure may, in some implementations, produce more accurate results by the incorporation of one or more of the following inputs: archform information V, interproximal reduction (IPR) information U, tooth dimension information P, tooth gap information Q, latent capsule representations of oral care meshes T, latent vector representations of oral care meshes A, procedure parameters K (which may describe a clinician’s intended treatment of the patient), doctor preferences L (which may describe the typical procedure parameters chosen by a doctor), flags regarding tooth status M (such as for fixed or pinned teeth), tooth position information N, tooth orientation information O, tooth name/dental notation R, oral care metrics S (comprising at least one of oral care metrics and restoration design metrics). [0015] Systems of this disclosure may, in some instances, be deployed at a clinical context (such as a dental or orthodontic office) for use by clinicians (e.g., doctors, dentists, orthodontists, nurses, hygienists, oral care technicians). Such systems which are deployed at a clinical context may enable clinicians to process oral care data (such as dental scans) in the clinic environment, or in some instances, in a "chairside" context (where the patient is present in the clinical environment). A non-limiting list of examples of techniques may include: segmentation, mesh cleanup, coordinate system prediction, CTA trimline generation, restoration design generation, appliance component generation or placement or assembly, generation of other oral care meshes, the validation of oral care meshes, setups prediction, removal of hardware from tooth meshes, hardware placement on teeth, imputation of missing values, clustering on oral care data, oral care mesh classification, setups comparison, metrics calculation, or metrics visualization. The execution of these techniques may, in some instances, enable patient data to be processed, analyzed and used in appliance generation by the clinician before the patient leaves the clinical environment (which may facilitate treatment planning because feedback may be received from the patient during the treatment planning process). [0016] Systems of this disclosure may automate operations in digital orthodontics (e.g., setups prediction, hardware placement, setups comparison), in digital dentistry (e.g., restoration design generation) or in combinations thereof. Some techniques may apply to either or both of digital orthodontics and digital dentistry. A non-limiting list of examples is as follows: segmentation, mesh cleanup, coordinate system prediction, oral care mesh validation, imputation of oral care parameters, oral care mesh generation or modification (e.g., using autoencoders, transformers, continuous normalizing flows or denoising diffusion models), metrics visualization, appliance component placement or appliance component generation or the like. In some instances, systems of this disclosure may enable a clinician or technician to process oral care data (such as scanned dental arches). In addition to segmentation, mesh cleanup, coordinate system prediction or validation operations, the systems of this disclosure may enable orthodontic treatment planning, which may involve setups prediction as at least one operation. Systems of this disclosure may also enable restoration design generation, where one or more restored tooth designs are generated and processed in the course of creating oral care appliances. Systems of this disclosure may enable either or both of orthodontic or dental treatment planning, or may enable automation steps in the generation of either or both of orthodontic or dental appliances. Some appliances may enable both of dental and orthodontic treatment, while other appliances may enable one or the other. [0017] Techniques of this disclosure may require a training dataset of hundreds or thousands of cohort patient cases, to ensure that the neural network is able to encode the distribution of patient cases which are likely to be encountered in clinical treatment. A cohort patient case may include a set of tooth crown meshes, a set of tooth root meshes, or a data file containing attributes of the case (e.g., a JSON file). A typical example of a cohort patient case may contain up to 32 crown meshes (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces), up to 32 root meshes (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces), multiple gingiva mesh (e.g., which may each contain tens of thousands of vertices or tens of thousands of faces) or one or more JSON files which may each contain tens of thousands of values (e.g., objects, arrays, strings, real values, Boolean values or Null values). [0018] Aspects of the present disclosure can provide a technical solution to the technical problem of generating (or modifying) 3D representations of oral care data, using encoder-decoder structures (e.g., autoencoders), for use in oral care appliance generation. In particular, by practicing techniques disclosed herein computing systems specifically adapted to perform 3D representation generation (or modification) for oral care appliance generation are improved. For example, aspects of the present disclosure improve the performance of a computing system having a 3D representation of the patient’s dentition by reducing the consumption of computing resources. In particular, aspects of the present disclosure reduce computing resource consumption by decimating 3D representations of the patient’s dentition (e.g., reducing the counts of mesh elements used to describe aspects of the patient’s dentition) so that computing resources are not unnecessarily wasted by processing excess quantities of mesh elements. Additionally, decimating the meshes does not reduce the overall predictive accuracy of the computing system (and indeed may actually improve predictions because the input provided to the ML model after decimation is a more accurate (or better) representation of the patient’s dentition). For example, noise or other artifacts which are unimportant (and which may reduce the accuracy of the predictive models) are removed. That is, aspects of the present invention provide for more efficient allocation of computing resources and in a way that improves the accuracy of the underlying system. [0019] Furthermore, aspects of the present disclosure may need to be executed in a time-constrained manner, such as when an oral care appliance must be generated for a patient immediately after intraoral scanning (e.g., while the patient waits in the clinician’s office). As such, aspects of the present disclosure are necessarily rooted in the underlying computer technology of generating (or modifying) 3D representations used in digital oral care (e.g., digital dentistry) and cannot be performed by a human, even with the aid of pen and paper. For instance, implementations of the present disclosure must be capable of: 1) storing thousands or millions of mesh elements of the patient’s dentition in a manner that can be processed by a computer processor; 2) performing calculation on thousands or millions of mesh elements, e.g., to quantify aspects of the shape and or/structure of an individual tooth in the 3D representation of the patient’s dentition; and 3) generating (or modifying) 3D representations of oral care data (e.g., tooth restoration designs, fixture model components, or appliance components, among others) for use in oral care appliance generation, and do so during the course of a short office visit. [0020] One or more oral care arguments may be defined to specify one or more aspects of an intended 3D oral care representation (e.g., a 3D mesh, a polyline, a 3D point cloud or a voxelized geometry), which is to be generated using the machine learning models described herein (e.g., 3D representation generation models using encoder-decoder structures – such as autoencoders) that have been trained for that purpose. In some implementations, oral care arguments may be defined to specify one or more aspects of a customized vector, matrix or any other numerical representation (e.g., to describe 3D oral care representations such as control points for a spline, an archform, a transform to place a tooth or appliance component relative to another 3D oral care representation, or a coordinate system), which is to be generated using the machine learning models described herein (e.g., 3D representation generation models using encoder-decoder structures) that have been trained for that purpose. A customized vector, matrix or other numerical representation may describe a 3D oral care representation which conforms to the intended outcome of the treatment of the patient. Oral care arguments may include oral care metrics or oral care parameters, among others. Oral care arguments may specify one or more aspects of an oral care procedure – such as orthodontic setups prediction or restoration design generation, among others. In some implementations, one or more oral care parameters may be defined which correspond to respective oral care metrics. Oral care arguments can be provided as the input to the machine learning models described herein and be taken as an instruction to that module to generate an oral care mesh with the specified customization, to place an oral care mesh for the generation of an orthodontic setup (or appliance), to segment an oral care mesh, or to clean up an oral care mesh, to generate or modify a 3D representation of oral care data, to name a few examples. This interplay between oral care metrics and oral care parameters may also apply to the training and deployment of other predictive models in oral care as well. [0021] This disclosure pertains to digital oral care, which encompasses the fields of digital dentistry and digital orthodontics. This disclosure generally describes methods of processing three-dimensional (3D) representations of oral care data. It should be understood, without loss of generality, that there are various types of 3D representations. One type of 3D representation is a 3D geometry. A 3D representation may include, be, or be part of one or more of a 3D polygon mesh, a 3D point cloud (e.g., such as derived from a 3D mesh), a 3D voxelized representation (e.g., a collection of voxels – for sparse processing), or 3D representations which are described by mathematical equations. Although the term “mesh” is used frequently throughout this disclosure, the term should be understood, in some implementations, to be interchangeable with other types of 3D representations. A 3D representation may describe elements of the 3D geometry and/or 3D structure of an object. [0022] Dental arches S1, S2, S3 and S4 all contain the exact same tooth meshes, but those tooth meshes are transformed differently, according to the following description. A first arch S1 includes a set of tooth meshes arranged (e.g., using transforms) in their positions in the mouth, where the teeth are in the mal positions and orientations. A second arch S2 includes the same set of tooth meshes from S1 arranged (e.g., using transforms) in their positions in the mouth, where the teeth are in the ground truth setup positions and orientations. A third arch S3 includes the same meshes as S1 and S2, which are arranged (e.g., using transforms) in their positions in the mouth, where the teeth are in the predicted final setup poses (e.g., as predicted by one or more of the techniques of this disclosure). S4 is a counterpart to S3, where the teeth are in the poses corresponding to one of the several intermediate stages of orthodontic treatment with clear tray aligners. [0023] It should be understood, without the loss of generality, that the techniques of this disclosure which apply to final setups are also applicable to intermediate staging in orthodontic treatment, particularly geometric deep learning (GDL) Setups, reinforcement learning (RL) Setups, variational autoencoder (VAE) Setups, Capsule Setups, multilayer perceptron (MLP) Setups, Diffusion Setups, pose transfer (PT) Setups, Similarity Setups, force directed graphs (FDG) Setups, Transformer Setups, Setups Comparison, or Setups Classification. The Metrics Visualization aspects of this disclosure may also be configured to visualize data from both final setups and intermediate stages. MLP Setups, VAE Setups and Capsule Setups each fall within the scope of Autoencoder Setups. Some implementations of MLP Setups may fall within the Scope of Transformer Setups. Representation Setups refers to any of MLP Setups, VAE Setups, Capsule Setups and any other setups prediction machine learning model which uses an autoencoder to create the representation for at least one tooth. [0024] Each of the setups prediction techniques of this disclosure is applicable to the fabrication of clear tray aligners and/or indirect bonding trays. The setups predictions techniques may also be applicable to other products that involve final teeth poses, also. A pose may comprise a position (or location) and a rotation (or orientation). [0025] A 3D mesh is a data structure which may describe the geometry or shape of an object related to oral care, including but not limited to a tooth, a hardware element, or a patient’s gum tissue. A 3D mesh may include one or more mesh elements such as one or more of vertices, edges, faces and combinations thereof. In some implementations, mesh elements may include voxels, such as in the context of sparse mesh processing operations. Various spatial and structural features may be computed for these mesh elements and be provided to the predictive models of this disclosure, with the predictive models of this disclosure providing the technical advantage of improving data precision in the form of the models of this disclosure outputting more accurate predictions. [0026] A patient’s dentition may include one or more 3D representations of the patient’s teeth (e.g., and/or associated transforms), gums and/or other oral anatomy. An orthodontic metric (OM) may, in some implementations, quantify the relative positions and/or orientations of at least one 3D representation of a tooth relative to at least one other 3D representation of a tooth. A restoration design metric (RDM) may, in some implementations, quantify at least one aspect of the structure and/or shape of a 3D representation of a tooth. An orthodontic landmark (OL) may, in some implementations, locate one or more points or other structural regions of interest on a 3D representation of a tooth. An OL may, in some implementations, be used in the generation of an orthodontic or dental appliance, such as a clear tray aligner or a dental restoration appliance. A mesh element may, in some implementations, comprise at least one constituent element of a 3D representation of oral care data. For example, in the case of a tooth that is represented by a 3D mesh, mesh elements may include at least: vertices, edges, faces and voxels. A mesh element feature may, in some implementations, quantify some aspect of a 3D representation in proximity to or in relation with one or more mesh elements, as described elsewhere in this disclosure. Orthodontic procedure parameters (OPP) may, in some implementations, specify at least one value which defines at least one aspect of planned orthodontic treatment for the patient (e.g., specifying desired target attributes of a final setup in final setups prediction). Orthodontic Doctor preferences (ODP) may, in some implementations, specify at least one typical value for an OPP, which may, in some instances, be derived from past cases which have been treated by one or more oral care practitioners. Restoration Design Parameters (RDP) may, in some implementations, specify at least one value which defines at least one aspect of planned dental restoration treatment for the patient (e.g., specifying desired target attributes of a tooth which is to undergo treatment with a dental restoration appliance). Doctor Restoration Design Preferences (DRDP) may, in some implementations, specify at least one typical value for an RDP, which may, in some instances, be derived from past cases which have been treated by one or more oral care practitioners. [0027] 3D oral care representations may include, but are not limited to: 1) a set of mesh element labels which may be applied to the 3D mesh elements of teeth/gums/hardware/appliance meshes (or point clouds) in the course of mesh segmentation or mesh cleanup; 2) 3D representation(s) for one or more teeth/gums/hardware/appliances for which shapes have been modified (e.g., trimmed, distorted, or filled- in) in the course of mesh segmentation or mesh cleanup; 3) one or more coordinate systems (e.g., describing one, two, three or more coordinate axes) for a single tooth or a group of teeth (such as a full arch – as with the LDE coordinate system); 4) 3D representation(s) for one or more teeth for which shapes have been modified or otherwise made suitable for use in dental restoration; 5) 3D representation(s) for one or more dental restoration appliance components; 6) one or more transforms to be applied to one or more of: dental restoration appliance library component placement relative to one or more teeth, a tooth to be placed for an orthodontic setup (either final setup or intermediate stage), a hardware element to be placed relative to one or more teeth or the like; 7) an orthodontic setup; 8) a 3D representation of a hardware element (such as facial bracket, lingual bracket, orthodontic attachment, button, hook, bite ramp, etc.) to be placed relative to one or more teeth, etc.; 8) a 3D representation of a bonding pad for a hardware element (which may be generated for a specific tooth by outlining a perimeter on the tooth, specifying a thickness to form a shell, and then subtracting-out the tooth via a Boolean operation); 9) 3D representation of a clear tray aligner (CTA); 10) the location or shape of a CTA trimline (e.g., described as either a mesh or polyline); 11) archform that describes the contours or layout of an arch of teeth (e.g., described as a 3D polyline or as a 3D mesh or surface), which may follow the incisal edges one or more teeth, which may follow the facial surfaces of one or more teeth, which may in some implementations correspond to the maloccluded arch and in other implementations correspond to the final setup arch (the effects of malocclusion on the shape of the archform may be diminished by smoothing or averaging of the shape of the archform), which may be described by one or more control points and/or a spline; 12) 3D representation of a fixture models (e.g., depictions of teeth and gums for use in thermoforming clear tray aligners, or depictions of teeth/gums/hardware for use in thermoforming indirect bonding trays); 13) one or more latent space vectors (or latent capsules) produced by the 3D encoder stage of a 3D autoencoder which has been trained on the reconstruction of oral care meshes (e.g., a variational autoencoder which has been trained for tooth reconstruction); 14) one or more oral care metrics values (e.g., such as orthodontic metrics or restoration design generation metrics) for one or more teeth; 15) one or more landmarks (e.g., 3D points) which describe the shapes and/or geometrical attributes of one or more teeth, other dentition structures or hardware structures (e.g., to be used in orthodontic setups creation or restoration appliance component generation or placement); 16) 3D representation created by scanning (e.g., optically scanning, CT scanning or MRI scanning) a 3D printed part corresponding to one or more teeth/gums/hardware/appliances (e.g., a scanned fixture model); 17) 3D printed aligners (including optionally local thickness, reinforcing rib geometry, flap positioning, or the like) 18) 3D representation of the patient's dentition that was captured chairside by a clinician or medical practitioner (e.g., in a context where the 3D representation is validated chairside, before the patient leaves the clinic, so that errors can be detected and re-scans performed as necessary); 19) dental restoration tooth design (e.g., for veneers, crowns, bridges or dental restoration appliances); 20) 3D representations of one or more teeth for use in digital oral care treatment; 21) other 3D printed parts pertaining to oral care procedures or other fields; 22) IPR cut surfaces – such as an IPR cut plane which may define a portion of enamel to be removed from a tooth; 23) one or more orthodontic setups transforms associated with one or more IPR cut surfaces; 24) a (digital) pontic tooth design which may fill at least a portion of the space between teeth to allow room in an orthodontic setup for an erupting tooth to later emerge from the gums; or 25) a component of a fixture model (e.g., comprising fixture model components such as interproximal webbing, block-out, bite locks, bite ramps, interproximal reinforcement, gingival ridges, torque points, power ridges, pontic tooth or dimples, among others). [0028] The techniques of this disclosure may be advantageously combined. For example, the Setups Comparison tool may be used to compare the output of the GDL Setups model against ground truth data, compare the output of the RL Setups model against ground truth data, compare the output of the VAE Setups model against ground truth data and compare the output of the MLP Setups model against ground truth data. With each of these setups prediction models compared against ground truth data, it may be possible to determine which model gives the best performance on a certain dataset or within a given problem domain. Furthermore, the Metrics Visualization tool can enable a global view of the final setups and intermediate stages produced by one or more of the setups prediction models, with the advantage of enabling the selection of the best setups prediction model. The Metrics Visualization tool, furthermore, enables the computation of metrics which have a global scope over a set of intermediate stages. These global metrics may, in some implementations, be consumed as inputs to the neural networks for predicting setups (e.g., GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups, among others). The global metrics may also be provided to FDG Setups. The local metrics from this disclosure (i.e., a local metric is a metric which may be computed for one stage or setup of treatment, rather than over several stages or setups) may, in some implementations, be consumed by the neural networks herein for predicting setups, with the advantage of improving predictive results. The metrics described in this disclosure may, in some implementations, be visualized using the Metric Visualization tool. [0029] The VAE and MAE models for mesh element labelling and mesh in-filling can be advantageously combined with the setups prediction neural networks, for the purpose of mesh cleanup ahead of or during the prediction process. In some implementations, the VAE for mesh element labelling may be used to flag mesh elements for further processing, such as metrics calculation, removal or modification. In some instances, such flagged mesh elements may be provided as inputs to a setups prediction neural network, to inform that neural network about important mesh features, attributes or geometries, with the advantage of improving the performance of the resulting setups prediction model. In some implementations, mesh in-filling may cause the geometry of a tooth to become more nearly complete, enabling the better functioning of a setups prediction model (i.e., improved correctness of prediction on account of better-formed geometry). In some instances, a neural network to classify a setup (i.e., the Setups Classifier) may aid in the functioning of a setups prediction neural network, because the setups classifier tells that setups prediction neural network when the predicted setup is acceptable for use and can be provided to a method for aligner tray generation. A Setups Classifier (e.g., GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups and FDG Setups, among others) may aid in the generation of final setups and also in the generation of intermediate stages. Furthermore, a Setups Classifier neural network may be combined with the Metrics Visualization tool. In other implementations, a Setups Classification neural network may be combined with the Setups Comparison tool (e.g., the Setup Comparison tool may output an indication of how a setup produced in part by the Setups Classifier compares to a setup produced by another setups prediction method). In some implementations, the VAE for mesh element labelling may identify one or more mesh elements for use in a metrics calculation. The resulting metrics outputs may be visualized by the Metrics Visualization tool. [0030] In some examples, the Setups Classifier neural network may aid in the setups prediction technique described in U.S. Patent Application No. US20210259808A1 (which is incorporated herein by reference in its entirety) or the setups prediction technique described in PCT Application with Publication No. WO2021245480A1 (which is incorporated herein by reference in its entirety) or in PCT Application No. PCT/IB2022/057373 (which is incorporated herein by reference in its entirety). The Setups Classifier would help one or more of those techniques to know when the predicted final setup is most nearly correct. In some instances, the Setups Classifier neural network may output an indication of how far away from final setup a given setup is (i.e., a progress indicator). [0031] In some implementations, the latent space embedding vector(s) from the reconstruction VAE can be concatenated with the inputs to the setups prediction neural network described in WO2021245480A1. The latent space vectors can also be incorporated as inputs to the other setups prediction models: GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups and Diffusion Setups, among others. The advantage is to impart the reconstruction characteristics (e.g., latent vector dimensions of a tooth mesh) to that neural network, hence improving the generated setups prediction. [0032] In some examples, the various setups prediction neural networks of this disclosure may work together to produce the setups required for orthodontic treatment. For example, the GDL Setups model may produce a final setup, and the RL Setups model may use that final setup as input to produce a series of intermediate stages setups. Alternatively, the VAE Setups model (or the MLP Setups model) may create a final setup which may be used by an RL Setups model to produce a series of intermediate stages setups. In some implementations, a setup prediction may be produced by one setups prediction neural network, and then taken as input to another setups prediction neural network for further improvements and adjustments to be made. In some implementations, such improvements may be performed in iterative fashion. [0033] In some implementations, a setups validation model, such as the model disclosed in US Provisional Application No. US63/366495, may be involved in this iterative setups prediction loop. First a setup may be generated (e.g., using a model trained for setups prediction, such as GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups and FDG Setups, among others), then the setup undergoes validation. If the setup passes validation, the setup may be outputted for use. If the setup fails validation, the setup may be sent back to one or more of the setups prediction models for corrections, improvements and/or adjustments. In some instances, the setups validation model may output an indication of what is wrong with the setup, enabling the setups generation model to make an improved version upon the next iteration. The process iterates until done. [0034] Generally speaking, in some implementations, two or more of the following techniques of the present disclosure may be combined in the course of orthodontic and/or dental treatment: GDL Setups, Setups Classification, Reinforcement Learning (RL) Setups, Setups Comparison, Autoencoder Setups (VAE Setups or Capsule Setups), VAE Mesh Element Labeling, Masked Autoencoder (MAE) Mesh In- filling, Multi-Layer Perceptron (MLP) Setups, Metrics Visualization, Imputation of Missing Oral Care Parameters Values, Tooth Classification Using Latent Vector, FDG Setups, Pose Transfer Setups, Restoration Design Metrics Calculation, Neural Network Techniques for Dental Restoration and/or Orthodontics (e.g., 3D Oral Care Representation Generation or Modification Using Transformers or Autoencoders), Landmark-based (LB) Setups, Diffusion Setups, Imputation of Tooth Movement Procedures, Capsule Autoencoder Segmentation, Diffusion Segmentation, Similarity Setups, Validation of Oral Care Representations (e.g., using autoencoders), Coordinate System Prediction, Restoration Design Generation, or 3D Oral Care Representation Generation or Modification Using Denoising Diffusion Models. [0035] In some instances, restoration design generation may be combined with orthodontic treatment. For example, orthodontic treatment, such as with clear aligners, may in some instances, be applied to move one or more teeth so that a target pre-restoration tooth is made more accessible for restoration treatment. Stated another way, upon the moving of one or more adjacent teeth, a target pre- restoration tooth may be made more accessible for treatment by a dental restoration appliance, such as the 3M FILTEK Matrix or access may be permitted for placement of an indirect restoration such as an inlay, onlay, crown or veneer. A scanned arch may be segmented, undergo mesh cleanup, or be involved in coordinate system prediction. Setups prediction models such as GDL Setups and others disclosed herein may be applied in the generation of final setups and/or intermediate stages. These setups may be assembled into fixture models, each of which may then be 3D printed, which may be followed by the thermoforming and trimming of an aligner tray for orthodontic treatment. The one or more aligner trays may be applied to the patient’s dentition, ahead of dental restoration treatment. Planning for the design of restorations may occur prior to tooth movement and/or after tooth movement, and at various levels of detail. For instance, tooth movements and tooth restoration plans may be planned early in treatment, and subsequently be updated mid-treatment based on the degree of progress in attainment of the treatment plan. In particular, high resolution mid-treatment scans may be used to design final contours for the restoration design of one or more teeth. In this way, the restoration contours may compensate for variability in the precise attainment of the orthodontic correction. In this way, orthodontic treatment and dental restoration treatment may be combined to produce outcomes for patients which are more optimal than would otherwise be possible with either technique used in isolation. [0036] Oral care parameters may include one or more values that specify orthodontic procedure parameters, or restoration design parameters (RDP), as described herein. Oral care parameters may define one or more intended aspects of a 3D oral care representation and may be provided to an ML model to promote that ML model to generate output which may be used in the generation of oral care appliances that are suitable for the treatment of a patient. Other types of values include doctor preferences and restoration design preferences, as described herein. Doctor preferences and restoration design preferences may define the typical treatment choices or practices of a particular clinician. Restoration design preferences are subjective to a particular clinician, and so differ from restoration design parameters. In some implementations, doctor preferences or restoration design preferences may be computed by unsupervised means, such as clustering, which may determine the typical values that a clinician uses in patient treatment. Those typical values may be stored in a datastore and recalled to be provided to an automated ML model as default values (e.g., default values which may be modified before execution of the model). [0037] For example, one clinician may prefer one value for a restoration design parameter (RDP), while another clinician may prefer a different value for that RDP, when faced with a similar diagnosis or treatment protocol. One example of such an RDP is dental restoration style. Procedure parameters and/or doctor preferences may, in some implementations, be provided to a setups prediction model for orthodontic treatment, for the purpose of improving the customization of the resulting orthodontic appliance. Restoration design parameters and doctor restoration preferences may in some implementations be used to design tooth geometry for use in the creation of a dental restoration appliance, for the purpose of improving the customization of that appliance. In addition to oral care parameters, doctor preferences, and doctor restoration preferences, some implementations of ML prediction models of this disclosure, in orthodontic treatment, may also take as input a setup (e.g., an arrangement of teeth). In some such implementations, an ML prediction model of this disclosure may take as input a final setup (i.e., final arrangement of teeth), such as in the case of a prediction model trained to generate intermediate stages. For simplicity, these preferences are referred to as doctor restoration preferences, but it is intended to be used in a non-limiting sense. Specifically, it should be appreciated that these preferences may be specified by any treating or otherwise appropriate medical professional and are not intended to be limited to doctor preferences per se (i.e., preferences from someone in possession of an M.D. or equivalent degree). [0038] An oral care professional or clinician, such as a dentist or orthodontist, may specify information about patient treatment in the form of a patient-specific set of procedure parameters. In some instances, an oral care professional may specify a set of general preferences (aka doctor preferences) for use over a broad range of cases, to use as default values in the set of procedure parameters specification process. Oral care parameters may in some implementations be incorporated into the techniques described in this disclosure, such as one or more of GDL Setups, VAE Setups, RL Setups, Setups Comparison, Setups Classification, VAE Mesh Element Labelling, MAE Mesh In-Filling, Validation Using Autoencoders, Imputation of Missing Procedure Parameters Values, Metrics Visualization, or FDG Setups. One or more of these models may take as input one or more procedure parameters vector K and/or one or more doctor preference vectors L. In some implementations, one or more of these models may introduce to one or more of a neural network’s hidden layers one or more procedure parameters vector K and/or one or more doctor preferences vectors L. In some implementations, one or more of these models may introduce either or both of K and L to a mathematical calculation, such as a force calculation, for the purpose of improving that calculation and the ultimate customization of the resulting appliance to the patient. [0039] Some implementations of a neural network for predicting a setup (such as GDL Setup, VAE Setup or RL Setup) may incorporate information from an oral care professional (aka doctor). This information may influence the arrangement of teeth in the final setup, bringing the positions and orientations of the teeth into conformance with a specification set by the doctor, within tolerances. In some implementations of the GDL Setup model, oral care parameters may be provided directly to the generator network as a separate input alongside the mesh data. In some implementations of GDL Setups, oral care parameters may be incorporated into the feature vector which is computed for each mesh element before the mesh elements are input to the generator for processing. Some implementations of a VAE Setup model may incorporate oral care parameters into the setups predictions. In some implementations, the procedure parameters K and/or the doctor preference information L may be concatenated with the latent space vector C. A doctor’s preferences (e.g., in an orthodontic context) and/or doctor’s restoration preferences may be indicated in a treatment form, or they could be based upon characteristics in treatment plans such as final setup characteristics (e.g., amount of bite correction or midline correction in planned final setups), intermediate staging characteristics (e.g., treatment duration, tooth movement protocols, or overcorrection strategies), or outcomes (e.g., number of revisions/refinements). [0040] The restoration treatment of the patient may involve the specification of one or more of the following: restoration guidelines, restoration design parameters, and/or restoration rules for modifying one or more aspects of a patient’s dentition. One or more of many possible factors may be considered in designing a 3D restoration, whether from an esthetic standpoint and/or from a technical standpoint. For instance, from an esthetic standpoint, the dental and facial midlines and angulation may provide overall guidance, as does the amount of tooth seen by others when the lips are at rest and/or when smiling. After those criteria are considered, a set of “golden proportions” may also inform the esthetic design of overall tooth sizes. Tooth-to-tooth proportion may be configured to reflect these “golden proportions,” which are: 1.618:1.0:0.618 for the central incisor, lateral incisor, and the canine, respectively. [0041] Limitations based on tooth position (i.e., malocclusion) and orientation (i.e., rotation and inclination) are balanced against trying to achieve proper symmetry, tooth proportion, and tooth-to-tooth proportion. After these parameters are established, a variety of tooth shapes may be leveraged to match the overall esthetic of the patient's face and smile. For example, tooth shapes may be generally rectangular with squared edges, or they may be generally ovoid with rounded edges. Additionally, tooth-to-tooth proportions may be manipulated to invoke a different overall esthetic. 3D Dental CAD programs often provide libraries of different tooth “styles” to choose from and offer designers the ability to tune the result to best match the esthetic and medical requirements of the doctor and patient. In some examples, symmetry may be observed in that the left side should mirror the right side, and symmetry may thereby be measured. [0042] Tooth length, width, and width-to-length esthetic relationships may be specified for one or more teeth. In one example, the length for a maxillary central incisor may be set to 11 mm, and the width- to-length esthetic relationship may be set to either 70% or 80%. In some examples, the lateral incisors may be between 1.0 mm and 2.5 mm shorter than the central incisors. Canine teeth may, in some instances, be between 0.5 mm and 1.0 mm shorter than the central incisors. Other proportions and measurements are possible for various teeth. [0043] From a technical standpoint, there are other considerations that may be taken into account. For instance, restorations produced from a given material must be of sufficient thickness to have the necessary mechanical strength required for long term use. Additionally, the tooth width and shape must be designed to provide a suitable contact with the adjacent teeth. [0044] The example Style options in the list below are from the LVI standards, from the Las Vegas Institute (LVI) of Advanced Dental Studies. Other style guides are commercially or freely available. [0045] In these and/or other examples, a neural network engine of this disclosure may incorporate as an input one or more of accepted “golden proportion” guidelines for the size of teeth, accepted “ideal” tooth shapes, patient preferences, practitioner preferences, etc. [0046] Restoration design parameters (RDP) may be used to encode aspects of smile design guidelines described herein, such as parameters which pertain to the intended dimensions of a restored tooth. Non- limiting examples of restoration design parameters are shown in Table 1. Restoration design parameters are intended as instructions and/or specifications which describe the shape and/or form that one or more teeth should assume after the completion of dental restoration treatment. One or more RDP may be received by a neural network or other machine learning or optimization algorithm for dental restoration design, with the advantage of providing guidance to that optimization algorithm. Some neural networks may be trained for dental restoration design generation, such as some examples of a GAN or an autoencoder. In some instances, a dental restoration design may be used to define the target shapes of one or more teeth for the generation of a dental restoration appliance. In some instances, a dental restoration design may be used to define the target teeth shapes for the generation of one or more veneers. [0047] A partial list of tooth dimensions may include length, width, height, circumference, diameter, diagonal measure, volume—any of which dimensions may be normalized in comparison to another tooth or teeth. In some implementations, one or more restoration design parameters may be defined which pertain to a gap between two or more teeth, and the amount, if any, of the gap which the patient wishes to remain after treatment (e.g., such as when a patient wishes to retain a small gap between the upper central incisors). [0048] Additional restoration design parameters may include the parameters specified in Table 1. In the event that one of these parameters contradicts another, the following order may determine precedence (i.e., let the first parameter in the following list be considered authoritative). If a parameter value is not specified, then that parameter may be ignored. In some implementations, default values may be introduced for one or more parameters. Such default values may be determined, for example, through clustering of prior patient cases. A golden proportion guideline may specify one or more numbers pertaining to the widths of adjacent teeth, such as: {1.6, 1, 0.6}. Parameter Name Parameter Value of Unit of Measure Golden proportion guideline {guideline01, guideline02, guideline03, guideline04, etc.} Tooth width at base (mesial to distal distance) [millimeters] Tooth width at incisal edge (mesial to distal [millimeters] distance) Tooth height (gingival to incisal distance) [millimeters] Width-to-length esthetic relationship [percentage] Tooth-to-tooth proportion – upper right central [real number] incisor width to upper lateral incisor width Tooth-to-tooth proportion – upper right lateral [real number] incisor width to upper cuspid width Tooth-to-tooth proportion – lower right central [real number] incisor width to lower lateral incisor width Tooth-to-tooth proportion – lower right lateral [real number] incisor width to lower cuspid width Tooth-to-tooth proportion – upper left central [real number] incisor width to upper lateral incisor width Tooth-to-tooth proportion – upper left lateral [real number] incisor width to upper cuspid width Tooth-to-tooth proportion – lower left central [real number] incisor width to lower lateral incisor width Tooth-to-tooth proportion – lower left lateral [real number] incisor width to lower cuspid width Overall tooth shape (more than one may apply) {rectangular or ovoid, squared edges or rounded edges} Amount of tooth display when the lips are at rest [millimeters] Dental restoration style {youth, geriatric, natural, oval, etc.} Style {dominant, aggressive, focused, enhanced, functional, natural, Hollywood, mature, vigorous, youthful, oval, softened, or other examples from the LVI style guide, etc.} Tooth morphology – shape style guide [triangular, oval and rectangular, etc.] Tooth morphology – angle lines [lines_style01, lines_style02, lines_style03, etc.] Tooth morphology – incisal angles and [angles_style01, angles_style02, angles_style03, embrasures etc.] Tooth morphology – buccal contour [contour_style01, contour_style02, contour_style03, etc.] Tooth morphology – Mamelon grooves [mamelon_style01, mamelon_style02, mamelon_style03, etc.] Tooth morphology – perikymata [perikymata_style01, perikymata_style02, perikymata_style03, etc.] Table 1 [0049] Tooth-to-tooth proportions may also be defined between other pairs of teeth as well. Proportions may be made relative to tooth widths, heights, diagonals, etc. Angle lines, incisal angles and buccal contours may describe primary aspects of tooth macro shape. Mamelon grooves may be vertical macro textures on the front of a tooth, and sometimes may take a V-shape. Striations or perikymata may be a horizontal micro texture on the teeth. Symmetry may be generally desired. There may be differences between male and female patients. [0050] Parameters may be defined to encode doctor restoration design preferences (DRP), as pertains to various use case scenarios. These use case scenarios may reflect information about the treatment preferences of one or more doctors, and directly affect the characteristics of one or more teeth in a dental restoration design or a veneer. In addition, DRDP may describe preferred or habitually involved values or ranges of values of RDP for a doctor or other treating medical professional. In some instances, such value or ranges of values may be derived from historical patient cases that were treated by that doctor or medical professional. [0051] Representation generation neural networks based on autoencoders, U-Nets, transformers, other types of encoder-decoder structures, convolution and/or pooling layers, or other models may benefit from the use of oral care arguments (e.g., oral care metrics or oral care parameters). For example, oral care metrics (e.g., orthodontic metrics or restoration design metrics) may convey aspects of the shape and/or structure of the patient’s dentition (e.g., the shape and/or structure of an individual tooth, or the special relationships between two or more teeth) to the neural network models of this disclosure. Each oral care metric describes distinct information about the patient’s dentition that may not be redundantly present in other input data that are provided to the neural network. For example, an “Overbite” metric may quantify the overlap between the upper and lower central incisors along the vertical Z-axis, information which may not otherwise, in some implementations, be readily ascertainable by a traditional neural network. Stated another way, the oral care metrics provide refined information about the patient’s dentition that a traditional neural network (e.g., a representation generation neural network) may not be adequately trained or configured to extract. However, a neural network which is specifically trained to generate oral care metrics may overcome such a shortcoming, because, for example loss may be computed in such a way as to facilitate accurate oral care metrics prediction. Mesh oral care metrics may provide a processed version of the structure and/or shape of the patient’s dentition, data which may not otherwise be available to the neural network. This processed information is often more accessible, or more amenable for encoding by the neural network. A system implementing the techniques disclosed herein has been utilized to run a number of experiments on 3D representations of teeth. For example, oral care metrics have been provided to a representation generation neural network which is based on a U-Net model. Based on experiments, it was found that systems using oral care metrics (e.g., “Overbite”, “Overjet” and “Canine Class Relationship” metrics) were at least 2.5% more accurate than systems that did not. Furthermore, training converges more quickly when the oral care metrics are used. Stated another way, the machine learning models trained using oral care metrics tended to be more accurate more quickly (at earlier epochs) than systems which did not. For an existing system observed to have a historical accuracy rate of 91%, an improvement in accuracy of 2.5% reduces the actual error rate by almost 30%. [0052] Examples of oral care metrics include Orthodontic Metrics (OM) and Restoration Design Metrics (RDM). RDM may describe the shape and/or form of one or more 3D representations of teeth for use in dental restoration. One use case example is in the creation of one or more dental restoration appliances. Another use case example is in the creation of one or more veneers (such as a zirconia veneer). Some RDM may quantify the shape and/or other characteristics of a tooth. Other RDM may quantify relationships (e.g., spatial relationships) between two or more teeth. RDM differ from restoration design parameters (RDP) in that restoration design metrics define a current state of a patient's dentition, whereas restoration design parameters serve as specifications to a machine learning or other optimization model to generate desired tooth shapes and/or forms. RDM describe the shapes of the teeth currently (e.g., in a starting or mal condition). Restoration design parameters specify how an oral care provider (such as a dentist or dental technician) intends for the teeth to look after the completion of restoration treatment. Either or both of RDM and RDP may be provided to a neural network or other machine learning or optimization algorithm for the purpose of dental restoration. In some implementations, RDM may be computed on the pre-restoration dentition of the patient (i.e., the primary implementation). In other implementations, RDM may be computed on the post-restoration dentition of the patient. A restoration design may comprise one or more teeth and may be referred to as a restoration arch. Restoration design generation may involve the generation of an improved geometry and/or structure of one or more teeth in a restoration arch. [0053] Aspects of RDM calculation are described below. In some implementations, RDM may be measured, for example, through locating landmarks in the teeth (or gums, hardware and/or other elements of the patient's dentition), and the measurements of distances between those landmarks, or otherwise made in relation to those landmarks. In some implementations, one or more neural networks or other machine learning models may be trained to identify or extract one or more RDM from one or more 3D representations of teeth (or gums, hardware and/or other elements of the patient's dentition). Techniques of this disclosure may use RDM in various ways. For instance, in some implementations, one or more neural networks or other machine learning models may be trained to classify or label one or more setups, arches, dentitions or other sets of teeth based at least in part on RDM. As such, in these examples, RDMs form a part of the training data used for training these models. [0054] In some implementations, a continuous normalizing flow (CNF) may be trained to construct a distribution over 3D oral care representations (e.g., tooth restoration designs, appliance components, fixture model components, archforms, mesh element labels for segmentation or mesh cleanup, coordinate systems, transforms for teeth or other 3D representations, or others described herein). A CNF may be trained to improve the predictive accuracy of a generative neural network (e.g., a reconstruction autoencoder – such as a variational autoencoder utilizing continuous normalizing flows) and may be used in accordance with techniques of this disclosure are described below. A reconstruction autoencoder which with trained with continuous normalizing flows may be trained to reconstruct 3D oral care representations, such as tooth meshes, appliance component meshes, fixture model meshes, archforms, mesh element labels for segmentation or mesh cleanup, coordinate systems, transforms for teeth or other 3D representations, or others described herein. A CNF may, in some implementations, comprise a series of invertible mappings which may transform a probability distribution. In some implementations, CNF may be implemented by a succession of blocks in the decoder of an autoencoder. Such blocks may constrict a complex probability distribution, thereby enabling the autoencoder’s decoder to learn to map a low-dimensional distribution to a higher-dimensional distribution and back, which leads to a data precision-related technical improvement that enables the distribution of tooth shapes after reconstruction (in deployment) to be more representative of the distribution of tooth shapes in the training dataset. The invertibility of a CNF provides for a technical advantage of improved mathematical efficiencies during training, thereby providing resource usage-related technical improvements. An autoencoder for restoration design generation is described in US Provisional Application No. US63/366514. This autoencoder (e.g., a variational autoencoder or VAE) takes as input a tooth mesh (or other 3D representation) that reflects a mal state (i.e., the pre-restoration tooth shape). The encoder component of the autoencoder converts that tooth mesh to a latent form (e.g., a latent vector). Modifications may be applied to this latent vector (e.g., based on a mapping of the latent space through prior experiments), for the purpose of altering the geometry and/or structure of the eventual reconstructed mesh. Additional vectors may, in some implementations, be included with the latent vector (e.g., through concatenation), and the resulting concatenation of vectors may be reconstructed by way of the decoder component of the autoencoder into a reconstructed tooth mesh which is a facsimile of the input tooth mesh. [0055] RDM and RDP may also be used as neural network inputs in the execution phase, in accordance with aspects of this disclosure. In some implementations, one or more RDM may be concatenated with the input to the encoder, for the purpose of telling the encoder specific information about the input 3D tooth representation. In some implementations, one or more RDM may be concatenated with the latent vector, before reconstruction, for the purpose of providing the decoder component with specific information about the input 3D tooth representation. Furthermore, in some implementations, one or more restoration design parameters (RDP) may be concatenated with the input to the encoder component, for the purpose of providing the encoder specific information about the input 3D tooth representation. Likewise, in some implementations, one or more restoration design parameters (RDP) may be concatenated with the latent vector, before reconstruction, for the purpose of providing the decoder specific information about the input 3D tooth representation. [0056] In this way, either or both of RDM and RDP may be introduced to the functioning of an autoencoder (e.g., a tooth reconstruction autoencoder), and serve to influence the geometry and/or structure of the reconstructed restoration design (i.e., influence the shape of the tooth on the output of the autoencoder). In some implementations, the variational autoencoder of US Provisional Application No. US63/366514 may be replaced by a capsule autoencoder (e.g., instead of converting the tooth mesh to a latent vector, the tooth mesh is converted to one or more latent capsules). [0057] In some implementations, clustering or other unsupervised techniques may be performed on RDM to cluster one or more setups, arches, dentitions or other sets of teeth based on the restoration characteristics of the teeth. Such clusters may be useful in treatment planning, as the clusters provide insight into categories of patients with different treatment needs. This information may be instructive to clinicians as they learn about possible treatment options. In some instances, best practices may be identified (such as default RDP values) for patient cases that fall into one or another cluster (e.g., as determined by a similarity measure, as in k-NN). After a new case is classified into a particular cluster, information about the relevant best practices may be provided to the clinician who is responsible for processing the case. Such default values may, in some instances, undergo further tuning or modifications. [0058] Case Assignment: Such clusters may be used to gain further insight into the kinds of patient cases which exist in a dataset. Analysis of such clusters may reveal that patient treatment cases with certain RDM values (or ranges of values) may take less time to treat (or alternatively more time to treat). Cases which take more time to treat (or are otherwise more difficult) may be assigned to experienced or senior technicians for processing. Cases which take less time to treat may be assigned to newer or less- experienced techniques for processing. Such an assignment may be further aided by finding correlations between RDM values for certain cases and the known processing durations associated with those cases. [0059] The following RDM may be measured and used in the creation of either or both of dental restoration appliances and veneers {veneers are a type of dental restoration appliance}, with the objective of making the resulting teeth natural looking. Symmetry is generally a preferred facet. There may be differences between patients based on demographic differences. The generation of dental restoration appliances may benefit from some or all of the following RDM. Shade and translucency may pertain, in particular, to the creation of veneers, though some implementations of dental restoration appliances may also consider this information. [0060] Examples of inter-tooth RDM are enumerated as follows. [0061] 1) Bilateral Symmetry and/or Ratios: A measure of the symmetry between one or more teeth and one or more other teeth on opposite sides of the dental. For example, for a pair of corresponding teeth, a measure of the width of each tooth. In one instance, the one tooth is of normal width, and the other tooth is too narrow. In another instance, both teeth are of normal width. The following is a list of attributes that can be measured for a tooth, and compared to the corresponding measurement for one or more corresponding teeth: a) width - mesial to distal distance; b) length - gingival to incisal distance; c) diagonal - distance across the tooth, e.g., from the mesial gingival corner to the distal incisal corner (this measure is one of many that can be used to quantify the shape of teeth beyond length and width). Ratios between a and b may be computed, such as a/b or b/a. Such ratios can be indicative of whether spatial symmetry exists (e.g., by measuring the ratio a/b on the left side and measuring the ratio a/b on the right side, then compare the left and right ratios). In some implementations, where spatial symmetry is "off", the length, width and/or ratios may not match. Such a ratio may, in some implementations, be computed relative to a standard. A number of esthetic standards are available in the dental literature. Examples include Golden Proportion and Recurring Esthetic Dental Proportion. In some implementations, spatial symmetry may be measured on a pair of teeth, where one tooth is on the right side of the arch, and the other tooth is on the left side of the arch. [0062] 2) Proportions of Adjacent Teeth: Measure the width proportions of adjacent teeth as measured as a projection along an arch onto a plane (e.g., a plane that is situated in front of the patient's face). The ideal proportions for use in the final restoration design can be, for example, the so-called golden proportions. The golden proportions relate adjacent teeth, such as central incisors and lateral incisors. This metric pertains to the measuring of these proportions as the proportions exist in the pre- restoration mal dentition. The ideal golden proportions are 1.6, 1, 0.6, for the central incisor, lateral incisor and cuspid, on a particular side (either left or right) for a particular arch (e.g., the upper arch). If one or more of these proportion values is off (e.g., in the case of "peg laterals"), the patient may wish for dental restoration treatment to correct the proportions. [0063] 3) Arch Discrepancies: A measure of any size discrepancies between the upper arch and lower arch, for example, pertaining to the widths of the teeth, for the purpose of dental restoration. For example, techniques of this disclosure may make adjacent tooth width proportion measurements in the upper arch and in the lower arch. In some implementations, Bolton analysis measurements may be made by measuring upper widths, lower widths, and proportions between those quantities. Arch discrepancies may be described in absolute measurements (e.g., in mm or other suitable units) or in terms of proportions or ratios, in various implementations. [0064] 4) Midline: A measure of the midline of the maxillary incisors, relative to the midline of the mandibular incisors. Techniques of this disclosure may measure the midline of the maxillary incisors, relative to the midline of the nose (if data about nose location is available). [0065] 5) Proximal Contacts: A measure of the size (area, volume, circumference, etc.) of the proximal contact between adjacent teeth. In the ideal circumstance, the teeth touch along the mesial/distal surfaces and the gums fill in gingivally to where the teeth touch. Black triangles may form if the gum tissue fails to fill the space below the proximal contact. In some instances, the size of the proximal contact may get progressively shorter for teeth located farther towards the posterior of the arch. In an ideal scenario, the proximal contact would be long enough so that there is an appropriately sized incisal embrasure and the gum tissue fills in the area below or gingival to the contact. [0066] 6) Embrasure: In some implementations, techniques of this disclosure may measure the size (area, volume, circumference, etc.) of an embrasure, the gap between teeth at either of the gingival or incisal edge. In some implementations, techniques of this disclosure may measure the symmetry between embrasures on opposite sides of the arch. An embrasure is based at least in part on the length of the length of the contact between teeth, and/or at least in part on the shape of the tooth. In some instances, the size of the embrasure may get progressively longer for teeth located farther towards the posterior of the arch. [0067] Examples of Intra-tooth RDM are enumerated below, continuing with the numbering of other RDM listed above. [0068] 7) Length and/or Width: A measure of the length of a tooth relative to the width of that tooth. This metric may reveal, for example, that a patient has long central incisors. Width and length are defined as: a) width - mesial to distal distance; b) length - gingival to incisal distance; c) other dimensions of tooth body - the portions of tooth between the gingival region and the incisal edge. In some implementations, either or both of a length and a width may be measured for a tooth and compared to the length and/or width of one or more teeth. [0069] 8) Tooth Morphology: A measure of the primary anatomy of the tooth shape, such as line angles, buccal contours, and/or incisal angles and/or embrasures. The frequency and/or dimensions may be measured. In some implementations, the observed primary tooth shape aspects may be matched to one or more known styles. Techniques of this disclosure may measure secondary anatomy of the tooth shape, such as mamelon grooves. For instance, the frequency and/or dimensions may be measured. In some implementations, the observed secondary tooth shape aspects may be matched to one or more known styles. In some examples, techniques of this disclosure may measure tertiary anatomy of the tooth shape, such as perikymata or striations. For instance, the frequency and/or dimensions may be measured. In some implementations, the observed tertiary tooth shape aspects may be matched to one or more known styles. [0070] 9) Shade and/or Translucency: A measure of tooth shade and/or translucency. Tooth shade is often described by the Vita Classical or 3D Master shade guide. Tooth translucency is described by transmittance or a contrast ratio. Tooth shade and translucency may be evaluated (or measured) based on one or more of the following kinds of data pertaining to teeth: the incisal edge, incisal third, body and gingival third. The enamel layer translucency is general higher than the dentin or cementum layer. Shade and translucency may, in some implementations, be measured on a per-voxel (local) basis. Shade and translucency may, in some implementations, be measured on a per-area basis, such as an incisal area, tooth body area, etc. Tooth body may pertain to the portions of the tooth between the gingival region and the incisal edge. [0071] 10) Height of Contour: A measure of the contour of a tooth. When viewed from the proximal view, all teeth have a specific contour or shape, moving from the gingival aspect to the incisal. This is referred to as the facial contour of the tooth. In each tooth, there is a height of contour, where that shape is the most pronounced. This height of contour changes from the teeth in the anterior of the arch to the teeth in the posterior of the arch. In some implementations, this measurement may take the form of fitting against a template of known dimensions and/or known proportions. In some implementations, this measurement may quantify a degree of curvature along the facial tooth surface. In some implementations, measure the location along the contour of the tooth where the height of the curvature is most pronounced. This location may be measured as a distance away from the gingival margin or a distance away from the incisal edge, or a percentage along the length of the tooth. [0072] In some instances, tooth shape-based inputs may be provided to a neural network for setups predictions. In other instances, non-shape-based inputs can be used, such as a tooth name or designation, as it pertains to dental notation. In some implementations, a vector R of flags may be provided to the neural network, where a ‘1’ value indicates that the tooth is present and a ‘0’ value indicates that the tooth is absent from the patient case (though other values are possible). The vector R may comprise a 1- hot vector, where each element in the vector corresponds to a tooth type, name or designation. Identifying information about a tooth (e.g., the tooth’s name) can be provided to the predictive neural networks of this disclosure, with the advantage of enabling the neural network to become trained to handle different teeth in tooth-specific ways. For example, the setups prediction model may learn to make setups transformations predictions for a specific tooth designation (e.g., upper right central incisor, or lower left cuspid, etc.). In the case of the mesh cleanup autoencoders (either for labelling mesh element or for in-filling missing mesh data), the autoencoder may be trained to provide specialized treatment to a tooth according to that tooth’s designation, in this manner. In the case of a setups classification neural network, a listing of tooth name(s) present in the patient’s arch may better enable the neural network to output an accurate determination of setup classification, because tooth designation is a valuable input to training such a neural network. Tooth designation/name may be defined, for example, according to the Universal Numbering System, Palmer System, or the FDI World Dental Federation notation (ISO 3950). [0073] In one example, where all except the (up to four) wisdom teeth are present in the case, a vector R may be defined as an optional input to the setups prediction neural networks of this disclosure, where there is a 0 in the vector element corresponding to each of the wisdom teeth, and a 1 in the elements corresponding to the following teeth: UR7, UR6, UR5, UR4, UR3, UR2, UR1, UL1, UL2, UL3, UL4, UL5, UL6, UL7, LL7, LL6, LL5, LL4, LL3, LL2, LL1, LR1, LR2, LR3, LR4, LR5, LR6, LR7 [0074] In some instances, the position of the tooth tip may be provided to a neural network for setups predictions. In other instances, one or more vectors S of the orthodontic metrics described elsewhere in this disclosure may be provided to a neural network for setups predictions. The advantage is an improved capacity for the network to become trained to understand the state of a maloccluded setup and therefore be able to predict a more accurate final setup or intermediate stage. [0075] In some implementations, the neural networks may take as input one or more indications of interproximal reduction (IPR) U, which may indicate the amount of enamel that is to be removed from a tooth during the course orthodontic treatment (either mesially or distally). In some implementations, IPR information (e.g., quantity of IPR that is to be performed on one or more teeth, as measured in millimeters, or one or more binary flags to indicate whether or not IPR is to be performed on each tooth identified by flagging) may be concatenated with a latent vector A which is produced by a VAE or a latent capsule T autoencoder. The vector(s) and/or capsule(s) resulting from such a concatenation may be provided to one or more of the neural networks of the present disclosure, with the technical improvement or added advantage of enabling that predictive neural network to account for IPR. IPR is especially relevant to setups prediction methods, which may determine the positions and poses of teeth at the end of treatment or during one or more stages during treatment. It is important to account for the amount of enamel that is to be removed ahead of predicted tooth movements. [0076] In some implementations, one or more procedure parameters K and/or doctor preferences vectors L may be introduced to a setups prediction model. In some implementations, one or more optional vectors or values of tooth position N (e.g., XYZ coordinates, in either tooth local or global coordinates), tooth orientation O (e.g., pose, such as in transformation matrices or quaternions, Euler angles or other forms described herein), dimensions of teeth P (e.g., length, width, height, circumference, diameter, diagonal measure, volume - any of which dimensions may be normalized in comparison to another tooth or teeth), distance between adjacent teeth Q. These “dimensions of teeth P” may in some instances be used to describe the intended dimensions of a tooth for dental restoration design generation. [0077] In some implementations, tooth dimensions P (e.g., such as length, width, height, or circumference) may be measured inside a plane, such as the plane that intersects the centroid of the tooth, or the plane that intersects a center point that is located midway between the centroid and either the incisal-most extent or the gingival-most extent of the tooth. The tooth dimension of height may be measured as the distance from gums to incisal edge. The tooth dimension of width may be measured as the distance from the mesial extent to the distal extent of the tooth. In some implementations, the circularity or roundness of the tooth cross-section may be measured and included in the vector P. Circularity or roundness may be defined as the ratio of the radii of inscribed and circumscribed circles. [0078] The distance Q between adjacent teeth can be implemented in different ways (and computed using different distance definitions, such as Euclidean or geodesic). In some implementations, a distance Q1 may be measured as an averaged distance between the mesh elements of two adjacent teeth. In some implementations, a distance Q2 may be measured as the distance between the centers or centroids of two adjacent teeth. In some implementations, a distance Q3 may be measured between the mesh elements of closest approach between two adjacent teeth. In some implementations, a distance Q4 may be measured between the cusp tips of two adjacent teeth. Teeth may, in some implementations, be considered adjacent within an arch. Teeth may, in some implementations, also be considered adjacent between opposing arches. In some implementations, any of Q1, Q2, Q3 and Q4 may be divided by a term for the purpose of normalizing the resulting value of Q. In some implementations, the normalizing term may involve one or more of: the volume of a tooth, the count of mesh elements in a tooth, the surface area of a tooth, the cross-sectional area of a tooth (e.g., as projected into the XY plane), or some other term related to tooth size. [0079] Other information about the patient’s dentition or treatment needs (or related parameters) may be concatenated with the other input vectors to one or more of MLP, GAN, generator, encoder structure, decoder structure, transformer, VAE, conditional VAE, regularized VAE, 3D U-Net, capsule autoencoder, diffusion model, and/or any of the neural networks models listed elsewhere in this disclosure. [0080] The vector M may contain flags which apply to one or more teeth. In some implementations, M contains at least one flag for each tooth to indicate whether the tooth is pinned. In some implementations, M contains at least one flag for each tooth to indicate whether the tooth is fixed. In some implementations, M contains at least one flag for each tooth to indicate whether the tooth is pontic. Other and additional flags are possible for teeth, as are combinations of fixed, pinned and pontic flags. A flag that is set to a value that indicates that a tooth should be fixed is a signal to the network that the tooth should not move over the course of treatment. In some implementations, the neural network loss function may be designed to be penalized for any movement in the indicated teeth (and in some particular cases, may be heavily penalized). A flag to indicate that a tooth is pontic informs the network that the tooth gap is to be maintained, although that gap is allowed to move. In some cases, M may contain a flag indicating that a tooth is missing. In some implementations, the presence of one or more fixed teeth in an arch may aid in setups prediction, because the one or more fixed teeth may provide an anchor for the poses of the other teeth in the arch (i.e., may provide a fixed reference for the pose transformations of one or more of the other teeth in the arch). In some implementations, one or more teeth may be intentionally fixed, so as to provide an anchor against which the other teeth may be positioned. In some implementations, a 3D representation (such as a mesh) which corresponds to the gums may be introduced, to provide a reference point against which teeth can be moved. [0081] Without the loss of generality, one or more of the optional input vectors K, L, M, N, O, P, Q, R, S, U and V described elsewhere in this disclosure may also be provided to the input or into an intermediate layer of one or more of the predictive models of this disclosure. In particular, these optional vectors may be provided to the MLP Setups, GDL Setups, RL Setups, VAE Setups, Capsule Setups and/or Diffusion Setups, with the advantage of enabling the respective model to generate setups which better meet the orthodontic treatment needs of the patient. In some implementations, such inputs may be provided, for example, by being concatenated with one or more latent vectors A which are also provided to one or more of the predictive models of this disclosure. In some implementations, such inputs may be introduced, for example, by being concatenated with one or more latent capsules T which are also provided to one or more of the predictive models of this disclosure. [0082] In some implementations, one or more of K, L, M, N, O, P, Q, R, S, U and V may be introduced to the neural network (e.g., MLP or Transformer) directly in a hidden layer of the network. In some instances, one or more of K, L, M, N, O, P, Q, R, S, U and V may be introduced directly into the internal processing of an encoder structure. [0083] In some implementations, a setups prediction model (such as GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, PT Setups, Similarity Setups and Diffusion Setups) may take as input one or more latent vectors A which correspond to one or more input oral care meshes (e.g., such as tooth meshes). In some implementations, a setups prediction model (such as GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups and Diffusion Setups) may take as input one or more latent capsules T which correspond to one or more input oral care meshes (e.g., such as tooth meshes). In some implementations, a setups prediction method may take as input both of A and T. [0084] Various loss calculation techniques are generally applicable to the techniques of this disclosure (e.g., GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups, Setups Classification, Tooth Classification, VAE Mesh Element Labelling, MAE Mesh In-Filling and the imputation of procedure parameters). [0085] These losses include L1 loss, L2 loss, mean squared error (MSE) loss, cross entropy loss, among others. Losses may be computed and used in the training of neural networks, such as multi-layer perceptron’s (MLP), U-Net structures, generators and discriminators (e.g., for GANs), autoencoders, variational autoencoders, regularized autoencoders, masked autoencoders, transformer structures, or the like. Some implementations may use either triplet loss or contrastive loss, for example, in the learning of sequences. [0086] Losses may also be used to train encoder structures and decoder structures. A KL- Divergence loss may be used, at least in part, to train one or more of the neural networks of the present disclosure, such as a mesh reconstruction autoencoder or the generator of GDL Setups, which the advantage of imparting Gaussian behavior to the optimization space. This Gaussian behavior may enable a reconstruction autoencoder to produce a better reconstruction (e.g., when a latent vector representation is modified and that modified latent vector is reconstructed using a decoder, the resulting reconstruction is more likely to be a valid instance of the inputted representation). There are other techniques for computing losses which may be described elsewhere in this disclosure. Such losses may be based on quantifying the difference between two or more 3D representations. [0087] MSE loss calculation may involve the calculation of an average squared distance between two sets, vectors or datasets. MSE may be generally minimized. MSE may be applicable to a regression problem, where the prediction generated by the neural network or other machine learning model may be a real number. In some implementations, a neural network may be equipped with one or more linear activation units on the output to generate an MSE prediction. Mean absolute error (MAE) loss and mean absolute percentage error (MAPE) loss can also be used in accordance with the techniques of this disclosure. [0088] Cross entropy may, in some implementations, be used to quantify the difference between two or more distributions. Cross entropy loss may, in some implementations, be used to train the neural networks of the present disclosure. Cross entropy loss may, in some implementations, involve comparing a predicted probability to a ground truth probability. Other names of cross entropy loss include “logarithmic loss,” “logistic loss,” and “log loss”. A small cross entropy loss may indicate a better (e.g., more accurate) model. Cross entropy loss may be logarithmic. Cross entropy loss may, in some implementations, be applied to binary classification problems. In some implementations, a neural network may be equipped with a sigmoid activation unit at the output to generate a probability prediction. In the case of multi-class classifications, cross entropy may also be used. In such a case, a neural network trained to make multi-class predictions may, in some implementations, be equipped with one or more softmax activation functions at the output (e.g., where there is one output node for class that is to be predicted). Other loss calculation techniques which may be applied in the training of the neural networks of this disclosure include one or more of: Huber loss, Hinge loss, Categorical hinge loss, cosine similarity, Poisson loss, Logcosh loss, or mean squared logarithmic error loss (MSLE). Other loss calculation methods are described herein and may be applied to the training of any of the neural networks described in the present disclosure. [0089] One or more of the neural networks of the present disclosure may, in some implementations, be trained, at least in part by a loss which is based on at least one of: a Point-wise Mesh Euclidean Distance (PMD) and an Earth Mover’s Distance (EMD). Some implementations may incorporate a Hausdorff Distance (HD) calculation into the loss calculation. Computing the Hausdorff distance between two or more 3D representations (such as 3D meshes) may provide one or more technical improvements, in that the HD not only accounts for the distances between two meshes, but also accounts for the way that those meshes are oriented, and the relationship between the mesh shapes in those orientations (or positions or poses). Hausdorff distance may improve the comparison of two or more tooth meshes, such as two or more instances of a tooth mesh which are in different poses (e.g., such as the comparison of predicted setup to ground truth setup which may be performed in the course of computing a loss value for training a setups prediction neural network). [0090] Reconstruction loss may compare a predicted output to a ground truth (or reference) output. Systems of this disclosure may compute reconstruction loss as a combination of L1 loss and MSE loss, as shown in the following line of pseudocode: reconstruction_loss = 0.5*L1(all_points_target,all_points_predicted) + 0.5*MSE(all_points_target,all_points_predicted). In the above example, all_points_target is a 3D representation (e.g., a 3D mesh or point cloud) corresponding to ground truth data (e.g., a ground truth tooth restoration design, or a ground truth example of some other 3D oral care representation). In the above example, all_points_predicted is a 3D representation (e.g., a 3D mesh or point cloud) corresponding to generated or predicted data (e.g., a generated tooth restoration design, or a generated example of some other kind of 3D oral care representation). Other implementations of reconstruction loss may additionally (or alternatively) involve L2 loss, mean absolute error (MAE) loss or Huber loss terms. [0091] Reconstruction error may compare reconstructed output data (e.g., as generated by a reconstruction autoencoder, such as a tooth design which has been generated for use in generating a dental restoration appliance) to the original input data (e.g., the data which were provided to the input of the reconstruction autoencoder, such as a pre-restoration tooth). Systems of this disclosure may compute reconstruction error as a combination of L1 loss and MSE loss, as shown in the following line of pseudocode: reconstruction_error = 0.5*L1(all_points_input, all_points_reconstructed) + 0.5*MSE(all_points_input, all_points_reconstructed). In the above example, all_points_input is a 3D representation (e.g., a 3D mesh or point cloud) corresponding to input data (e.g., the pre-restoration tooth design which was provided to a reconstruction autoencoder, or another 3D oral care representation which is provided to the input of an ML model). In the above example, all_points_reconstructed is a 3D representation (e.g., 3D mesh or point cloud) corresponding to reconstructed (or generated) data (e.g., a reconstructed tooth restoration design, or another example of a generated 3D oral care representation). [0092] In other words, reconstruction loss is concerned with computing a difference between a predicted output and a reference output, whereas reconstruction error is concerned with computing a difference between a reconstructed output and an original input from which the reconstructed data are derived. [0093] The techniques of this disclosure may include operations such as 3D convolution, 3D pooling, 3D unconvolution and 3D unpooling.3D convolution may aid segmentation processing, for example in down sampling a 3D mesh.3D un-convolution undoes 3D convolution, for example, in a U- Net.3D pooling may aid the segmentation processing, for example in summarized neural network feature maps.3D un-pooling undoes 3D pooling, for example in a U-Net. These operations may be implemented by way of one or more layers in the predictive or generative neural networks described herein. These operations may be applied directly on mesh elements, such as mesh edges or mesh faces. These operations provide for technical improvements over other approaches because the operations are invariant to mesh rotation, scale, and translation changes. In general, these operations depend on edge (or face) connectivity, therefore these operations remain invariant to mesh changes in 3D space as long as edge (or face) connectivity is preserved. That is, the operations may be applied to an oral care mesh and produce the same output regardless of the orientation, position or scale of that oral care mesh, which may lead to data precision improvement. MeshCNN is a general-purpose deep neural network library for 3D triangular meshes, which can be used for tasks such as 3D shape classification or mesh element labelling (e.g., for segmentation or mesh cleanup). MeshCNN implements these operations on mesh edges. Other toolkits and implementations may operate on edges or faces. [0094] In some implementations of the techniques of this disclosure, neural networks may be trained to operate on 2D representations (such as images). In some implementations of the techniques of this disclosure, neural networks may be trained to operate on 3D representations (such as meshes or point clouds). An intraoral scanner may capture 2D images of the patient's dentition from various views. An intraoral scanner may also (or alternatively) capture 3D mesh or 3D point cloud data which describes the patient's dentition. According to various techniques, autoencoders (or other neural networks described herein) may be trained to operate on either or both of 2D representations and 3D representations. [0095] A 2D autoencoder (comprising a 2D encoder and a 2D decoder) may be trained on 2D image data to encode an input 2D image into a latent form (such as a latent vector or a latent capsule) using the 2D encoder, and then reconstruct a facsimile of the input 2D image using the 2D decoder. In the case of a handheld mobile app which has been developed for such analysis (e.g., for the analysis of dental anatomy), 2D images may be readily captured using one or more of the onboard cameras. In other examples, 2D images may be captured using an intraoral scanner which is configured for such a function. Among the operations which may be used in the implementation a 2D autoencoder (or other 2D neural network) for 2D image analysis are 2D convolution, 2D pooling and 2D reconstruction error calculation. [0096] 2D image convolution may involve the "sliding" of a kernel across a 2D image and the calculation of elementwise multiplications and the summing of those elementwise multiplications into an output pixel. The output pixel that results from each new position of the kernel is saved into an output 2D feature matrix. In some implementations, neighboring elements (e.g., pixels) may be in well-defined locations (e.g., above, below, left and right) in a rectilinear grid. [0097] A 2D pooling layer may be used to down sample a feature map and summarize the presence of certain features in that feature map. [0098] 2D reconstruction error may be computed between the pixels of the input and reconstructed images. The mapping between pixels may be well understood (e.g., the upper pixel [23,134] of the input image is directly compared to pixel [23,134] of the reconstructed image, assuming both images have the same dimensions). [0099] Among the advantages provided by the 2D autoencoder-based techniques of this disclosure is the ease of capturing 2D image data with a handheld device. In some instances, where outside data sources provide the data for analysis, there may be instances where only 2D image data are available. When only 2D image data are available, then analysis using a 2D autoencoder is warranted. [00100] Modern mobile devices (such as commercially available smartphones) may also have the capability of generating 3D data (e.g., using multiple cameras and stereophotogrammetry, or one camera which is moved around the subject to capture multiple images from different views, or both), which in some implementations, may be arranged into 3D representations such as 3D meshes, 3D point clouds and/or 3D voxelized representations. The analysis of a 3D representation of the subject may in some instances provide technical improvements over 2D analysis of the same subject. For example, a 3D representation may describe the geometry and/or structure of the subject with less ambiguity than a 2D representation (which may contain shadows and other artifacts which complicate the depiction of depth from the subject and texture of the subject). In some implementations, 3D processing may enable technical improvements because of the inverse optics problem which may, in some instances, affect 2D representations. The inverse optics problem refers to the phenomenon where, in some instances, the size of a subject, the orientation of the subject and the distance between the subject and the imaging device may be conflated in a 2D image of that subject. Any given projection of the subject on the imaging sensor could map to an infinite count of {size, orientation, distance} pairings. 3D representations enable the technical improvement in that 3D representations remove the ambiguities introduced by the inverse optics problem. [00101] A device that is configured with the dedicated purpose of 3D scanning, such as a 3D intraoral scanner (or a CT scanner or MRI scanner), may generate 3D representations of the subject (e.g., the patient's dentition) which have significantly higher fidelity and precision than is possible with a handheld device. When such high-fidelity 3D data are available (e.g., in the application of oral care mesh classification or other 3D techniques described herein), the use of a 3D autoencoder is offers technical improvements (such as increased data precision), to extract the best possible signal out of those 3D data (i.e., to get the signal out of the 3D crown meshes used in tooth classification or setups classification). [00102] A 3D autoencoder (comprising a 3D encoder and a 3D decoder) may be trained on 3D data representations to encode an input 3D representation into a latent form (such as a latent vector or a latent capsule) using the 3D encoder, and then reconstruct a facsimile of the input 3D representation using the 3D decoder. Among the operations which may be used to implement a 3D autoencoder for the analysis of a 3D representation (e.g., 3D mesh or 3D point cloud) are 3D convolution, 3D pooling and 3D reconstruction error calculation. [00103] For each mesh element, a 3D convolution may be performed to aggregate local features from nearby mesh elements. Processing may be performed above and beyond the techniques for 2D convolution, to account for the differing count and locations of neighboring mesh elements (relative to a particular mesh element). A particular 3D mesh element may have a variable count of neighbors and those neighbors may not be found in expected locations (as opposed to a pixel in 2D convolution which may have a fixed count of neighboring pixels which may be found in known or expected locations). In some instances, the order of neighboring mesh elements may be relevant to 3D convolution. [00104] A 3D pooling operation may enable the combining of features from a 3D mesh (or other 3D representation) at multiple scales. 3D pooling may iteratively reduce a 3D mesh into mesh elements which are most highly relevant to a given application (e.g., for which a neural network has been trained). Similarly to 3D convolution, 3D pooling may benefit from special processing beyond that entailed in 2D convolution, to account for the differing count and locations of neighboring mesh elements (relative to a particular mesh element). In some instances, the order of neighboring mesh elements may be less relevant to 3D pooling than to 3D convolution. [00105] 3D reconstruction error may be computed using one or more of the techniques described herein, such as computing Euclidean distances between corresponding mesh elements, between the two meshes. Other techniques are possible in accordance with aspects of this disclosure. 3D reconstruction error may generally be computed on 3D mesh elements, rather than the 2D pixels of 2D reconstruction error. 3D reconstruction error may enable technical improvements over 2D reconstruction error, because a 3D representation may, in some instances, have less ambiguity than a 2D representation (i.e., have less ambiguity in form, shape and/or structure). Additional processing may, in some implementations, be entailed for 3D reconstruction which is above and beyond that of 2D reconstruction, because of the complexity of mapping between the input and reconstructed mesh elements (i.e., the input and reconstructed meshes may have different mesh element counts, and there may be a less clear mapping between mesh elements than there is for the mapping between pixels in 2D reconstruction). The technical improvements of 3D reconstruction error calculation include data precision improvement. [00106] A 3D representation may be produced using a 3D scanner, such as an intraoral scanner, a computerized tomography (CT) scanner, ultrasound scanner, a magnetic resonance imaging (MRI) machine or a mobile device which is enabled to perform stereophotogrammetry. A 3D representation may describe the shape and/or structure of a subject. A 3D representation may include one or more 3D mesh, 3D point cloud, and/or a 3D voxelized representation, among others. A 3D mesh includes edges, vertices, or faces. Though interrelated in some instances, these three types of data are distinct. The vertices are the points in 3D space that define the boundaries of the mesh. These points would alternatively be described as a point cloud but for the additional information about how the points are connected to each other, as described by the edges. An edge is described by two points and can also be referred to as a line segment. A face is described by a number of edges and vertices. For instance, in the case of a triangle mesh, a face comprises three vertices, where the vertices are interconnected to form three contiguous edges. Some meshes may contain degenerate elements, such as non-manifold mesh elements, which may be removed, to the benefit of later processing. Other mesh pre-processing operations are possible in accordance with aspects of this disclosure.3D meshes are commonly formed using triangles, but may in other implementations be formed using quadrilaterals, pentagons, or some other n-sided polygon. In some implementations, a 3D mesh may be converted to one or more voxelized geometries (i.e., comprising voxels), such as in the case that sparse processing is performed. The techniques of this disclosure which operate on 3D meshes may receive as input one or more tooth meshes (e.g., arranged in one or more dental arches). Each of these meshes may undergo pre-processing before being input to the predictive architecture (e.g., including at least one of an encoder, decoder, pyramid encoder-decoder and U-Net). This pre-processing may include the conversion of the mesh into lists of mesh elements, such as vertices, edges, faces or in the case of sparse processing - voxels. For the chosen mesh element type or types, (e.g., vertices), feature vectors may be generated. In some examples, one feature vector is generated per vertex of the mesh. Each feature vector may contain a combination of spatial and/or structural features, as specified in Table 2. Element Spatial Features Structural Features Edges XYZ position of an edge Edge curvature (depends on a midpoint, XYZ positions of the connectivity neighborhood, edge vertices, or the normal average curvature of two vector at an edge midpoint vertices), dihedral angles, edge (average of the normal vectors length, density measure such as of two vertices). a count of incident edges (i.e., a count of the other neighboring edges which share the vertices of that edge). Faces XYZ position of a face centroid, Face curvature (average surface normal vector. curvature of the vertices of the face), face area, density measure such as count of adjacent faces (i.e., which share at least one edge with the face). Points XYZ position Density measure such as the count of neighboring points within a radius of the point Vertices XYZ position, normal vector Vertex curvature, density (weighted average of the normal measure such as the count of vectors of the connecting faces vertices within a radius of the for the vertex). vertex, density measure such as the count of incident edges. Voxels XYZ centroid. Volume, [height x depth x width] dimensions, density measure such as a count of contained vertices, density measure such as count of intersected faces, density measure such as count of intersected edges. Table 2 [00107] Table 2 discloses non-limiting examples of mesh element features. In some implementations, color (or other visual cues/identifiers) may be considered as a mesh element feature in addition to the spatial or structural mesh element features described in Table 2. As used herein (e.g., in Table 2), a point differs from a vertex in that a point is part of a 3D point cloud, whereas a vertex is part of a 3D mesh and may have incident faces or edges. A dihedral angle (which may be expressed in either radians or degrees) may be computed as the angle (e.g., a signed angle) between two connected faces (e.g., two faces which are connected along an edge). A sign on a dihedral angle may reveal information about the convexity or concavity of a mesh surface. For example, a positively signed angle may, in some implementations, indicate a convex surface. Furthermore, a negatively signed angle may, in some implementations, indicate a concave surface. To calculate the principal curvature of a mesh vertex, directional curvatures may first be calculated to each adjacent vertex around the vertex. These directional curvatures may be sorted in circular order (e.g., 0, 49, 127, 210, 305 degrees) in proximity to the vertex normal vector and may comprise a subsampled version of the complete curvature tensor. Circular order means: sorted in by angle around an axis. The sorted directional curvatures may contribute to a linear system of equations amenable to a closed form solution which may estimate the two principal curvatures and directions, which may characterize the complete curvature tensor. Consistent with Table 2, a voxel may also have features which are computed as the aggregates of the other mesh elements (e.g., vertices, edges and faces) which either intersect the voxel or, in some implementations, are predominantly or fully contained within the voxel. Rotating the mesh may not change structural features but may change spatial features. And, as described elsewhere in this disclosure, the term “mesh” should be considered in a non- limiting sense to be inclusive of 3D mesh, 3D point cloud and 3D voxelized representation. In some implementations, apart from mesh element features, there are alternative methods of describing the geometry of a mesh, such as 3D keypoints and 3D descriptors. Examples of such 3D keypoints and 3D descriptors are found in “TONIONI A, et al. in ‘Learning to detect good 3D keypoints.’, Int J Comput. Vis.2018 Vol .126, pages 1-20.”.3D keypoints and 3D descriptors may, in some implementations, describe extrema (either minima or maxima) of the surface of a 3D representation. In some implementations, one or more mesh element features may be computed, at least in part, via deep feature synthesis (DFS), e.g. as described in: J. M. Kanter and K. Veeramachaneni, "Deep feature synthesis: Towards automating data science endeavors," 2015 IEEE International Conference on Data Science and Advanced Analytics (DSAA), 2015, pp.1-10, doi: 10.1109/DSAA.2015.7344858. [00108] Representation generation neural networks based on autoencoders, U-Nets, transformers, other types of encoder-decoder structures, convolution and/or pooling layers, or other models may benefit from the use of mesh element features. Mesh element features may convey aspects of a 3D representation’s surface shape and/or structure to the neural network models of this disclosure. Each mesh element feature describes distinct information about the 3D representation that may not be redundantly present in other input data that are provided to the neural network. For example, a vertex curvature may quantify aspects of the concavity or convexity of the surface of a 3D representation which would not otherwise be understood by the network. Stated differently, mesh element features may provide a processed version of the structure and/or shape of the 3D representation; data that would not otherwise be available to the neural network. This processed information is often more accessible, or more amenable for encoding by the neural network. A system implementing the techniques disclosed herein has been utilized to run a number of experiments on 3D representations of teeth. For example, mesh element features have been provided to a representation generation neural network which is based on a U-Net model, and also to a representation generation model based on a variational autoencoder with continuous normalizing flows. Based on experiments, it was found that systems using a full complement of mesh element features (e.g., “XYZ” coordinates tuple, “Normal vector”, “Vertex Curvature”, Points- Pivoted, and Normals-Pivoted) were at least 3% more accurate than systems that did not. Points-Pivoted describes “XYZ” coordinates tuples that have local coordinate systems (e.g., at the centroid of the respective tooth). Normals-Pivoted describes “Normal Vectors” which have local coordinate systems (e.g., at the centroid of the respective tooth). Furthermore, training converges more quickly when the full complement of mesh element features are used. Stated another way, the machine learning models trained using the full complement of mesh element features tended to be more accurate more quickly (at earlier epochs) than systems which did not. For an existing system observed to have a historical accuracy rate of 91%, an improvement in accuracy of 3% reduces the actual error rate by more than 30%. [00109] Predictive models which may operate on feature vectors of the aforementioned features include but are not limited to: GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups, Tooth Classification, Setups Classification, Setups Comparison, VAE Mesh Element Labeling, MAE Mesh In-filling, Mesh Reconstruction Autoencoder, Validation Using Autoencoders, Mesh Segmentation, Coordinate System Prediction, Mesh Cleanup, Restoration Design Generation, Appliance Component Generation and/or Placement, and Archform Prediction. Such feature vectors may be presented to the input of a predictive model. In some implementations, such feature vectors may be presented to one or more internal layers of a neural network which is part of one or more of those predictive models. [00110] The neural networks of this disclosure may exploit one or more benefits of the operation of parameter tuning, whereby the inputs and parameters of a neural network are optimized to produce more data-precise results. One parameter which may be tuned is neural network learning rate (e.g., which may have values such as 0.1, 0.01, 0.001, etc.). Data augmentation schemes may also be tuned or optimized, such as schemes where “shiver” is added to the tooth meshes before being input to the neural network (i.e., small random rotations, translations and/or scaling may be applied to vary the dataset and make the neural network robust to variations in data). A subset of the neural network model parameters available for tuning are as follows: o Learning rate (LR) decay rate (e.g., how much the LR decays during a training run) o Learning rate (LR). The floating-point value (e.g., 0.001) that is used by the optimizer. o LR schedule (e.g., cosine annealing, step, exponential) o Voxel size (for cases with sparse mesh processing operations) o Dropout % (e.g., dropout which may be performed in a linear encoder) o LR decay step size (e.g., decay every 10 or 20 or 30 epochs) o Model scaling, which may increase or decrease the count of layers and/or the count of parameters per layer. [00111] Parameter tuning may be advantageously applied to the training of a neural network for the prediction of final setups or intermediate staging to provide data precision-oriented technical improvements. Parameter tuning may also be advantageously applied to the training of a neural network for mesh element labeling or a neural network for mesh in-filling. In some examples, parameter tuning may be advantageously applied to the training of a neural network for tooth reconstruction. In terms of classifier models of this disclosure, parameter tuning may be advantageously applied to a neural network for the classification of one or more setups (i.e., classification of one or more arrangements of teeth). The advantage of parameter tuning is to improve the data precision of the output of a predictive model or a classification model. Parameter tuning may, in some instances, provide the advantage of obtaining the last remaining few percentage points of validation accuracy out of a predictive or classification model. [00112] Various neural network models of this disclosure may draw benefits from data augmentation. Examples include models of this which are trained on 3D meshes, such as GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups, FDG Setups, Setups Classification, Setups Comparison, VAE Mesh Element Labeling, MAE Mesh In-filling, Mesh Reconstruction VAE, and Validation Using Autoencoders. Data augmentation, such as by way of the method shown in FIG.1, may increase the size of the training dataset of dental arches. Data augmentation can provide additional training examples by adding random rotations, translations, and/or rescaling to copies of existing dental arches. In some implementations of the techniques of this disclosure, data augmentation may be carried out by perturbing or jittering the vertices of the mesh, in a manner similar to that described in (“Equidistant and Uniform Data Augmentation for 3D Objects”, IEEE Access, Digital Object Identifier 10.1109/ACCESS.2021.3138162). The position of a vertex may be perturbed through the addition of Gaussian noise, for example with zero mean, and 0.1 standard deviation. Other mean and standard deviation values are possible in accordance with the techniques of this disclosure. [00113] FIG. 1 shows a data augmentation method that systems of this disclosure may apply to 3D oral care representations. A non-limiting example of a 3D oral care representation is a tooth mesh or a set of tooth meshes. Tooth data 100 (e.g., 3D meshes) are received at the input. The systems of this disclosure may generate copies of the tooth data 100 (102). In the example of FIG. 1, the systems of this disclosure may apply one or more stochastic rotations to the tooth data 100 (104). In the example of FIG. 1, the systems of this disclosure may apply stochastic translations to the tooth data 100 (106). The systems of this disclosure may apply stochastic scaling operations to the tooth data 100 (108). The systems of this disclosure may apply stochastic perturbations to one or more mesh elements of the tooth data 100 (110). The systems of this disclosure may output augmented tooth data 112 that are formed by way of the method of FIG. 1. [00114] Because generator networks of this disclosure can be implemented as one or more neural networks, the generator may contain an activation function. When executed, an activation function outputs a determination of whether or not a neuron in a neural network will fire (e.g., send output to the next layer). Some activation functions may include binary step functions, or linear activation functions. Other activation functions impart non-linear behavior to the network, including sigmoid/logistic activation functions, Tanh (hyperbolic tangent) functions, rectified linear units (ReLU), leaky ReLU functions, parametric ReLU functions, exponential linear units (ELU), softmax function, swish function, Gaussian error linear unit (GELU), or scaled exponential linear unit (SELU). A linear activation function may be well suited to some regression applications (among other applications), in an output layer. A sigmoid/logistic activation function may be well suited to some binary classification applications (among other applications), in an output layer. A softmax activation function may be well suited to some multiclass classification applications (among other applications), in an output layer. A sigmoid activation function may be well suited to some multilabel classification applications (among other applications), in an output layer. A ReLU activation function may be well suited in some convolutional neural network (CNN) applications (among other applications), in a hidden layer. A Tanh and/or sigmoid activation function may be well suited in some recurrent neural network (RNN) applications (among other applications), for example, in a hidden layer. There are multiple optimization algorithms which can be used in the training of the neural networks of this disclosure (such as in updating the neural network weights), including gradient descent (which determines a training gradient using first-order derivatives and is commonly used in the training of neural networks), Newton's method (which may make use of second derivatives in loss calculation to find better training directions than gradient descent, but may require calculations involving Hessian matrices), and conjugate gradient methods (which may yield faster convergence than gradient descent, but do not require the Hessian matrix calculations which may be required by Newton's method). In some implementations, additional methods may be employed to update weights, in addition to or in place of the techniques described above. These additional methods include the Levenberg-Marquardt method and/or simulated annealing. The backpropagation algorithm is used to transfer the results of loss calculation back into the network so that network weights can be adjusted, and learning can progress. [00115] Neural networks contribute to the functioning of many of the applications of the present disclosure, including but not limited to: GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups, Diffusion Setups, PT Setups, Similarity Setups, Tooth Classification, Setups Classification, Setups Comparison, VAE Mesh Element Labeling, MAE Mesh In-filling, Mesh Reconstruction Autoencoder, Validation Using Autoencoders, imputation of oral care parameters, 3D mesh segmentation (3D representation segmentation), Coordinate System Prediction, Mesh Cleanup, Restoration Design Generation, Appliance Component Generation and/or Placement, or Archform Prediction. The neural networks of the present disclosure may embody part or all of a variety of different neural network models. Examples include the U-Net architecture, multi-later perceptron (MLP), transformer, pyramid architecture, recurrent neural network (RNN), autoencoder, variational autoencoder, regularized autoencoder, conditional autoencoder, capsule network, capsule autoencoder, stacked capsule autoencoder, denoising autoencoder, sparse autoencoder, conditional autoencoder, long/short term memory (LSTM), gated recurrent unit (GRU), deep belief network (DBN), deep convolutional network (DCN), deep convolutional inverse graphics network (DCIGN), liquid state machine (LSM), extreme learning machine (ELM), echo state network (ESN), deep residual network (DRN), Kohonen network (KN), neural Turing machine (NTM), or generative adversarial network (GAN). In some implementations, an encoder structure or a decoder structure may be used. Each of these models provides one or more of its own particular advantages. For example, a particular neural networks architecture may be especially well suited to a particular ML technique. For example, autoencoders are particularly suited to the classification of 3D oral care representations, due to the ability to convert the 3D oral care representation into a form which is more easily classifiable. [00116] In some implementations, the neural networks of this disclosure can be adapted to operate on 3D point cloud data (alternatively on 3D meshes or 3D voxelized representation). Numerous neural network implementations may be applied to the processing of 3D representations and may be applied to training predictive and/or generative models for oral care applications, including: PointNet, PointNet++, SO-Net, spherical convolutions, Monte Carlo convolutions and dynamic graph networks, PointCNN, ResNet, MeshNet, DGCNN, VoxNet, 3D-ShapeNets, Kd-Net, Point GCN, Grid-GCN, KCNet, PD-Flow, PU-Flow, MeshCNN and DSG-Net. Oral care applications include, but are not limited to: setups prediction (e.g., using VAE, RL, MLP, GDL, Capsule, Diffusion, etc. which have been trained for setups prediction), 3D representation segmentation, 3D representation coordinate system prediction, element labeling for 3D representation clean-up (VAE for Mesh Element labeling), in-filling of missing elements in 3D representation (MAE for Mesh In-Filling), dental restoration design generation, setups classification, appliance component generation and/or placement, archform prediction, imputation of oral care parameters, setups validation, or other validation applications and tooth 3D representation classification. [00117] Some implementations of the techniques of this disclosure incorporate the use of an autoencoder. Autoencoders that can be used in accordance with aspects of this disclosure include but are not limited to: AtlasNet, FoldingNet and 3D-PointCapsNet. Some autoencoders may be implemented based on PointNet. [00118] Representation learning may be applied to setups prediction techniques of this disclosure by training a neural network to learn a representation of the teeth, and then using another neural network to generate transforms for the teeth. Some implementations may use a VAE or a Capsule Autoencoder to generate a representation of the essential characteristics of the one or more meshes related to the oral care domain (including, in some instances, information about the structures of the tooth meshes). Then that representation (either a latent vector or a latent capsule) may be used as input to a module which generates the one or more transforms for the one or more teeth. These transforms may in some implementations place the teeth into final setups poses. These transforms may in some implementations place the teeth into intermediate staging poses. In some implementations, a transform may be described by a 9x1 transformation vector (e.g., that specifies a translation vector and a quaternion). In other implementations, a transform may be described by a transformation matrix (e.g., a 4x4 affine transformation matrix). [00119] In some implementations, systems of this disclosure may implement a principal components analysis (PCA) on an oral care mesh and use the resulting principal components as at least a portion of the representation of the oral care mesh in subsequent machine learning and/or other predictive or generative processing. [00120] An autoencoder may be trained to generate a latent form of a 3D oral care representation. An autoencoder may contain a 3D encoder (which converts a 3D oral care representation into a latent form), and/or a 3D decoder (which reconstructs that latent from into a facsimile of the inputted 3D oral care representation). Although this disclosure refers to 3D encoders and 3D decoders, the term 3D should be interpreted in a non-limiting fashion to encompass multi-dimensional modes of operation. For example, systems of this disclosure may train multi-dimensional encoders and/or multi-dimensional decoders. [00121] Systems of this disclosure may implement end-to-end training. Some of the end-to-end training-based techniques of this disclosure may involve two or more neural networks, where the two or more neural networks are trained together (i.e., the weights are updated concurrently during the processing of each batch of input oral care data). End-to-end training may, in some implementations, be applied to setups prediction by concurrently training a neural network which learns a representation of the teeth, along with a neural network which generates the tooth transforms. [00122] According to some of the transfer learning-based implementations of this disclosure, a neural network (e.g., a U-Net) may be trained on a first task (e.g., such as coordinate system prediction). The neural network trained on the first task may be executed to provide one or more of the starting neural network weights for the training of another neural network that is trained to perform a second task (e.g., setups prediction). The first network may learn the low-level neural network features of oral care meshes and be shown to work well at the first task. The second network may exhibit faster training and/or improved performance by using the first network as a starting point in training. Certain layers may be trained to encode neural network features for the oral care meshes that were in the training dataset. These layers may thereafter be fixed (or be subjected to minor changes over the course of training) and be combined with other neural network components, such as additional layers, which are trained for one or more oral care tasks (such as setups prediction). In this manner, a portion of a neural network for one or more of the techniques of the present disclosure (e.g., setups prediction) may receive initial training on another task, which may yield important learning in the trained network layers. This encoded learning may then be built upon with further task-specific training of another network. [00123] In accordance with this disclosure, transfer learning may be used for setups prediction, as well as for other oral care applications, such as mesh classification (e.g., tooth or setups classification), mesh element labeling, mesh element in-filling, procedure parameter imputation, mesh segmentation, coordinate system prediction, restoration design generation, mesh validation (for any of the applications disclosed herein). In some implementations, a neural network trained to output predictions based on oral care meshes may first be partially trained on one of the following publicly available datasets, before being further trained on oral care data: Google PartNet dataset, ShapeNet dataset, ShapeNetCore dataset, Princeton Shape Benchmark dataset, ModelNet dataset, ObjectNet3D dataset, Thingi10K dataset (which is especially relevant to 3D printed parts validation), ABC: A Big CAD Model Dataset For Geometric Deep Learning, ScanObjectNN, VOCASET, 3D-FUTURE, MCB: Mechanical Components Benchmark, PoseNet dataset, PointCNN dataset, MeshNet dataset, MeshCNN dataset, PointNet++ dataset, PointNet dataset, or PointCNN dataset. [00124] In some implementations, a neural network which was previously trained on a first dataset (either oral care data or other data) may subsequently receive further training on oral care data and be applied to oral care applications (such as setups prediction). Transfer learning may be employed to further train any of the following networks: GCN (Graph Convolutional Networks), PointNet, ResNet or any of the other neural networks from the published literature which are listed above. [00125] In some implementations, a first neural network may be trained to predict coordinate systems for teeth (such as by using the techniques described in WO2022123402A1 or US Provisional Application No. US63/366492). A second neural network may be trained for setups prediction, according to any of the setups prediction techniques of the present disclosure (or a combination of any two or more of the techniques described herein). Transfer learning may transfer at least a portion of the knowledge or capability of the first neural network to the second neural network. As such, transfer learning may provide the second neural network an accelerated training phase to reach convergence. In some implementations, the training of the second network may, after being augmented with the transferred learning, then be completed using one or more of the techniques of this disclosure. [00126] Systems of this disclosure may train ML models with representation learning. The advantages of representation learning include that the generative network (e.g., neural network that predicts a transform for use in setups prediction) can be configured to receive input with a known size and/or standard format, as opposed to receiving input with a variable size or structure. Representation learning may produce improved performance over other techniques, because noise in the input data may be reduced (e.g., because the representation generation model extracts hierarchical neural network features and/or reconstruction characteristics of an inputted representation (e.g., a mesh or point cloud) through loss calculations or network architectures chosen for that purpose). [00127] Reconstruction characteristics may comprise values in of a latent representation (e.g., a latent vector) that describe aspects of the shape and/or structure of the 3D representation that was provided to the representation generation module that generated the latent representation. The weights of the encoder module of a reconstruction autoencoder, for example, may be trained to encode a 3D representation (e.g., a 3D mesh, or others described herein) into a latent vector representation (e.g., a latent vector). Stated another way, the capability to encode a large set (e.g., hundreds, thousands or millions) of mesh elements into a latent vector (e.g., of hundreds or a thousand real values – e.g., 512, 1024, etc.) may be learned by the weights of the encoder. Each dimension of that latent vector may contain a real number which describes some aspect of the shape and/or structure of the original 3D representation. The weights of the decoder module of the reconstruction autoencoder may be trained to reconstruct the latent vector into a close facsimile of the original 3D representation. Stated another way, the capability to interpret the dimensions of the latent vector, and to decode the values within those dimensions, may be learned by the decoder. In summary, the encoder and decoder neural network modules are trained to perform the mapping of a 3D representation into a latent vector, which may then be mapped back (or otherwise reconstructed) into a 3D representation that is substantially similar to an original 3D representation for which the latent vector was generated. [00128] Returning to loss calculation, examples of loss calculation may include KL-divergence loss, reconstruction loss or other losses disclosed herein. Representation learning may reduce the size of the dataset required for training a model, because the representation model learns the representation, enabling the generative network to focus on learning the generative task. The result may be improved model generalization because meaningful neural network features of the input data (e.g., local and/or global features) are made available to the generative network. Stated another way, a first network may learn the representation, and a second network may make the predictive decision. By training two networks to perform their own separate tasks, each of the networks may generate more accurate results for their respective tasks than with a single network which is trained to both learn a representation and make a decision. In some instances, transfer learning may first train a representation generation model. That representation generation model (in whole or in part) may then be used to pre-train a subsequent model, such as a generative model (e.g., that generates transform predictions). A representation generation model may benefit from taking mesh element features as input, to improve the capability of a second ML module to encode the structure and/or shape of the inputted 3D oral care representations in the training dataset. [00129] One or more of the neural networks models of this disclosure may have attention gates integrated within. Attention gate integration provides the enhancement of enabling the associated neural network architecture to focus resources on one or more input values. In some implementations, an attention gate may be integrated with a U-Net architecture, with the advantage of enabling the U-Net to focus on certain inputs, such as input flags which correspond to teeth which are meant to be fixed (e.g,. prevented from moving) during orthodontic treatment (or which require other special handling). An attention gate may also be integrated with an encoder or with an autoencoder (such as VAE or capsule autoencoder) to improve predictive accuracy, in accordance with aspects of this disclosure. For example, attention gates can be used to configure a machine learning model to give higher weight to aspects of the data which are more likely to be relevant to correctly generated outputs. As such, and because a machine learning model configured with these attention gates (or mechanisms) utilizes aspects of the data that are more likely to be relevant to correctly generated outputs, the ultimate predictive accuracy of those machine learning models is improved. [00130] The quality and makeup of the training dataset for a neural network can impact the performance of the neural network in its execution phase. Dataset filtering and outlier removal can be advantageously applied to the training of the neural networks for the various techniques of the present disclosure (e.g., for the prediction of final setups or intermediate staging, for mesh element labeling or a neural network for mesh in-filling, for tooth reconstruction, for 3D mesh classification, etc.), because dataset filtering and outlier removal may remove noise from the dataset. And while the mechanism for realizing an improvement is different than using attention gates, that ultimate outcome is that this approach allows for the machine learning model to focus on relevant aspects of the dataset and may lead to improvements in accuracy similar to improvements in accuracy realized vis-à-vis attention gates. [00131] In the case of a neural network configured to predict a final setup, a patient case may contain at least one of a set of segmented tooth meshes for that patient, a mal transform for each tooth, and/or a ground truth setup transform for each tooth. In the case of a neural network to predict a set of intermediate stage setups, a patient case may contain at least one of a set of segmented tooth meshes for that patient, a mal transform for each tooth, and/or a set of ground truth intermediate stage transforms for each tooth. In some implementations, a training dataset may exclude patient cases which contact passive stages (i.e., stages where the teeth of an arch do not move). In some implementations, the dataset may exclude cases where passive stages exist at the end of treatment. In some implementations, a dataset may exclude cases where overcrowding is present at the end of treatment (i.e., where the oral care provider, such as an orthodontist or dentist) has chosen a final setup where the tooth meshes overlap to some degree. In some implementations, the dataset may exclude cases of a certain level (or levels) of difficulty (e.g., easy, medium and hard). [00132] In some implementations, the dataset may include cases with zero pinned teeth (or may include cases where at least one tooth is pinned). A pinned tooth may be designated by a technician as they design the treatment to stop the various tools from moving that particular tooth. In some implementations, a dataset may exclude cases without any fixed teeth (conversely, where at least one tooth is fixed). A fixed tooth may be defined as a tooth that shall not move in the course of treatment. In some implementations, a dataset may exclude cases without any pontic teeth (conversely, cases in which at least one tooth is pontic). A pontic tooth may be described as a “ghost” tooth that is represented in the digital model of the arch but is either not actually present in the patient’s dentition or where there may be a small or partial tooth that may benefit from future work (such as the addition of composite material through a dental restoration appliance). The advantage of including a pontic tooth in a patient’s case is to leave space in the arch as a part of a plan for the movements of other teeth, in the course of orthodontic treatment. In some instances, a pontic tooth may save space in the patient’s dentition for future dental or orthodontic work, such as the installation of an implant or crown, or the application of a dental restoration appliance, such as to add composite material to an existing tooth that is too small or has an undesired shape. In some implementations, the dataset may exclude cases where the patient does not meet an age requirement (e.g., younger than 12). In some implementations, the dataset may exclude cases with interproximal reduction (IPR) beyond a certain threshold amount (e.g., more than 1.0 mm). The dataset to train a neural network to predict setups for clear tray aligners (CTA) may exclude patient cases which are not related to CTA treatment. The dataset to train a neural network to predict setups for an indirect bonding tray product may exclude cases which are not related to indirect bonding tray treatment. In some implementations, the dataset may exclude cases where only certain teeth are treated. In such implementations, a dataset may comprise of only cases where at least one of the following are treated: anterior teeth, posterior teeth, bicuspids, molars, incisors, and/or cuspids. [00133] Some autoencoder-based implementations of this disclosure use capsule autoencoders to automate processing steps in the creation of oral care appliances (e.g., for orthodontic treatment or dental restoration). The advantage of using capsule autoencoders which have been trained on oral care data is to leverage latent space techniques which reduce the dimensionality of oral care mesh data and thereby refine those data, making the signal in the data stronger and more readily usable by downstream processing modules, whether those downstream modules may be other autoencoder(s), decoder(s), other neural networks, or other types of ML models (such as the supervised and unsupervised models described elsewhere in this disclosure). Capsule autoencoders were originally applied in the 2D domain to perform object recognition in 2D images, where capsules were trained to create a model of the object that was to be recognized. Such an approach enabled an object to be recognized in the 2D image, even if the object was imaged from a new view that was not present in the training dataset. Later research extended capsule autoencoders to the domain of 3D point clouds, such as in “3D Point Capsule Networks” in the proceedings of CVPR 2019, which is incorporated herein by reference in its entirety. [00134] The present disclosure extends the outcomes of this research to apply capsule autoencoders to the domain of digital oral care, dealing with 3D point clouds, 3D meshes and 3D voxelized representation. The term “mesh” in the following should be considered to be interchangeable with 3D point cloud and 3D voxelized representations, in particular implementations. A 3D autoencoder may encode one or more 3D geometries (point clouds or meshes) into latent capsules which encode the reconstruction characteristics of the input 3D representation. These latent capsules exist in two or more dimensions and describe features of the input mesh (or point cloud) and the likelihoods of those features. A set of latent capsules stands in contrast to the latent vector which may be produced by a variational autoencoder (VaE), which may be encoded as a 1D vector. Among the contributions of the present technique is to advantageously apply capsule autoencoders to the digital oral care space, with the data precision-oriented technical advantage of improving predictive results. [00135] Particular examples of applications include segmentation of 3D oral care geometries, setups prediction (both final setups and intermediate stages), mesh cleanup of 3D oral care geometries (e.g., both for the labeling of mesh elements and the filling-in of missing mesh elements), tooth classification (e.g., according to standard dental notation schemes), setups classification (e.g., as mal, staging and final setup) and automated dental restoration design generation. [00136] The one or more latent capsules describing an input 3D representation (e.g., oral care geometries such as point clouds and/or meshes representing unsegmented dental arches, segmented teeth - such as arranged in a maloccluded setup, teeth with hardware attached, teeth without hardware attached, etc.) can be provided to a capsule decoder, to reconstruct a facsimile of the input 3D representation. This facsimile can be compared to the input 3D representation through the calculation of a reconstruction error, thereby demonstrating the information-rich nature of the latent capsule (i.e., that the latent capsule describes sufficient reconstruction characteristics of the input mesh, such that the mesh can be reconstructed from that latent capsule). A low reconstruction error (e.g., below a predetermined loss threshold) indicates that the reconstruction was a success. Some of the applications disclosed herein use this information-rich latent capsule for further processing (e.g., such as setups prediction, mesh segmentation, coordinate system prediction, mesh element labelling for mesh cleanup, in-filling of missing mesh elements or of holes in meshes, classification of setups, classification of oral care meshes, validation of setups and other validation appliances too). Some of the applications disclosed herein make one or more changes to the latent capsule, such as to effectuate changes in the reconstructed mesh, which may then outputted for further use (e.g., to create a dental restoration appliance). [00137] FIG. 2 shows a capsule autoencoder pipeline for mesh reconstruction, which are primarily applied to oral care meshes in the non-limiting examples described herein, but which may also be applied to other healthcare meshes, or to personal safety meshes, such as meshes pertaining to the design, shape, function, and/or use of personal protective equipment, such as disposable respirators. The deployment method omits the two modules on the bottom. The training method encompasses the whole diagram. The latent capsule T may be a reduced dimensionality form of the inputted oral care mesh and may be used as an input to other processing. [00138] Some existing techniques rely on inputting 3D point cloud data into a capsule autoencoder. Techniques of the present disclosure expand the input geometries to include 3D mesh data and 3D voxelized representations. In some instances, an input point cloud or mesh (such as containing oral care data) may be rearranged into one or more vectors of mesh elements. Such a vector may be Nx3 (in the case representing the XYZ coordinates of points or vertices). Such a vector may be Nx3 (in the case of representing mesh faces, each of which may be defined by 3 indices, each of which indexes into a list of vertices/points). Such a vector may be Nx2 (in the case of representing mesh edges, each of which may be defined by 2 indices, each of which can be indexed into a list of vertices/points). Such a vector may be Nx3 (in the case of representing voxels, each of which has an XYZ location, such as a centroid, where the Length x Width x Height of each voxel is known). [00139] In some examples in accordance with aspects of this disclosure, a neural network, such as an MLP, may be used to extract features from the Nx3 mesh element input list, yielding an Nx128 list of feature vectors, one feature vector per mesh element. In some instances, a vector of one or more computed mesh element features (as defined elsewhere in this disclosure) may be computed for one or more of the N inputted mesh elements. In some implementations, these mesh element features may be used in place of the MLP-generated features. In some implementations, each mesh element may be given a feature which is a hybrid of MLP-generated features and the computed mesh element features, in which case the layer dimension may be augmented to be Nx(128+aug_len), where aug_len is the length of the augmentation vector, consisting of the computed mesh element features. For ease of discussion, and without the loss of generality, this layer will simply be referred to as Nx128 hereafter. [00140] The length ‘aug_len’ may vary from implementation to implementation, depending on which mesh elements are analyzed and which mesh element features are chosen for use. In some instances, information from more than one type of mesh element may be introduced with the Nx128 vector (e.g., point/vertex information may be combined with face information, point/vertex information may be combined with edge information, or point/vertex information may be combined with voxel information). The analysis of different kinds of oral care meshes may call for one mesh element type or another, or for a particular set of mesh features, according to various applications. [00141] The Nx128 layer may be passed to a set of subsequent convolutions layers, each of which has been trained to have its own parameter values. The purpose of each of these independent convolution layers may encode the individual mesh element capsules. The output of each of the convolution layers may be maxpooled to a size of 1024 elements. The count of these convolution layers may be a power of two (e.g., 8, 16, 32, 64). In some implementations, there may be 32 such convolution layers, each of which outputs a 1024 element vector from the maxpooling operation. These 32 maxpooling output vectors may be concatenated, forming a layer that may be 1024x32, called the Primary Mesh Element Capsules (PMEC). A dynamic routing module converts these PMECs into one or more latent capsules, each of which may have square dimensions (e.g., 16x16, 32x32, 64x64, or 128x128). Non-square dimensions are also possible. [00142] In some implementations, a dynamic routing module may enable the output of a latent capsule to be routed to a suitable neural network layer in a subsequent processing module of the capsule autoencoder. The dynamic routing module uses unsupervised techniques (e.g., clustering and/or other unsupervised techniques) to arrange the output of the set of max-pooled feature maps into one or more stacked latent capsules. These latent capsules summarize feature information from the input 3D representation (e.g., one or more tooth meshes or point clouds) and also the likelihood information associated with each capsule. These stacked capsules contain sufficient information about the input 3D representation to reconstruct that 3D representation via the Capsule-Decoder module. [00143] A grid of mesh elements (i.e., such as points/vertices, edges, face or voxels) may be generated by Grid Patches module. Points will be used for the mesh element, in this example. In some implementations, this grid may comprise of randomly arranged points. In other implementations, this grid may reflect a regular and/or rectilinear arrangement of points. The points in each of these grid patches are the "raw material" from which the reconstructed 3D representation may be formed. [00144] The latent capsule (e.g., with dimension 128x128) may be replicated β times, and each of those β latent capsules may be appended with each of the grid patch of randomly generated mesh elements (e.g., points/vertices) in turn, before being input to one or more MLPs. In some examples, such an MLP may comprise of fully connected layers with the following dimensions: {64 − 64 − 32 − 16 – 3}. The goal of such an operation is to tailor the mesh elements to a specific local area of the 3D representation which may be to be reconstructed. The decoder iterates, generating additional random grid patches and outputting more random portions of the reconstructed 3D representation (i.e., as point cloud patches). These point cloud patches are accumulated until a reconstruction loss drops below a target threshold. The reconstruction loss may be computed using one or more of reconstruction loss (as defined herein) and KL-Divergence loss. [00145] An autoencoder, such as a variational autoencoder (VAE), may be trained to encode 3D mesh data in a latent space vector A, which may exist in an information-rich low-dimensional latent space. This latent space vector A may be particularly suitable for later processing by digital oral care applications (e.g., such as mesh cleanup, mesh segmentation, mesh validation, mesh classification, setups classification, setups prediction and restoration design generation, among others), because A enables high-dimensional tooth mesh data to be efficiently manipulated. Such a VAE may be trained to reconstruct the latent space vector A back into a facsimile of the input mesh (or transform or other data structure describing a 3D oral care representation). In some implementations, the latent space vector A may be strategically modified, so as to result in changes to the reconstructed mesh (or other data structure). In some instances, the reconstructed mesh may be a tooth mesh with an altered and/or improved shape, such as would be suitable for use in the design of a dental restoration appliance, such as a 3M FILTEK Matrix or a veneer. The term mesh should be considered in a non-limiting sense to be inclusive of 3D mesh, 3D point cloud and 3D voxelized representation. [00146] The tooth reconstruction VAE may advantageously make use of loss functions, nonlinearities (aka neural network activation functions) and/or solvers which are not mentioned by existing techniques. Examples of loss functions may include: mean absolute error (MAE), mean squared error (MSE), L1- loss, L2-loss, KL-divergence, entropy, and reconstruction loss. Such loss functions enable each generated prediction to be compared against the corresponding ground truth value in a quantified manner, leading to one or more loss values which can be used to train, at least in part, one or more of the neural networks. Examples of solvers may include: dopri5, bdf, rk4, midpoint, adams, explicit_adams, and fixed_adams. The solvers may enable the neural networks to solve systems of equations and corresponding unknown variables. Examples of nonlinearities may include: tanh, relu, softplus, elu, swish, square, and identity. The activation functions may be used to introduce nonlinear behavior to the neural networks in a manner that enables the neural networks to better represent the training data. Losses may be computed through the process of training the neural networks via backpropagation. Neural network layers such as the following may be used: ignore, concat, concat_v2, squash, concatsquash, scale and concatscale. [00147] In some implementations, the tooth reconstruction VAE model may be trained on patient cases of teeth in mal occlusion, or alternatively in local coordinates. FIG 3 shows a method of training such a VAE. FIG. 3 illustrates an example of training of the mesh reconstruction VAE of this disclosure. [00148] According to the mesh reconstruction VAE training shown in FIG.3, a 3D oral care representation F may be provided to the encoder E1 (along with optional tooth type information R), which may generate latent vector A. Latent vector A may be reconstructed into reconstructed 3D oral care representation G. Loss may be computed between the reconstructed 3D oral care representation G and ground truth 3D oral care representation GT (e.g., using the VAE loss calculation methods or other loss calculation methods described herein). Backpropagation may be used to train E1 and D1 with such loss. [00149] FIG 4 shows the trained mesh reconstruction VAE in deployment. FIG. 4 illustrates an example of the mesh reconstruction VAE of this disclosure. The mesh reconstruction VAE is shown in FIG.4 reconstructing a tooth mesh in deployment. R is an optional input, particularly in the case of tooth mesh classification, when such information R is not yet available (due to the tooth mesh classification neural network being trained to generate tooth type information R as an output, according to particular implementations). R may, in some implementations, be used to improve other techniques such as mesh element labelling techniques, mesh reconstruction techniques, oral care mesh classification techniques (e.g., such as tooth classification or setups classification), among others. [00150] FIGs 5 and 6 show reconstructed tooth meshes. FIG. 5 illustrates examples of an input tooth mesh (left) and the outputted reconstructed tooth mesh (right). FIG. 6 illustrates additional examples of a input tooth mesh (left) and the outputted reconstructed tooth mesh (right). The use cases shown in FIG. 6 are different from the use cases shown in FIG.5. FIG.7 shows a depiction of the reconstruction error from the reconstructed tooth shown in FIG.6, called a reconstruction error plot. That is, FIG. 7 depicts reconstruction error in the above results, in a form referred to as a “reconstruction error plot.” Units are in millimeters (mm) in FIG.7. Notice that the reconstruction error is less than 50 microns at the cusp tips, and much less than 50 microns over most of the tooth surface. Compared to a typical tooth with a size of 1.0 cm, an error rate of 50 microns (or less) means that the tooth surface was reconstructed with an error rate of less than 0.5%. [00151] FIG.8 is a histogram in which each bar or bin represents an individual tooth and represents the mean absolute distance of all vertices involved in the reconstruction of that tooth in a data that was used to evaluate a mesh reconstruction model. [00152] The tooth mesh reconstruction autoencoder, of which a variational autoencoder (VAE) is an example, may be trained to encode a tooth as a reduced-dimensionality form, called a latent space vector. The reconstruction VAE may be trained on example tooth meshes. The tooth mesh may be received by the VAE, deconstructed into a latent space vector using a 3D encoder and then reconstructed into a facsimile of the input mesh using a 3D decoder. Existing techniques for setups prediction lack such a deconstruction/reconstruction method. One advantage of this method is that the encoder E1 may become trained to convert a tooth mesh (or mesh of a dental appliance, gums, or other body part or anatomy) into a reduced-dimension form that can be used in the training and deployment of any of suite of powerful setups prediction methods (e.g., GDL Setups, RL Setups, VAE Setups, Capsule Setups, MLP Setups and Diffusion Setups, among others). This reduced-dimensionality form of the tooth may enable the setups prediction neural network to more efficiently encode the reconstruction characteristics of the tooth, and better learn to place the tooth into a pose suitable for either final setups or intermediate stages, thereby providing technical improvements in terms of both data precision and resource footprint. [00153] Furthermore, the reduced dimensionality representations of the teeth (or other 3D oral care representations, such as tooth transforms, mesh element labels or others described herein) may be provided to a decoder (e.g., an autoencoder decoder or a transformer decoder), which may reconstruct the reduced dimensionality latent representations of the teeth (or other 3D oral care representations) into 3D representations of teeth (or into the respective data structures of other types of 3D oral care representations). Using a low dimensionality representation can provide a number of advantages. For example, when a generative technique entails the modification of the latent vector (e.g., using an LRMM, or other techniques of this disclosure), that modification process is aided by the low dimensionality of the representation. Stated another way, an LRMM may be trained to modify low-dimensional data with greater accuracy and faster convergence time than high-dimensional data. That is, the modifications may be made more easily to a low-dimensional latent vector, than modifications can be made to the original 3D oral care representation. A small, efficient change to a latent vector may have a significant impact on the shape and/or structure of the reconstructed 3D oral care representation (e.g., which results in a reduction of computing resources). In a hypothetical example, one or two values in a latent vector could be modified instead of making hundreds of changes to the original 3D representation (e.g., adjusting hundreds of mesh elements). As a result, improvements to the efficiencies realized by the use of the latent representation relate not only to the size of the data, but also to the number and speed of computations performed on the data. The modified latent representation may then be reconstructed (e.g., using an autoencoder decoder), generating a 3D oral care representation (e.g., a tooth restoration design, or a set of mesh element labels) which is suitable for use in oral care appliance generation. [00154] The reconstructed mesh may be compared to the input mesh, for example using a reconstruction error (as described elsewhere in this disclosure), which quantifies the differences between the meshes. This reconstruction error may be computed using Euclidean distances between corresponding mesh elements between the two meshes. There are other methods of computing this error too which may be derived from material described elsewhere in this disclosure. FIGS 7 and 8 show example reconstruction errors, in accordance with the techniques described herein. [00155] In some implementations, the mesh or meshes which are provided to the mesh reconstruction VAE my first be converted to vertex lists (or point clouds) before being provided to the encoder E1. This manner of handling the input to E1 may be conducive to either a single mesh input (such as in a tooth mesh classification task) or a set of multiple teeth (such as in the setups classification task). The input meshes do not need to be connected. [00156] The encoder E1 may be trained to convert a tooth mesh into a latent space vector A (or “tooth representation vector”). In the course of the restoration design task, encoder E1 may arrange an input tooth mesh into a mesh element vector F, and convert it into a latent space vector A. This latent space vector A may be a reduced dimensionality representation of F that describes the important geometrical attributes of F. Latent space vector A may be provided to the decoder D1 to be restored to full resolution or near full resolution, along with the desired geometrical changes. The restored full resolution mesh or near-full resolution mesh may be described by G, which may then be arranged into the output mesh. [00157] In some implementations, such as in restoration design generation, the tooth name, the tooth designation and/or tooth type R may be concatenated with the latent vector A, as a means of conditioning the VAE on such information, to improve the ability of the VAE to respond to specific tooth types or designations. [00158] The performance of the mesh reconstruction VAE can be measured using reconstruction error calculations. In some examples, reconstruction error may be computed as element-to-element distances between two meshes, for example using Euclidean distances. Other distance measures are possible in accordance with various implementations of the techniques of this disclosure, such as Cosine distance, Manhattan distance, Minkowski distance, Chebyshev distance, Jaccard distance (e.g. intersection over union of meshes), Haversine distance (e.g., distance across a surface), and Sorensen- Dice distance. [00159] The performance of a mesh reconstruction VAE may, in some implementations, be verified via reconstruction error plots and/or other key performance indicators. The latent space vectors for one or more input tooth meshes may be plotted (e.g., in 2D) using UMAP or t-SNE dimensionality reduction techniques and compared, to select the best available separability between classes of tooth (molar, premolar, incisor, etc.), indicating that the model has an awareness of the strong geometric variation between classes, and a strong similarity within a class. This would be illustrated by clear, non- overlapping clusters in the resulting UMAP / t-SNE plots. [00160] In some instances, the latent vector corresponding to a mesh may be used as a part of a classifier to classify that mesh. For example, classification may be performed to identify a tooth type, or to detect errors in the mesh (or an arrangement of meshes), such as in a validation operation. The latent vector and/or computed mesh element features (such as spatial and/or structural mesh features described herein) may be provided to a supervised machine learning model to classify the mesh. A non-exhaustive list of possible supervised ML models is found elsewhere in this disclosure. [00161] In some implementations, a reconstruction VAE may be trained to reconstruct any arbitrary tooth type. In other implementations, a reconstruction VAE may be trained to reconstruct a specific tooth type (e.g., a 1^st molar, or a central incisor). [00162] FIG.9 describes the training of a mesh reconstruction VAE (a type of encoder-decoder structure). The encoder module of the VAE may, in some implementations, may be used to convert a tooth mesh (or other 3D oral care representation) into a latent representation (e.g., a latent vector) A. The encoder of the VAE may also be trained to convert other kinds of 3D representations (e.g., transform, mesh element labels, or meshes that describe gums, fixture model components, oral care hardware such as brackets and/or attachments, dental restoration appliance components, other portions of anatomy, or the like) into a latent vector A. The latent representation(s) may undergo modification (e.g., using a LRMM or via other methods described herein), and subsequently be provided to the decoder portion of the VAE. The decoder portion of the VAE may reconstruct the latent representation(s) into a modified form of the original tooth mesh (or other 3D oral care representation) that was provided at the input. FIG.9 provides further details on training a tooth crown reconstruction VAE. [00163] FIG.9 shows a method that systems of this disclosure may implement to train a reconstruction autoencoder for reconstructing a 3D representation of the patient’s dentition. The particular example of FIG. 9 illustrates training of a variational autoencoder (VAE) for reconstructing a tooth mesh 900. For each tooth in a patient case (908), the systems of this disclosure may generate a watertight mesh by merging the tooth’s crown mesh with the corresponding root mesh such that the vertices on the open edge of the crown mesh match up with the vertices on the open edge of the root mesh (902). The systems of this disclosure may perform a registration step (904) to align a tooth mesh with a template tooth mesh (e.g., using the iterative closest point technique or by applying the inverse mal transform for that tooth), with the technical enhancement of improving the accuracy and data precision of the mesh correspondence computation at 906. The systems of this disclosure may compute correspondences between a tooth mesh and the corresponding template tooth mesh, with the technical improvement of conditioning the tooth mesh to be ready to be provided to the reconstruction autoencoder. The dataset of prepared tooth meshes are split into train, validation and holdout test sets (910), which are then used to train a reconstruction autoencoder (912), described herein as a tooth VAE, tooth reconstruction VAE or more generally as a reconstruction autoencoder. The tooth VAE may comprise a 3D encoder which converts a tooth mesh into a latent form (e.g., a latent vector A), and a subsequent 3D decoder reconstructs that tooth into a facsimile of the inputted tooth mesh. The tooth VAE of this disclosure may be trained using a combination of reconstruction loss and KL-Divergence loss, and optionally other of the loss functions described herein. The output of this method is a trained tooth VAE 914. [00164] FIG.10 shows non-limiting code implementing an example 3D encoder and an example 3D decoder for a mesh reconstruction VAE. FIG.10 illustrates source code (in Python) corresponding to the encoder and the decoder. These implementations may include: convolution operations, batch norm operations, linear neural network layers, Gaussian operations, and continuous normalizing flows (CNF), among others. [00165] One of the steps which may take place in the VAE training data pre-processing is the calculation of mesh correspondences. Correspondences may be computed between the mesh elements of the input mesh and the mesh elements of a reference or template mesh with known structure (e.g., template representation). A template representation may include one or more mesh elements which are arranged in a standardized order (e.g., in a manner that is consistent with an arrangement that was used in training the autoencoder). In deployment, a trial 3D representation (e.g., a mesh of a pre-restoration tooth mesh of a patient, an appliance component which is to undergo modification, or a fixture model which is to undergo modification) may undergo correspondence calculation, to compute one or more correspondences between the trial 3D representation and a corresponding template representation. These correspondences enable the mesh elements of the trial 3D representation to be rearranged into an ordering which is consistent with the arrangements of mesh elements of the training examples that were used in training the autoencoder. This leads to improved autoencoder reconstruction accuracy, due to an improvement in the signal to noise ratio. [00166] Stated another way, the aim of mesh correspondence calculation is to compute correspondences between the mesh elements of the surfaces of a trial input mesh and a template (reference) mesh (e.g., template representation). Mesh correspondence may generate point to point correspondences between input and template meshes by mapping each vertex from the input mesh to at least one vertex in the template mesh. Correspondences may be computed between the mesh elements of the input mesh and the mesh elements of a reference or template mesh with known or pre-confirmed structure. In one example, a range of entries in the vector may correspond to the mesial lingual cusp tip; another range of elements may correspond to the distal lingual cusp tip; another range of elements may correspond to the mesial surface of that tooth; another range of elements may correspond to the lingual surface of that tooth, and so on. In the case of a tooth mesh reconstruction autoencoder (such as a VAE), in some implementations, the autoencoder may be trained on just a subset of teeth (e.g., only molars or only upper left first molars). In other implementations, the autoencoder may be trained on a larger subset or all of the teeth in the mouth. In some implementations, an input vector may be provided to the autoencoder (e.g., a vector of flags) which may define or otherwise influence the autoencoder as to which type of tooth mesh may have been received by the autoencoder as input. A data precision improvement of this approach is to mesh correspondences in mesh reconstruction to reduce sampling error, improve alignment, and improve mesh generation quality. Further details on the use of mesh correspondences with the autoencoder models of this disclosure is found elsewhere in this disclosure. [00167] In some implementations, an iterative closest point (ICP) algorithm may be run between the input tooth mesh and a template tooth mesh, during the computation of mesh correspondences. The correspondences may be computed to establish vertex-to-vertex relationships (between the input tooth mesh and the reconstructed tooth mesh), for use in computing reconstruction error. [00168] In some implementations, an inverse mal transform may be applied to bring the input tooth mesh into at least approximate alignment with a template tooth mesh, during the computation of mesh correspondences. In some implementations, both ICP and an inverse mal transform may be applied. [00169] According to particular implementations, training data may be generalized to one or more arches of teeth (e.g., among other 3D oral care representations) or may be more specific to particular teeth within an arch (e.g., among other 3D oral care representations). In situations in which more specific training data is leveraged, the specific training data can be presented as a tooth template. For instance, a tooth template may be specific to one or more tooth types (e.g., lower right central incisor). In some implementations, a tooth template may be generated which is an average of many examples of a certain type of tooth (such as an average of lower first molars). In some implementations, a tooth template may be generated which is an average of many examples of more than one tooth type (such as an average of first and second bicuspids from both upper and lower arches). [00170] In some implementations, the pre-processing procedure may involve one or more of the following steps: generation of watertight meshes (e.g. making sure that the boundary of the root mesh seals cleanly against the boundary of the crown mesh), registration to align the tooth mesh with a template mesh (e.g., using either ICP or the inverse mal transform), and the computation of mesh correspondences (i.e., to generate mesh element-to-mesh element correspondences between the input tooth mesh and a template tooth mesh). [00171] FIG. 11 illustrates tooth reconstructions generated after training epoch 849 of a tooth reconstruction autoencoder. In FIG. 11, the left side (labelled as "Training Data (ICP)") shows a tooth mesh (in the form of a 3D point cloud) after the completion of the pre-processing steps, where pre- processing used ICP to do the registration. The right side shows two things: the output of the tooth reconstruction VAE (in the left column) and the corresponding ground truth tooth 3D representation. In this instance as well, the 3D representation of each tooth is represented by a point cloud. This output was generated at epoch 849 of the reconstruction VAE training. [00172] The above description deals primarily with the processing of mesh, point cloud and/or voxel data into latent space vectors, as a means for reducing the dimensionality of those data and strengthening the signal-to-noise ratio of those data, such that an ML classifier can make decisions based on those data. Applications include but are not limited to VAE Setups, MLP Setups, MAE Mesh In-Filling, VAE Mesh Element Labelling, VAE for Tooth Mesh Classification, and some examples of Setups Classification. A reconstruction autoencoder trained based on the above material is also relevant to validation operations, such as segmentation validation, coordinate system validation, mesh cleanup validation, restoration design validation, fixture model validation, clear tray aligner (CTA) trimline validation, setups validation, oral care appliance component validation (either or both of placement and generation), and hardware (bracket, attachment, etc.) placement validation, to name some examples. [00173] Autoencoders of this disclosure (such as a VAE or capsule autoencoder) may process other types of oral care data, such as text data, categorical data, spatiotemporal data, real-time data and/or vectors of real numbers, such as may be found among the procedure parameters. Data may be qualitative or quantitative. Data may be nominal or ordinal. Data may be discrete or continuous. Data may be structured, unstructured or semi-structured. The autoencoders of this disclosure may also convert such data into latent space vectors (or latent capsules) for later reconstruction. Those latent vectors/latent capsules may be used for prediction and/or classification. The reconstructions may be used for model verification, and for validation applications, for example, through the calculation of reconstruction error and/or the labeling of data elements. [00174] A latent vector A which may be generated by the encoder E1 in a fully trained mesh reconstruction autoencoder (e.g., for tooth meshes), may be a reduced-dimensionality representation of the input mesh (e.g., a tooth mesh). In some implementations, the latent vector A may be a vector of 128 real numbers (or some other size, such as 256 or 512). The decoder D1 of the fully trained mesh reconstruction autoencoder may be capable of taking the latent vector A as input and reconstruct a close facsimile of the input tooth mesh, with low reconstruction error. In some implementations, modifications may be made to the latent vector A, so as to effect changes in the shape of the reconstructed mesh that is generated from the decoder D2. Such modifications may be made after first mapping-out the latent space, to gain insight into the effects of making particular change. There are a variety of loss functions which may be used in the training of E1 and D1, which may involve terms related to reconstruction loss and/or KL-Divergence between distributions (e.g., in some instances to minimize the distance between the latent space distribution and a multidimensional Gaussian distribution). One purpose of the reconstruction loss term is to compare the predicted reconstructed tooth 3D representation to the corresponding ground truth reconstructed tooth 3D representation. One purpose of the KL-divergence term is to make the latent space more Gaussian, and therefore improve the quality of reconstructed meshes (i.e., especially in the case where the latent space vector may be modified, to change the shape of the outputted mesh, for example to segment a 3D mesh, or to perform tooth design generation for use in generating a dental reconstruction appliance). [00175] In some implementations, modifications may be made to the latent vector A so as to change the characteristics of the reconstructed mesh (such as with the generation of a dental restoration tooth design mesh). If the loss L is computed using only reconstruction loss, and changes are made to the latent vector A, then in some use case scenarios, the reconstructed mesh may reflect the expected form of output (e.g., be a recognizable tooth). In other use case scenarios however, the output of the reconstructed mesh may not conform to the expected form of output (e.g., not be a recognizable tooth). [00176] FIG. 12 shows a latent space in which loss incorporates reconstruction loss but does not incorporate KL-Divergence loss. In FIG. 12, point P1 corresponds to the original form of a latent space vector A. Point P2 corresponds to a different location in the latent space, which may be sampled as a result of making modifications to the latent vector A, but where the mesh which is reconstructed from P2 may not give good output (e.g., does not look like a recognizable or otherwise suitable tooth). Point P3 corresponds to still a different location in the latent space, which may be sampled as a result of making a different set of modifications to the latent vector A, but where the mesh which is reconstructed from P3 may give good output (e.g., has the appearance of a tooth design which is suitable for use in generating a dental restoration appliance). In the case where loss involves only reconstruction loss, the subset of the latent space which can be sampled to produce a latent space vector P3 which yielding a valid reconstructed mesh may be irregular or hard to predict. [00177] FIG.13 illustrates a latent space in which loss includes both reconstruction loss and KL- divergence loss. A loss calculation may, in some implementations, incorporate losses from a CNF as described herein. A loss calculation may, in some implementations, incorporate a KL-divergence term. If the loss is improved by incorporating a KL-divergence term, the quality of the latent space may improve significantly. The latent space may become more Gaussian under this new scenario (as shown in FIG.13), a latent supervector A corresponds to point P4 near the center of a multidimensional Gaussian curve. Changes may be made to the latent supervector A, yielding point P5 nearby P4, where the resulting reconstructed mesh is highly likely to reflect desired attributes (e.g., is highly likely to be a valid tooth). The introduction of the KL-divergence term to loss may make the process of modifying the latent space vector A and getting a valid reconstructed mesh more reliable. In some implementations, as with a capsule autoencoder, the latent vector may be replaced with a latent capsule, which may undergo modification and subsequently be reconstructed. This autoencoder framework may, in some implementations, be adapted to the segmentation of tooth meshes. Additionally, this autoencoder framework may, in some implementations, be adapted to the task of tooth coordinate system prediction. In some implementations, a mesh reconstruction autoencoder for coordinate system prediction may compress the tooth data into latent vector form, and then provide the latent vector as input to a second ML module (e.g., an MLP) which may have been trained for coordinate system prediction (e.g., for coordinate system prediction on a mesh, with the goal of defining a local coordinate system for that mesh, such as a tooth mesh). [00178] For a given domain (e.g., tooth restoration design generation, MAE tooth in-filling, or setups design, etc.), the latent space can be mapped-out, so that changes to the latent space vector A may lead to reasonably well reconstructed meshes. The latent space may be systematically mapped by generating latent vectors with carefully chosen variations in value (e.g., by experimenting with different combinations of 128 values in an example latent vector). In some instances, a grid search of values may be performed, with the advantage of efficiently exploring the latent space. With the latent space mapped- out, the shape of a mesh may be modified by nudging the values in one or more elements of the latent vector values towards the portion of the mapped out latent space which has been found to correspond to the desired tooth characteristics. The use of KL-divergence in the loss calculation increases the likelihood that the modified latent vector gets reconstructed into a valid example of the inputted 3D oral care representation (e.g., 3D tooth mesh). [00179] In the case of restoration design generation, the mesh may correspond to at least some portion of a tooth. Changes may be made to a latent vector A, such that the resulting reconstructed tooth mesh may have characteristics which meet the specification set by the restoration design parameters. A neural network for tooth restoration design generation is described in US Provisional Application No. US63/366514, the entire disclosure of which is incorporated herein by reference. [00180] A tooth setup may be designed at least in part, by modifying a latent vector that corresponds to one or more teeth (e.g., each described as 3D point clouds, voxels or meshes) of an arch or arches which are to be placed in a setup configuration. This mesh may be encoded into a latent vector A which then undergoes modification to adjust the poses of the resulting tooth poses. The modified latent vector A’ may then be reconstructed into the mesh or meshes which describe the setup. Such a technique may be used to design a final setup configuration or an intermediate stage configuration, or the like. [00181] The modifications to a latent vector may, in some implementations, be carried out via an ML model, such as one of the neural network models or other ML models disclosed elsewhere in this disclosure. In some implementations, a neural network may be trained to operate within the latent space of such vectors A of setups meshes. The mapping of the latent space of A may have been previously generated by making controlled adjustments to trial latent vectors and observing the resulting changes to a setups configuration (i.e., after the modified A has been reconstructed back into a full mesh or meshes of the dental arch). The mapping of the latent space may, in some instances, follow methodical search patterns, such as in a grid search. Sampling latent space for mesh generation: [00182] In some implementations, a tooth reconstruction VAE may take a single input of tooth name/type/designation R, which may command the VAE to output a tooth mesh of the designated type. This can be accomplished by generating a latent vector A' for use in reconstructing a suitable tooth mesh. In some implementations, this latent vector A' may be sampled or generated "on the fly", out of a prior mapping of the latent vector space. Such a mapping may have been performed to understand which portions of the latent vector space correspond to different shapes, structures and/or geometries of tooth. For example, out of the 128 real values in an example latent vector A' (other sizes are possible), certain elements, and perhaps certain ranges of values for those vector elements may have been determined to correspond to a certain type/name/designation of tooth and/or a tooth with a certain shape or other intended characteristics. This model for tooth mesh generation may also apply to the generation of oral care hardware, appliances and appliance components (such as to be used for orthodontic treatment). This model may also be trained for the generation of other types of anatomy. This model may also be trained for the generation of other types on non-oral care meshes as well. [00183] FIG.14 illustrates an example of training a masked capsule autoencoder generate a dental restoration design. A capsule autoencoder (such as shown in FIG.14) may be trained to apply shape interpolation for dental restoration design automation (for the creation of a dental restoration appliance). A point cloud, mesh or voxelized representation for a tooth crown may be the subject for dental restoration and may be called the “mal” tooth. In some instances, a new shape may be chosen from a library of commercially available designs. In other instances, a new tooth shape may be produced by encoding the tooth crown mesh into one or more latent vectors A using a VAE (which has been trained for that purpose), making modifications to that latent vector A, and then reconstructing the latent vector A into a new and improved version of the mal tooth mesh. [00184] The techniques of the present disclosure may use the 3D Capsule-Encoder portion of a capsule autoencoder to convert the mal tooth mesh into one or more latent capsules T. Such a latent capsule T may have two or more dimensions (e.g., 1024 x 16), whereas the latent vector A produced by a VAE may, in some implementations, be 1-dimensional. A latent capsule may describe the reconstruction characteristics of the mal tooth mesh and can be reconstructed into a facsimile of the inputted mal tooth mesh (assuming no changes were made to the latent capsule). The techniques of the present disclosure may involve executing one or more arithmetic operations on the latent capsule, such that the outputted tooth mesh has one or more desired attributes, qualities or features (such as improved tooth shape) which differ from that of the input tooth mesh. Such an improved tooth mesh may then be used in the production of a dental restoration appliance. One or more input vectors: tooth name/designation info R, Restoration Design Parameters, and/or Doctor Restoration Preferences may be concatenated with the one or more latent capsules T (such as generated by a reconstruction capsule autoencoder). Such a concatenation may benefit from the input vectors being reformed to accommodate the 2D (or higher dimensional) format of the one or more latent capsules. In some implementations, empty, zero or null values may be used to fill-in extra matrix cells which may result from such a merger or concatenation. When the augmented latent capsules are reconstructed by the capsule-decoder structure, the resulting reconstructed tooth mesh may have improved qualities (including shape and/or structure) which meet the esthetic and/or medical requirements of the patient’s treatment (e.g., to make the tooth wider or longer or both; to make the tooth have rounded corners or square corners). [00185] A VAE for tooth restoration design may also take as input: tooth name/designation info R, Restoration Design Parameters, and/or Doctor Restoration Preferences. These inputs may, in some implementations, be introduced to the input of the VAE’s encoder structure and/or, in some implementations, be concatenated to the latent vector A of the VAE. [00186] Techniques are described for machine learning models trained to generate one or more portions of a restoration design. A restoration design may describe the target shape that one or more teeth (e.g., crown or root) is intended to assume after the completion of restorative dental treatment. In some instances, restorative treatment may be implemented using an artificial crown, which may be installed in the patient’s mouth to introduce new geometry to the patient’s dentition. In some instances, restorative treatment may be implemented by installing veneers onto one or more teeth (e.g., a zirconia veneer). In some instances, restorative treatment may be implemented using the addition of dental composite (e.g., 3M FILTEK dental composites) to one or more teeth, such as through the use of a dental restoration appliance (e.g., the 3M FILTEK Matrix). [00187] Neural networks may be trained to generate restoration designs, such as for the design of veneers or of dental restoration appliances. In some examples, generative adversarial neural networks (GANs) may be trained to generate the 3D representation of a tooth for restoration design, where a generator of the GAN is trained to create a tooth design, and a discriminator of the GAN is trained to distinguish between a reference restoration design and a generated restoration design. The generator and discriminator may train in tandem, competing with each other to yield better performance. In some examples, autoencoders (e.g., variational autoencoders and/or capsule autoencoders) may be used to generate tooth restoration designs. In some implementations, an autoencoder may contain at least one encoder and at least one decoder. The encoder may be trained to convert an input data sample (e.g., a 3D mesh of a tooth) into a latent space form (such as a latent vector or a latent capsule) which may represent a reduced dimensionality form of the input data sample. This latent space form may contain a sufficiently rich description of the input data sample, that a decoder (which has been specifically trained for the purpose) may reconstruct that latent space form into a facsimile of the input data sample. The input data sample (e.g., a 3D mesh of a tooth) and the reconstructed data sample (e.g., a reconstructed 3D mesh of that same tooth) may be compared through the calculation of a reconstruction error. Such a reconstruction error may entail at least one of the reconstruction loss and/or KL-divergence loss described elsewhere in this disclosure. A low reconstruction error may indicate a highly performing tooth reconstruction autoencoder. [00188] In some implementations, one or more of the optional inputs described elsewhere in this disclosure may be received by a tooth reconstruction autoencoder. Such optional inputs may provide the advantage of influencing the design of the reconstructed tooth mesh (e.g., a tooth mesh that is reconstructed by the decoder) to produce a restored tooth shape which is suitable for use in dental restoration (e.g., for use in creating a veneer or a dental restoration appliance). Oral care parameters, such as Restoration Design Parameters (RDP) and/or Doctor Restoration Design Preferences (DRDP), may be concatenated to either or both of the 1) input to the encoder and/or 2) the latent vector (which lies between the encoder and the decoder), in the case that the latent space representation takes the form of a vector (alternatively a capsule). Such oral care parameters may enable the tooth reconstruction autoencoder to incorporate clinical instructions from a doctor/dentist/healthcare practitioner. [00189] Alterations may be introduced to the latent space representation of a tooth mesh (e.g., a latent vector of size 128, 512, 1024, etc.) that is produced by the 3D encoder, to alter the shape of the reconstructed tooth mesh that is outputted by the 3D decoder. Such alterations may be performed to cause the reconstructed tooth mesh to have characteristics that are suitable for use in dental restoration. Such controlled changes to the latent vector may be performed once the desired latent space has been trained. This latent space may correspond to a disentangled representation of the training data. A series of experiments may have previously been performed by making a set of changes of the latent space vector (e.g., in the form of a grid search or otherwise incremental search of the latent space) and observing the effects on the resulting reconstructed tooth mesh. Once the dentist or other clinician determines the desired characteristics of the target tooth shape, alterations may be introduced the latent vector according to the prior mapping to bring about a desired tooth shape (e.g., a tooth shape that is suitable for use in dental restoration). [00190] The latent representation (e.g., latent vector) of a tooth (or other 3D oral care representation) may be modified, for example, using a latent representation modification module (LRMM). Such modifications may be used to condition the shape and/or structure of a 3D representation which is generated (or modified) according to the techniques described herein. The following is an example set of five levels of tooth design may be considered when making changes to the latent vector. A mapping of the latent space, formed through a set of experiments, may enable controlled changes to be made to the restored tooth design which impact the following tooth shape characteristics. The advantage provided by these techniques is to generate a tooth restoration design which reflects one or more of the following tooth characteristics. 0 – tooth silhouette, e.g., as projected onto a plane in front of the face 1 – main tooth shape (primary anatomy) 2 – surface vertical and horizontal macro textures, e.g., mamelon grooves (secondary anatomy) 3 – surface horizontal micro texture, e.g., perikymata (tertiary anatomy) 4 – volumetric representation of the tooth’s interior structure (dentine, enamel, etc.) 5 – occlusal surface textures, e.g., fossae or grooves (secondary anatomy) [00191] Examples of vertical striations and mamelon grooves are shown in FIG.15. Surface vertical macro textures may include small linear depressions along the surface of a tooth. Surface horizontal macro textures may include fossae, or mamelon grooves (rounded bumps along the incisal edge of a tooth – such as an incisor), among others. Tooth fossae may include central fossae (depression located along the occlusal surface of mandibular second bicuspids or molars), lingual fossae (irregular depression on incisors or cuspids, located lingual surface), or triangular fossae (located on posterior teeth, adjacent to marginal ridges), among others. Fossae may include development groove-fissures located between the cusps of a crown (e.g., a molar). Surface horizontal micro textures may include perikymata (wavelike horizontal patterns which may appear on the surfaces of teeth – such as the facial surfaces). [00192] In some implementations, the latent vector (or latent capsule) associated with a tooth mesh may undergo modifications, for the purpose of realizing changes in the shape or other characteristics of the reconstructed tooth mesh. Experiments may be performed whereby changes are made to the latent vector, and the characteristics of the resulting reconstructed tooth mesh are documented, to get an understanding on the landscape of the latent space representation of that tooth mesh. In some examples, a tooth mesh may be converted to a 128-element latent vector (other sizes are possible in accordance with this disclosure as well, such as 256, 1024, 2056, etc.). Each element of that vector may undergo a change, in turn, and then the vector may be reconstructed. The characteristics of the resulting reconstructed tooth mesh are then documented, to yield insight into which elements of the latent vector correspond to the desired characteristic(s) of the target restoration design. In some implementations, one of more ranges of values in one of more latent vector elements may be found to be associated with one of more characteristics of a target restoration design, for example a tooth shape or style, or with the presence, size, prominence or magnitude of certain aspects of a tooth (e.g., the size or shape of cusp tips, the shape of incisal edges, or the presence or shape of mamelon grooves, vertical striations or perkimata). [00193] The following is one possible experiment to gain insight into link between changes to the latent vector and the resulting effects on the reconstructed tooth mesh. [00194] For each dimension of the latent space (e.g., for each cell in the latent vector of perhaps 128 cells – though 64, 512, 1024 and other latent vector sizes are possible), take 5 datapoints (0,1,2,3,4) with point 2 centered on the mean of that dimension (i.e., a value of 0, in the center of the Gaussian distribution). Use a trained tooth reconstruction autoencoder (e.g., a VAE or Capsule Autoencoder) to reconstruct a tooth mesh using a latent vector of all zeros. This is our "default" or "average" tooth. Then generate 2 samples at each side of this dimension’s distribution (datapoints 0,1,3,4 from above). These may, for example, be located at 1, 1.5, or 2 standard deviations from the center of this dimension’s distribution at each side (positive and negative), enabling the experimenter to gain insight into which aspects of the reconstructed tooth correspond to this dimension of the latent vector. Note that any one of these dimensions may impact multiple aspects of the reconstructed tooth. In some instances, linear algebra-based operations may be used to isolate independent features, such as by identifying the vector dimensions which most greatly impact a particular aspect of the reconstructed tooth shape and/or structure. [00195] In some instances, reconstructed teeth may be clustered, to gain insight into the relationships therebetween, and to help in understanding the link between changes to the latent vector and the characteristics of the reconstructed tooth. Suppose that mesh (A) is the input to the reconstruction autoencoder, and mesh (B) is the reconstructed tooth that is generated by the tooth reconstruction autoencoder. By generating latent codes for both A and B, a vector may be computed that moves from A into B (e.g., B-A). A large set of such mapping vectors may be compiled and used to identify the dominant sub-vector(s) responsible for pushing a point in latent vector space towards "generalized" restored tooth characteristics. Such a mapping vector may then be added to the latent vector for a tooth to generate a reconstructed tooth mesh with the intended shape and/or structural characteristics. [00196] In some instances, a viewer may be invoked to view three (3) or five (5) meshes at once, and store images of these teeth at various orientations for offline analysis and comparisons. Although this experiment is directed to a use case of five (5) data points, any other number of data points may be used in other experiments in accordance with this disclosure. [00197] Table 3 describes the input data and generated data for several non-limiting examples of the generative implementations described herein. Encoder-decoder structures such as autoencoders or transformers may be trained to generate (or modify) point clouds as described herein. In some implementations, such models may be trained for the generation (or modification) of the input data in Table 3, yielding the generated data in Table 3. [00198] Techniques of this disclosure may be trained to generate (or modify) point clouds (e.g., where a point may be described as a 1D vector - such as (x, y, z)), polylines (points connected in order by edges), meshes (points connected via edges to form faces), splines (which may be computed through a set of generated control points), sparse voxelized representations (which may be described as a set of points corresponding to the centroid of each voxel or to some other landmark of the voxel – such as the boundary of the voxel), a transform (which may take the form of one or more 1D vectors or one or more 2D matrices – such as a 4x4 matrix) or the like. In some implementations, a voxelized representation may be computed from a 3D point cloud or a 3D mesh. In some implementations, a 3D point cloud may be computed from a voxelized representation. In some implementations, a 3D mesh may be computed from a 3D point cloud. Generative Input data Generated data Implementation Segmentation 3D representation of patient's pre- One or more mesh element labels for one or segmentation dentition (e.g., a more aspects of the patient's dentition. A label mesh including teeth and gums) may indicate which mesh elements should be included in which segmented portion of the patient's dentition. Coordinate One or more (segmented) teeth Coordinate system for one or more teeth (or system an arch). May comprise one or more transforms. Mesh cleanup 3D representation of patient's One or more mesh element labels for one or dentition (e.g., a mesh including more aspects of the patient's dentition. A label teeth and gums) may flag a mesh element for removal or modification. Restoration 3D representation of patient's pre- 3D representation of patient's intended post- design restoration tooth restoration tooth generation CTA trimline 3D representation of patient's 3D representation of trimline (e.g., 3D mesh dentition (e.g., a mesh including or 3D polyline) teeth and gums) CTA setups Two or more tooth meshes and/or Transforms for one or more teeth (for final setups tooth transforms. Tooth meshes or intermediate may be in their maloccluded poses. staging) Transforms may correspond to maloccluded poses. Hardware (e.g., One or more (segmented) teeth Transform for placement of hardware relative bracket/attachm to the one or more teeth ent) placement Archform 3D representation of patient's 3D polyline or a 3D mesh or surface, that generation dentition (e.g., a mesh including describes the contours or layout of an arch of teeth and gums). May comprise teeth one or more segmented teeth. Generated oral 3D representation of patient's One or more oral care appliance components care appliance dentition (e.g., a mesh including with shape and/or structure that is customized component teeth and gums). May comprise to aspects of the patient's dentition (e.g., for dental one or more segmented teeth. restoration) Placed oral care 3D representation of patient's One or more transforms which place a library appliance dentition (e.g., a mesh including component relative to aspects of the patient's component teeth and gums). May comprise dentition (e.g., for dental one or more segmented teeth. restoration) Table 3. [00199] Techniques described herein may be trained to generate 3D oral care representations (e.g., tooth restoration designs, appliance components, and other examples of 3D oral care representations described herein). Such 3D oral care representations may comprise point clouds, polylines, meshes, voxels and the like. Such 3D oral care representation may be generated according to the requirements of the oral care arguments which may, in some implementations, be supplied to the generative model. Oral care arguments may include oral care parameters as disclosed herein, or other real-valued, text-based or categorical inputs which specify intended aspects of the one or more 3D oral care representations which are to be generated. In some instances, oral care arguments may include oral care metrics, which may describe intended aspects of the one or more 3D oral care representations which are to be generated. Oral care arguments are specifically adapted to the implementations described herein. For example, the oral care arguments may specify the intended the designs (e.g., including shape and/or structure) of 3D oral care representations which may be generated (or modified) according to techniques described herein. In short, implementations using the specific oral care arguments disclosed herein generate more accurate 3D oral care representations than implementations that do not use the specific oral care arguments. In some instances, a text encoder may encode a set of natural language instructions from the clinician (e.g., generate a text embedding). A text string may comprise tokens. An encoder for generating text embeddings may, in some implementations, apply either mean-pooling or max-pooling between the token vectors. In some instances, a transformer (e.g., BERT or Siamese BERT) may be trained to extract embeddings of text for use in digital oral care (e.g., by training the transformer on examples of clinical text, such as those given below). In some instances, such a model for generating text embeddings may be trained using transfer learning (e.g., initially trained on another corpus of text, and then receive further training on text related to digital oral care). Some text embeddings may encode text at the word level. Some text embeddings may encode text at the token level. A transformer for generating a text embedding may, in some implementations, be trained, at least in part, with a loss calculation which compares predicted outputs to ground truth outputs (e.g., softmax loss, multiple negatives ranking loss, MSE margin loss, cross-entropy loss or the like). In some instances, the non-text arguments, such as real values or categorical values, may be converted to text, and subsequently embedded using the techniques described herein. The following are examples of natural language instructions that may be issued by a clinician to the generative models described herein: “Generate a restoration design (alternatively a veneer design) which closes the diastema between tooth #8-9 by evenly adding width onto the mesial of both teeth”, “Generate a restoration design (alternatively a veneer design) which ensures that the incisal edges of #6-11 form an even semicircle with the incisal edges of the posterior teeth (when looking from the incisal view)”, or “Generate a customized crown for an upper left central incisor, to be implanted. The crown shape should take into consideration the shape of adjacent teeth and should have no more than x mm (e.g.: 0.1mm) space between the adjacent teeth." [00200] Techniques of this disclosure may, in some implementations, use PointNet, PointNet++, or derivative neural networks (e.g., networks trained via transfer learning using either PointNet or PointNet++ as a basis for training) to extract local or global neural network features from a 3D point cloud or other 3D representation (e.g., a 3D point cloud describing aspects of the patient’s dentition – such as teeth or gums). Techniques of this disclosure may, in some implementations, use U-Nets to extract local or global neural network features from a 3D point cloud or other 3D representation. [00201] 3D oral care representations are described herein as such because 3-dimensional representations are currently state of the art. Nevertheless, 3D oral care representations are intended to be used in a non-limiting fashion to encompass any representations of 3-dimensions or higher orders of dimensionality (e.g., 4D, 5D, etc.), and it should be appreciated that machine learning models can be trained using the techniques disclosed herein to operate on representations of higher orders of dimensionality. [00202] In some instances, input data may comprise 3D mesh data, 3D point cloud data, 3D surface data, 3D polyline data, 3D voxel data, or data pertaining to a spline (e.g., control points). An encoder- decoder structure may comprise one or more encoders, or one or more decoders. In some implementations, the encoder may take as input mesh element feature vectors for one or more of the inputted mesh elements. By processing mesh element feature vectors, the encoder is trained in a manner to generate more accurate representations of the input data. For example, the mesh element feature vectors may provide the encoder with more information about the shape and/or structure of the mesh, and therefore the additional information provided allows the encoder to make better-informed decisions and/or generate more-accurate latent representations of the mesh. Examples of encoder-decoder structures include U-Nets, autoencoders or transformers (among others). A representation generation module may comprise one or more encoder-decoder structures (or portions of encoders-decoder structures – such as individual encoders or individual decoders). A representation generation module may generate an information-rich (optionally reduced-dimensionality) representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models. [00203] A U-Net may comprise an encoder, followed by a decoder. The architecture of a U-Net may resemble a U shape. The encoder may extract one or more global neural network features from the input 3D representation, zero or more intermediate-level neural network features, or one or more local neural network features (at the most local level as contrasted with the most global level). The output from each level of the encoder may be passed along to the input of corresponding levels of a decoder (e.g., by way of skip connections). Like the encoder, the decoder may operate on multiple levels of global-to-local neural network features. For instance, the decoder may output a representation of the input data which may contain global, intermediate or local information about the input data. The U-Net may, in some implementations, generate an information-rich (optionally reduced-dimensionality) representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models. [00204] An autoencoder may be configured to encode the input data into a latent form. An autoencoder may train an encoder to reformat the input data into a reduced-dimensionality latent form in between the encoder and the decoder, and then train a decoder to reconstruct the input data from that latent form of the data. A reconstruction error may be computed to quantify the extent to which the reconstructed form of the data differs from the input data. The latent form may, in some implementations, be used as an information-rich reduced-dimensionality representation of the input data which may be more easily consumed by other generative or discriminative machine learning models. In most scenarios, an autoencoder may be trained to input a 3D representation, convert that 3D representation into a latent form (e.g., a latent embedding), and then reconstruct a close facsimile of that input 3D representation as the output. [00205] A transformer may be trained to use self-attention to generate, at least in part, representations of its input. A transformer may encode long-range dependencies (e.g., encode relationships between a large number of inputs). A transformer may comprise an encoder or a decoder. Such an encoder may, in some implementations, operate in a bi-directional fashion or may operate a self-attention mechanism. Such a decoder may, in some implementations, may operate a masked self-attention mechanism, may operate a cross-attention mechanism, or may operate in an auto-regressive manner. The self-attention operations of the transformers described herein may, in some implementations, relate different positions or aspects of an individual 3D oral care representation in order to compute a reduced-dimensionality representation of that 3D oral care representation. The cross-attention operations of the transformers described herein may, in some implementations, mix or combine aspects of two (or more) different 3D oral care representations. The auto-regressive operations of the transformers described herein may, in some implementations, consume previously generated aspects of 3D oral care representations (e.g., previously generated points, point clouds, transforms, etc.) as additional input when generating a new or modified 3D oral care representation. The transformer may, in some implementations, generate a latent form of the input data, which may be used as an information-rich reduced-dimensionality representation of the input data, which may be more easily consumed by other generative or discriminative machine learning models. [00206] In some implementations, an encoder-decoder structure may first be trained as an autoencoder. In deployment, one or more modifications may be made to the latent form of the input data. This modified latent form may then proceed to be reconstructed by the decoder, yielding a reconstructed form of the input data which differs from the input data in one or more intended aspects. Oral care arguments, such as oral care parameters or oral care metrics may be supplied to the encoder, the decoder, or may be used in the modification of the latent form, to influence the encoder-decoder structure in generating a reconstructed form that has desired characteristics (e.g., characteristics which may differ from that of the input data). [00207] Techniques of this disclosure may, in some instances, be trained using federated learning. Federated learning may enable multiple remote clinicians to iteratively improve a machine learning model (e.g., validation of 3D oral care representations, mesh segmentation, mesh cleanup, other techniques which involve labeling mesh elements, coordinate system prediction, non-organic object placement on teeth, appliance component generation, tooth restoration design generation, techniques for placing 3D oral care representations, setups prediction, generation or modification of 3D oral care representations using autoencoders, generation or modification of 3D oral care representations using transformers, generation or modification of 3D oral care representations using diffusion models, 3D oral care representation classification, imputation of missing values), while protecting data privacy (e.g., the clinical data may not need to be sent “over the wire” to a third party). Data privacy is particularly important to clinical data, which is protected by applicable laws. A clinician may receive a copy of a machine learning model, use a local machine learning program to further train that ML model using locally available data from the local clinic, and then send the updated ML model back to the central hub or third party. The central hub or third party may integrate the updated ML models from multiple clinicians into a single updated ML model which benefits from the learnings of recently collected patient data at the various clinical sites. In this way, a new ML model may be trained which benefits from additional and updated patient data (possibly from multiple clinical sites), while those patient data are never actually sent to the 3rd party. Training on a local in-clinic device may, in some instances, be performed when the device is idle or otherwise be performed during off-hours (e.g., when patients are not being treated in the clinic). Devices in the clinical environment for the collection of data and/or the training of ML models for techniques described herein may include intra-oral scanners, CT scanners, X- ray machines, laptop computers, servers, desktop computers or handheld devices (such as smart phones with image collection capability). In addition to federated learning techniques, in some implementations, contrastive learning may be used to train, at least in part, the ML models described herein. Contrastive learning may, in some instances, augment samples in a training dataset to accentuate the differences in samples from different classes and/or increase the similarity of samples of the same class. [00208] In some instances, a local coordinate system for a 3D oral care representation, such as a tooth, may be described by one or more transforms (e.g., an affine transformation matrix, translation vector or quaternion). Systems of this disclosure may be trained for coordinate system prediction using past cohort patient case data. The past patient data may include at least: one or more tooth meshes or one or more ground truth tooth coordinate systems. Machine learning models such as: U-Nets, encoders, autoencoders, pyramid encoder-decoders, transformers, or convolution and/or pooling layers, may be trained for coordinate system prediction. Representation learning may determine a representation of a tooth (e.g., converting a mesh or point cloud into a latent representation, for example, using a U-Net, encoder, transformer, convolution and/or pooling layers or the like), and then predict a transform for that representation (e.g., using a trained multilayer perceptron, transformer, encoder, transformer, or the like) that defines a local coordinate system for that representation (e.g., comprising one or more coordinate axes). In the instance where the coordinate system is predicted for a tooth mesh, the mesh convolutional techniques described herein can leverage invariance to rotations, translations, and/or scaling of that tooth mesh to generate predications that techniques that are not invariant to the rotations, translations, and/or scaling of that tooth mesh cannot generate. Pose transfer techniques may be trained for coordinate system prediction, in the form of predicting a transform for a tooth. Reinforcement learning techniques may be trained for coordinate system prediction, in the form of predicting a transform for a tooth. [00209] Machine learning models such as: U-Nets, encoders, autoencoders, pyramid encoder- decoders, transformers, or convolution and/or pooling layers, may be trained as a part of a workflow for hardware (or appliance component) placement. Representation learning may train a first module to determine an embedded representation of a 3D oral care representation (e.g., converting a mesh or point cloud into a latent form using an autoencoder, or using a U-Net, encoder, transformer, block of convolution and/or pooling layers or the like). That representation may comprise a reduced dimensionality form and/or information-rich version of the inputted 3D oral care representation. In some implementations, the generation of a representation may be aided by the calculation of a mesh element feature vector for one or more mesh elements (e.g., each mesh element). In some implementations, a representation may be computed for a hardware element (or appliance component). Such representations are suitable to be provided to a second module, which may perform a generative task, such as transform prediction (e.g., a transform to place a 3D oral care representation relative to another 3D oral care representation, such as to place a hardware element or appliance component relative to one or more teeth) or 3D point cloud generation. Such a transform may comprise an affine transformation matrix, translation vector or quaternion or the like. Machine learning models which may be trained to predict a transform to place a hardware element (or appliance component) relative to elements of patient dentition include: MLP, transformer, encoder, or the like. Systems of this disclosure may be trained for 3D oral care appliance placement using past cohort patient case data. The past patient data may include at least: one or more ground truth transforms and one or more 3D oral care representations (such as tooth meshes, or other elements of patient dentition). In the instance where a U-Net (among other neural networks) is trained to generate the representations of tooth meshes, the mesh convolution and/or mesh pooling techniques described herein leverage invariance to rotations, translations, and/or scaling of that tooth mesh to generate predications that techniques that are not invariant to the rotations, translations, and/or scaling of that tooth mesh cannot generate. Pose transfer techniques may be trained for hardware or appliance component placement. Reinforcement learning techniques may be trained for hardware or appliance component placement. [00210] Techniques of this disclosure offer technical improvements over existing systems and techniques. For instance, techniques of this disclosure offer improvements to the technical problem of generating (or modifying) digital 3D oral care representations for use in generating oral care appliances (both digital appliances and corresponding physical manifestations of those digital designs – such as physical manifestations which have been 3D printed), particularly vis-a-vis the providing mesh element features, oral care metrics, or oral care parameters to train one or more machine learning models, which improve the quality (e.g., accuracy) of the generated 3D oral care representations. [00211] Furthermore, in some implementations, techniques of this disclosure may be trained to generate other kinds of data representations which are not contemplated by existing systems and techniques, including transforms, coordinate system axes (e.g., for teeth or other aspects of the patient’s dentition) or mesh element labels to name two examples. Techniques of this disclosure may be trained on oral care data (e.g., meshes, point clouds or voxelized representations which describe dental anatomy or appliance components, transforms which place teeth or appliance components into poses which are suitable for clinical treatment, mesh element labels which may be defined for use with segmentation or mesh cleanup operations, or other examples of 3D oral care representations described herein) to generate 3D oral care representations which are suited to the generation of oral care appliances. [00212] During either training or deployment, the techniques of this disclosure may take as input a 3D oral care representation, which may be converted into a latent form or latent representation by a first neural network (e.g., an encoder, or a set of linear layers). The first neural network may, in some implementations, be trained, at least in part, by the calculation of a reconstruction loss (e.g., a cross- entropy loss), which may compare a generated output to a ground truth reference. When mesh, voxel or point cloud data (or data describing other 3D representations) are processed by the techniques of this disclosure, a technical improvement is realized by the calculation of mesh element feature vectors for one or more mesh elements. Such mesh element feature vectors may be computed by a mesh element feature module. Such mesh element feature vectors may be provided to the first neural network and may improve the accuracy or fidelity of the latent form which is generated by that first neural network. The improved accuracy of the latent form may enable the latter generative steps to output an improved generated (or modified) result (e.g., a 3D representation of a tooth for restoration, a set of transforms for use in orthodontic setups generation, one or more coordinate system axes, or mesh element labels for use in segmentation or in mesh cleanup). Furthermore, the accuracy of downstream processes that utilize the latent form are likewise improved, which also improves the accuracy and capabilities of underlying computing systems that implement the techniques described herein. For example, a neural network for setups transform generation is improved through a more accurate encoding of the shapes and/or boundaries of the patient’s teeth. Stated another way, a setups prediction model that utilizes an awareness of tooth boundaries is able to minimize tooth collisions. Furthermore, a neural network for 3D representation generation (e.g., the generation of tooth restoration designs, oral care appliance components, fixture model components, or the like) is improved through a more-accurate encoding of the shapes and/or structures of the patient’s teeth. Stated another way, a machine learning model (e.g., a restoration design generation neural network) which is intended to generate a tooth with a precise shape and/or structure will necessarily benefit from the reconstruction of a latent representation that accurately encodes the shape and/or structure of the pre-restoration tooth. [00213] Further technical improvements are realized by techniques of this disclosure by the use of oral care parameters (e.g., which may specify customized characteristics of an intended 3D oral care representation which is to be generated or modified) or oral care metrics (e.g., which may quantify or measure physical aspects of one or more teeth, which may quantify the shape and/or structure of an individual tooth or appliance component, or may quantify the poses and/or physical arrangements between two or more teeth or appliance components), collectively referred to as oral care arguments. Oral care metrics may be computed for a training example (e.g., the set of the patient’s teeth) and be provided in connection with either training the model or deploying the model as described herein. Such oral care metrics may improve the augmented shape representation y by quantifying specific key aspects of the inputted 3D oral care representation Z (e.g., by quantifying the shapes of one or more teeth or appliances components, or by measuring the special relationships between one or more teeth or appliance components) that the continuous normalizing flow (CNF) model may use to generate customized output which is suitable for use in clinical treatment (e.g., generating customized tooth restoration designs, customized appliance components, customized orthodontic setups transforms, coordinate axes or the like). The oral care metrics may be provided to the generator module at training time, to teach the CNF model about the shape and/or structure of the provided input data. After deployment, values which are of the same format as the oral care metrics may be provided to the CNF model to influence the CNF model about the intended shape and/or structure of the 3D oral care representation which is intended to appear at the output of the CNF model (e.g., a new geometry or a modified version of an inputted geometry). The generator module may be trained, at least in part, by a loss which compares predicted to ground truth reference outputs. [00214] A 3D representation (e.g., a 3D point cloud) may be generated (or modified), at least in part, using one or more neural networks which can be combined with continuous normalizing flows (aka a CNF model), which have been trained for 3D point cloud generation (or modification). The one or more neural networks may include one or more transformers or one or more autoencoders. In some implementations, such a CNF model, may modify the shape of a 3D point cloud. Such a point cloud may be based on an existing 3D oral care representation which requires modification, or such a point cloud may correspond to a newly generated or newly initialized example. A CNF model may also generate (or modify) other types of data structures, such as transforms (e.g., a matrix to define rotation, translation or scaling) or vectors (e.g., an coordinate tuple which may define a point or the like). A CNF model may be trained on cohort patient case data, which may comprise one or more 3D oral care representations, as defined herein. Such a model may be trained to learn the distribution of such training data and generate new examples of 3D oral care representations which are suitable for clinical use (e.g., suitable for use in generating a tooth restoration design, an appliance component, a trimline, an archform, a transform, or the like). [00215] CNF models described herein may, in some implementations, be trained to generate transforms. Such transforms may be described using transformation matrices or vectors, quaternions, or others suitable data representations disclosed herein. Such transforms may place teeth or appliance components relative to elements of the patient’s dentition (e.g., such as in appliance design or setups prediction). In some implementations, the techniques may be trained to generate (or modify) mesh element labels (e.g., for use in labelling mesh elements as a part of segmentation or mesh cleanup operations). In some implementations, the techniques may be trained to generate (or modify) tooth coordinate systems (e.g., which may be used by setups prediction models in the placement of teeth). [00216] The continuous normalizing flow (CNF) modelling techniques described herein may generate (or modify) 3D oral care representations. The generated (or modified) 3D oral care representations may be used in digital oral care (e.g., the automatic generation of aspects of an oral care appliance - such as aligner trays, indirect bonding trays or a dental restoration appliance, to name a few examples). [00217] Techniques are described which use CNF to generate a 3D oral care representation (e.g., generate a tooth design for use in dental restoration treatment, or generate a transform to place a tooth in a final setups pose). In some implementations, a CNF may be used to modify a 3D oral care representation (e.g., modifying aspects of the patient's dentition in the course of a mesh cleanup operation - such as to remove extraneous material or correct flaws left over from intra-oral scanning). The continuous normalizing flows techniques described herein may be trained on cohort patient case data. An example of such case data is referred to herein as Z or z. Z may consist of point cloud (or other 3D representation) data describing a tooth or teeth, point cloud (or other 3D representation) data describing an appliance component; one or more transforms; one or more mesh element labels, a polyline describing a trimline or an archform, or other examples of 3D oral care representations described herein. [00218] An inverse CNF f(z)^-1 may, in some implementations, map a complicated distribution (e.g., a point cloud, or other high dimensionality data representation, describing aspects of digital oral care treatment) into a simplified or reduced dimensionality distribution (e.g., a latent representation, such as a latent vector or latent capsule). [00219] A neural network to describe a CNF may comprise one or more layers, each of which may map between a first distribution and a second distribution. In some instances, the first distribution may be a relatively more complex distribution (i.e., distribution having a high dimensionality), and the second distribution may be a relatively more simplified distribution (i.e., a distribution having a lower order of dimensionality). In some instances, the first distribution may be a multi-modal distribution, and the second distribution may be a uni-modal distribution. In some instances, the first distribution may correspond to a 3D representation of the patient’s dentition, and the second distribution may be initialized using a 3D Gaussian distribution. In some instances, the first distribution may correspond to a 3D representation of an oral care appliance component, and the second distribution may be initialized using a 3D Gaussian distribution. In some instances, the first distribution may correspond to a transform for use in placing a tooth or an appliance (among other items), and the second distribution may be a matrix or vector with randomly assigned values (or values from a unimodal or default distribution). In some instances, the first distribution may comprise a set of mesh element labels which is suitable for use in the segmentation or cleanup of a 3D representation of the patient’s dentition, and the second distribution may be a set of mesh element labels which have been randomly initialized (or initialized to default or random values). The layers of the CNF f(z) may be stacked and may be executed in succession. The inverse CNF f(z)^-1 of a CNF may, in some implementations, be derived by reversing the order of the layers in f(z). The operations within each of the layers may be computed in inverse using linear algebra, to complete the formulation of CNF f(z)^-1. Stated another way, CNF f(z)^-1 may be derived from the invertible module CNF f(z) by 1) inverting the linear algebra operations within each layer of CNF f(z) and 2) reversing the order of the layers within CNF f(z), in no particular order. [00220] Techniques of this disclosure may train a CNF f(z) which may transform a simplified distribution q_hat (e.g., some aspects of which may correspond to a Gaussian distribution, noise or stochastic aspects) into a distribution with greater complexity v_hat. In some implementations, the function f(z) may be invertible. f(z)^-1 may enable a sample v which is drawn from a distribution of greater complexity to be transformed into simpler representation q (e.g., a representation of lesser complexity and/or lower dimensionality). [00221] A CNF may be used in deployment to generate (or modify) a 3D oral care representation, as shown in FIG.17. The generated (or modified) 3D oral care representation Z_hat 1710 may have aspects (e.g., shape and/or structure) which are within the distribution of the dataset of cohort patient case data which was used to train the CNF (e.g., which may comprise at least one or both of functions CNF f(z) 1702 or CNF g(z) 1708). In some implementations, a CNF may train an ML model (e.g., a neural network) to serve as CNF f(z) 1702 or CNF g(z) 1708. A shape representation v_hat 1704 (e.g., a shape representation for the 3D oral care representation which is to be generated or modified) may be sampled by transforming q_hat 1700 according to CNF f(z) 1702. [00222] In some implementations, q_hat 1700 may be drawn from a 3D Gaussian prior distribution (e.g., in the use case of generating a 3D oral care representation Z_hat 1710 for use in digital oral care treatment). In some implementations, q_hat 1700 may comprise an existing 3D oral care representation which requires modification before the existing 3D oral care representation may be used in digital oral care treatment (e.g., the shape of a 3D representation of a tooth may require modification before that tooth may be used in the generation of a dental restoration appliance). In some implementations, q_hat 1700 may comprise points of a point cloud (or voxels of a sparse representation, or faces/edges/vertices of a mesh). In some implementations, q_hat 1700 may comprise one or more latent vectors (e.g., such as latent vectors which contain values drawn from Gaussian distributions). [00223] The generated (or modified) representation Z_hat 1710 may comprise mesh elements, such as points (e.g., in the case of a point cloud) or voxels (e.g., in the case of a sparse representation). Mesh elements Y_j 1706 (e.g., points) may be sampled from a 3D Gaussian prior distribution (or another type of distribution). The mesh elements Y_j 1706 may be transformed according to the CNF g(z) 1708 parameterized by the shape representation v_hat 1704. Stated another way, a set of mesh elements Yj 1706 may be initialized according to some distribution (e.g., a Gaussian distribution) and then transformed by g(z) so that the mesh elements Y_j 1706 are assigned positions (and/or orientations) in proximity to the surface of the shape which is described by the shape representation v_hat 1704. Representation v_hat 1704 may facilitate transforming the mesh elements Y_j 1706. The mesh elements of Z_hat 1710 may comprise these transformed mesh elements Y_j' 1706. After sufficiently many mesh elements (e.g., vectors or matrices for transforms or labels) have been sampled, the generated (or modified) 3D oral care representation Z_hat 1710 is outputted by the CNF model. The CNF g(z) 1708 may transform data from a simple distribution (e.g., pre-transformation data which is drawn from a less complex distribution) into data which has a more complex shape and/or structure. For example, in the case of tooth restoration design generation, a set of mesh elements Y_j 1706 may be generated according to a 3D Gaussian and then transformed according to CNF g(z) 1708 as parameterized by the shape representation v_hat 1704, so that the mesh elements Y_j 1706 are assigned positions that describe the target tooth which is to be generated (e.g., an upper right cuspid or lower left central incisor). Other examples of data which may be provided to CNF g(x) 1708 include one or more transforms which have initial values; one or more mesh element labels which have initial values; one or more points describing an archform or polyline; or other simplified data structures which may described 3D oral care representations described herein. Either or both of CNF f(z) 1702 and CNF g(z) 1708 may take as input oral care parameters. These oral care parameters may facilitate the geometry generation (or modification) operations of the CNF model. These oral care parameters may influence the CNF model regarding the intended shape and/or structure of the outputted 3D oral care representation Z_hat 1710. [00224] The CNF may be trained on cohort patient case data which describes aspects of the type of 3D oral care representation which is to be generated (or modified), such as tooth restoration designs, appliance components, IPR cut surfaces, transforms for placing teeth or hardware or appliance components into poses that are suitable for digital oral care treatment (e.g., orthodontic treatment or dental restoration), mesh element labels (e.g., for segmentation or mesh cleanup), definitions of coordinates systems (e.g., such as a transform to define a local coordinate system for a tooth or for an arch), or other 3D oral care representations described herein. [00225] In some implementations, one or more mesh element features may be provided to a first neural network, such as p(z) (e.g., a representation generation neural network). The first neural network, p(z), may comprise one or more encoders, or one or more linear layers (e.g., linear layers which have been trained to generate latent embeddings or latent representations). p(z) may also take as input, in some implementations, a mesh element feature vector for one or more of the respective mesh elements. Such mesh element features (as described herein) may enable the first neural network to get a better understanding of the shape and/or structure of the representation (e.g., to better understand the shape and/or structure of the 3D oral care representation), which may improve data precision of representations which are generated by the respective neural networks (e.g., the first neural network, which may generate a shape representation y, and the mesh element features may improve the fidelity of y). [00226] A sample of cohort patient case data 1606 (e.g., a point cloud representing a particular tooth) may be received at the input of the training method, as seen in FIG.16. The mesh elements (e.g., points, etc.) of a training example Z 1606 may undergo (optional) mesh element feature vector calculation (1604), and then be provided to the first neural network 1602, which may infer (1608) a posterior over shape (or structure) representations given the mesh elements contained within Z, and then may sample (1612) an augmented shape representation v from that posterior. L_posterior may be computed as the entropy of the posterior v ~ p(y|Z). Representation v may describe aspects of the shape and/or structure of Z. The probability of v in the prior distribution (L_y) may be computed (1618) using the inverse CNF f(z)^-11616 and w 1620. Augmented shape representation v may comprise a latent vector, latent capsule or some other latent form. f(z)^-1 may in some implementations, provide a mapping from a relatively complex distribution (e.g., y) to a simplified distribution (e.g., q). In some instances, noise 1610 may be introduced in the calculation of y. Such noise may be Gaussian or be drawn from another distribution. Optional oral care arguments 1600 may be provided to the first neural network 1602, to influence the generation of latent representations by the first neural network 1602. [00227] The inverse function g(z)^-11614 may take as input the mesh elements of the training example Z, and the augmented shape representation y. The inverse function g(z)^-1 may condition on the augmented shape representation v to reconstruct the mesh elements of the training example Z into a reconstructed form of the input Z’ 1622. Reconstruction loss (L_xprime) may be computed (1624) through a comparison of the reconstructed form of the input Z’ 1622 and the original input Z 1606. [00228] The CNF functions f(z) and g(z) may each be trained, at least in part, in an end-to-end manner. In some implementations, the CNF functions f(z) and g(z) may each be trained, at least in part, by training either or both of the respective inverse functions f(z)^-1 and g(z)^-1. The neural networks of the CNF model may, in some implementations, be trained, at least in part, to maximize the CNF Loss 1626, which is the sum of L_posterior, L_xprime and L_y. In some implementations, the neural networks of the CNF model may be trained to minimize one or more of the loss values described herein. [00229] The generative implementations described herein may include one or more hierarchical feature extraction modules (e.g., modules which extract global, intermediate or local neural network features from a 3D representation – such as a point cloud). Examples of hierarchical neural network feature extraction modules (HNNFEM) include 3D SWIN Transformer architectures, U-Nets or pyramid encoder-decoders, among others. A HNNFEM may be trained to generate multi-scale voxel (or point) embeddings of a 3D representation (or multi-scale embeddings of other mesh elements described herein). For example, a HNNFEM of one or more layers (or levels) may be trained on 3D representations of patient dentitions to generate neural network feature embeddings which encompass global, intermediate or local aspects of the 3D representation of the patient’s dentition. [00230] Techniques of this disclosure may perform style transfer between 3D representations, with application to digital oral care. While examples are disclosed for style transfer between 3D point clouds, it should be understood that the style transfer techniques also apply to 3D meshes, voxelized representations, 3D polylines or other types of 3D representations disclosed herein. Aspects of a style (or reference) 3D representation S may be transferred onto a target 3D representation C, resulting in a stylized (or modified) 3D representation P. An example of a target 3D representation is a pre-restoration tooth mesh which is intended to receive the style of a reference mesh (e.g., a post-restoration tooth mesh with one or more styles which are desired for oral care treatment). Stated another way, in some examples, aspects of a style 3D point cloud S may be transferred to a target 3D point cloud C, resulting in a stylized 3D point cloud (or voxelized representation or 3D mesh, etc.) P. A stylized 3D point cloud (or voxelized representation or 3D mesh) is designated P*. The style transferring may be performed to minimize one or more loss functions (e.g., loss functions pertaining to spatial geometry, structural geometry or color). The examples described herein may update the spatial or structural style aspects of P, P*_spatial and P^* _structural. P*_spatial and P^* _structural may, in some implementations, be updated iteratively using an optimizer (e.g., stochastic gradient descent, or another gradient-based optimization method). In some be updated according to one or more of the losses described below, until convergence. [00231] In some implementations, an ML model may be trained to perform neural style transfer, to assign aspects of the style of a reference 3D representation of oral care data to a target 3D representation of oral care data. The fully trained ML model may extract hierarchical neural network features from the target 3D representations and/or reference 3D representations, which may be provided to the loss calculations described herein, for example, as vectorized arrangements of the mesh elements in each of P, C and S. Examples of a fully trained ML model for hierarchical neural network feature extraction for use in neural style transfer are shown in FIG.18 and FIG.19. Such an ML model may be trained on cohort patient case data. The ML model may include a first style-transfer module comprising one or more U- Nets, one or more 3D SWIN transformer structures, one or more pyramid encoder-decoder structures, or one or more neural network feature extraction layers (e.g., a sequence of layers of increasing width), which may extract global, intermediate or local neural network features from a 3D representation from the training dataset (e.g., using a HNNFEM). For example, the neural network features may be extracted from a 3D representation by analyzing that 3D representation at each of a succession of levels of decreasing resolution. That is, local features may be extracted from the 3D representation when the 3D representation is at full resolution. Then the 3D resolution may be downsampled, after which the first set of intermediate features may be extracted. Then the 3D resolution may be further downsampled, after which a further set of intermediate neural network features (e.g., increasingly global neural network features) may be extracted, and so on. At the lowest resolution (e.g., after all downsampling steps have been applied), the most-global set of neural network features may be extracted from the 3D representation. This local, intermediate, or global neural network feature extraction process may be implemented with a hierarchical neural network feature extraction module. The mesh elements of S and the mesh elements of C may be provided to the first style transfer module as inputs. Mesh element feature vectors may, in some implementations, be computed for the mesh elements of S or C. The output of the first style transfer module may be provided to a second style transfer module, which may output S. In some implementations, C may optionally also be provided as input to the second style transfer module. Such an ML model may be trained, at least in part, by one or more loss values (e.g., losses which compare expected outputs to reference or ground truth outputs). Such losses may include one or more of the following losses, among others disclosed herein. P*_spatial = arg_min_over_P_spatial ( α_{spatial *} L_{spatial_target} (P_spatial, C_spatial) + β_{spatial *} L_{spatial_style} (P_spatial, S_spatial)) P^* _structural = arg_min_over_P_structural ( α_{structural *} L_{structural_target} (P_structural, C_structural) + β_{structural *} L_{structural_style} feature extraction blocks (NNFEB) (e.g., which may comprise one or more neural networks or neural network layers which may extract neural network features from the input) to encode neural network features (e.g., on local scales, global scales or intermediate scales in-between). Techniques of this disclosure may transfer one or more aspects of a style 3D oral care representation (e.g., as described by a 3D point cloud) onto one or more target 3D oral care representations, resulting in one or more stylized 3D oral care representations. A 3D oral care representation may include a tooth mesh (e.g., for use in dental restoration), a mesh describing an appliance or appliance component (e.g., for dental restoration or orthodontics), or other examples of 3D oral care representations described herein (e.g., trimlines described by 3D polylines, IPR cut surfaces, or mesh element labels for use in segmentation or mesh cleanup). Aspects of style which may be transferred include the shape of a 3D representation (e.g., of a 3D point cloud, 3D mesh, or others disclosed herein), the structure of a 3D representation (e.g., of a 3D mesh, or others disclosed herein), or the color of a 3D representation (e.g., a point cloud, mesh or voxelized representation, or others disclosed herein). [00233] The style transfer techniques of this disclosure may, in some implementations, assign aspects of the shape and/or structure of a mesh of a reference tooth to a mesh of a target tooth, resulting in a stylized tooth. The methods may, in some implementations, generate a stylized tooth design by assigning one or more of the following tooth characteristics from the reference mesh to the target mesh: 0 – tooth silhouette, e.g., as projected onto a plane in front of the face 1 – main tooth shape (primary anatomy) 2 – surface vertical and horizontal macro textures, e.g., mamelon grooves (secondary anatomy) 3 – surface horizontal micro texture, e.g., perikymata (tertiary anatomy) 4 – volumetric representation of the tooth’s interior structure (dentine, enamel, etc.) 5 – occlusal surface textures, e.g., fossae or grooves (secondary anatomy) [00234] Techniques of this disclosure may, in some implementations, use PointNet, PointNet++, or derivative neural networks (e.g., networks trained via transfer learning using either PointNet or PointNet++ as a basis for training) to extract local or global neural network features from a 3D point cloud (or other 3D representation). Techniques of this disclosure may, in some implementations, use U- Nets or pyramid encoder-decoder structures to extract local or global neural network features from a 3D point cloud. For example, PointNet may learn a local spatial encoding for each point of a point cloud, and then aggregate those local spatial encodings into one or more increasingly aggregated encodings (e.g., a global encoding corresponding to global neural network features). In another example, PointNet++ may partition the points of a point cloud into overlapping local partitions (e.g., local partitions with a specified dimension or scale). Local neural network features may be extracted from each local partition. Those local neural network features may be aggregated into larger units, resulting in higher-level neural network features (e.g., features may be aggregated at each of a series of increasingly larger-scale partitions, eventually resulting in global neural network features at the top-level). [00235] Techniques of this disclosure may, in some implementations, use one or more neural network feature extraction blocks (NNFEB) to extract local or global neural network features from a 3D point cloud (or other 3D representation). In some implementations, a NNFEB may comprise one or more MLPs, one or more pyramid encoder-decoders (as shown in FIG.20) or one or more U-Nets (as shown in FIG.21). When the NNFEB contains MLP layers, such layers may be stacked in order of (for example) increasing width (e.g., width 64, followed by 256, 1024, 2048, etc.). The higher-width layers towards the end of the stack in the NNFEB may correspond to increasingly global neural network features. When such a NNFEB encodes color, the 2048-width layer may correspond to global neural network color features. In a further example, for a stack of layers which encodes spatial mesh element features of a 3D oral care representation (e.g., 3D representation of the patient’s dentition, an appliance, or appliance component), the 2048-width layer may correspond to global neural network features which correspond to the spatial distribution or to the shape of the 3D representation that was provided at the input. In yet example, for a stack of layers which encodes structural mesh element features of a 3D oral care representation, the 2048-width layer may correspond to global neural network features which describe the structure of the 3D representation that was provided at the input. Table 2 describes structural mesh element features which are particularly helpful in the automated processing of digital oral care objects. When the 3D representation which is under consideration is presented as a 3D mesh, for example, the structural features exploit information about the 3D representation’s topology that is inherent in the connections between vertices (e.g., edges and faces). Stated another way, there are clear neighbor relationships between vertices, because of the edges or faces which connect those vertices. Similar information about the 3D representation’s structure is also available in a voxelized representation, because there are clearly defined neighbor relationships between voxels. When the 3D representation is provided as a point cloud, the neighbor relationships between points may be less clearly defined (than in 3D meshes or voxelized representations). [00236] In some implementations, there may be l stacked layers in a NNFEB. In some implementations, an NNFEB may contain a pyramid encoder-decoder which has l levels. In some implementations, an NNFEB may contain a U-Net which has l levels. H^l() may describe aspects of the content of the input 3D representation (e.g., each row of H^l() may contain local, intermediate or global neural network features). In some implementations, the Gram matrix of H^l() may be computed by multiplying H^l() by the transpose of H^l(). The Gram matrix of H^l() may describe aspects of the style representation of the l^th NNFEB layer (e.g., when the NNFEB contains an MLP) or the l^th level of the NNFEB (e.g., when the NNFEB contains a pyramid encoder-decoder or a U-Net). The whole Gram matrix may have dimensions m_l by m_l, and is denoted as G(H^l()). A point cloud, 3D mesh, voxelized representation, 3D polyline or other 3D representation may be provided as input to a NNFEB. The 3D representation 1800 may comprise an appliance component, aspects of the patient’s dentition or other 3D oral care representations described herein. The mesh elements (e.g., points, vertices, edges, faces or voxels) of the 3D representation may be arranged into vectors or matrices. In some implementations, one or more spatial mesh element features may be computed for each mesh element by the mesh element feature module 1804. In some implementations, one or more structural mesh element features may be computed for each mesh element by the mesh element feature module 1804. In some implementations, one or more color mesh element features may be computed for each mesh element by the mesh element feature module 1804. The mesh element feature vectors 1806, along with optional oral care parameters, or optional oral care metrics may be provided to the NNFEB 1808. When NNFEB contains an l layers of MLP, the output contains neural network features for each of those t layers. When NNFEB contains a U- Net of l levels, the output contains neural network features for each of those l levels. When NNFEB contains a pyramid encoder-decoder of l levels, the output contains neural network features for each of those l levels. H^l designates the output of the l^th level or layer. The local/intermediate/global neural network features 1810 may, in some implementations, be provided to the output of the method. The local/intermediate/global neural network features 1810 may, in some implementations, be provided to a concatenation operation, which may combine the results of multiple parallel methods. The output of the optional concatenation operation may be provided to the MLP 1814, which may output refined local/intermediate/global neural network features 1816. An example of such an MLP may have the following layer dimensions: 1024, 256, 64, 16. The resulting refined features may be outputted, for use in computing the style transfer losses. Computing an NNFEB stage H^l may be comprise multiplying each row of the input matrix A^l-1 with a weight matrix W^l. H^l may comprise one or more vectors and may be interpreted as an augmented target representation (e.g., augmented through the use of mesh element features, oral care parameters or oral care metrics). [00237] The following augmented style loss terms may be computed, and used to train, at least in part, the style transfer ML models of this disclosure. L_{spatial_style} is the augmented style loss for spatial geometry and may be computed by comparing aspects of the spatial geometry (e.g., spatial mesh element features such as “normal vector” or others disclosed herein) of the stylized 3D point cloud P and the style 3D point cloud S. 3D point cloud is meant to be inclusive of other 3D representations described herein, including 3D meshes. L_{structural_style} is the augmented style loss for structural geometry and may be computed by comparing aspects of the structural geometry (e.g., mesh element features such as “curvatures” or others disclosed herein) of the stylized 3D point cloud P and the style 3D point cloud S. L_{color_style} is the augmented style loss for color and may be computed by comparing the color aspects (e.g., point color values in RGB, HSV or other encoding schemes described herein) of the stylized 3D point cloud P and the style 3D point cloud S. {S_layers} is the set of layers or levels in the NNFEB that are used in the calculation of the augmented style loss (e.g., layers from which neural network features are extracted). ^_{^^^^^^^_^^^^^}(^_^^^^^^^, ^_^^^^^^^) = ^ ^2_^^^^^^(^^{^}(^_^^^ )) − ^(^^{^}(^ ))^ ^^{∈{^ }} _{^^^^ ^^^^^^^} _^^^^^^ at least in spatial geometry and may be computed by comparing aspects of the spatial geometry (e.g., mesh element features such as normal vectors or others disclosed herein) of the stylized 3D point cloud P and the target 3D point cloud C. L_{structural_style} is the augmented target loss for structural geometry and may be computed by comparing aspects of the structural geometry (e.g., mesh element features such as curvatures, or others disclosed herein) of the stylized 3D point cloud P and the target 3D point cloud C. L_{color_target} is the augmented target loss for color and may be computed by comparing the color aspects (e.g., point color values in RGB, HSV or other encoding schemes described herein) of the stylized 3D point cloud P and the target 3D point cloud C. {C_layers} is the set of NNFEB layers that are used in the calculation of the augmented target loss (e.g., layers from which neural network features are extracted). ^{^} _{^^^^^^^_^^^^^^^} ^{(^} _^^^^^^^ ^{, ^} _^^^^^^^ ^{) =} _^ ^{^2_^^^^} ^{^ ∈{^ }} _^ ^{^^(^} _^^^^^^^ ^{) − ^^(^} _^^^^^^^ ⁾ _^ _^^^^^^ (e.g., a pre- restoration tooth or an appliance component) may be received as the input (e.g., as style point cloud S or target point cloud C). A mesh element feature vector may be computed for one or more points of the point cloud (e.g., according to the descriptions in Table 2 and elsewhere in this disclosure). In some examples, the mesh element features may comprise spatial mesh element features or structural mesh element features. In some examples, the mesh element features may comprise color information pertaining to the point (e.g., RGB or HSV information). In other examples, the mesh element features may comprise other of the mesh element features described herein. In some examples, the mesh element feature vectors may be provided to a neural network feature extraction block (NNFEB). An example of a NNFEB is a stack of layers of width 64, followed by layers of width 256, 1024, 2028, etc. Another example of a NNFEB is a HNNFEM, as described herein. The NNFEB may generate a latent encoding which includes neural network features (e.g., hierarchical neural network features when the NNFEB includes a HNNFEM). The output of the global-most layer of the NNFEB may, in some implementations, undergo pooling (1812) (e.g., max pooling or average pooling) and subsequently be provided to an MLP 1814, as shown in FIG.18. [00240] FIG.18 shows a generalized example of the feature extraction module. 3D representations of the patient’s dentition 1800 (e.g., 3D point clouds, meshes, voxels or others described herein) may be provided to mesh element feature module 1804, so that mesh element feature vectors may be computed (1804) for the mesh elements of the 3D representation 1800. The mesh elements of 1800 and the associated mesh element feature vectors 1806 may be provided to NNFEB 1808, which may generate neural network features 1810. When NNFEB contains a HNNFEM 1808, the output 1810 contains hierarchical neural network features. The neural network features 1810 may undergo pooling (1812) (e.g., max pooling or average pooling). The result may undergo refinement by an MLP 1814 (e.g., comprising fully connected layers 1024, 256, 64 and 16, among other architectures), which may output vectors 1816 containing refined neural network features (e.g., global, intermediate, or local neural network features). Optional oral care arguments 1802 (e.g., oral care parameters, or oral care metrics) may be provided to NNFEB 1808 or MLP 1814, to influence the feature extraction and refinement functions of those modules. The 3D representations of the patient’s dentition 1800 may contain optional color information, optional temperature information, optional tissue impedance or other information pertaining to other types of sensor measurements. Such information may, in some implementations, be associated with mesh elements of 3D representation 1800, such as in the form of RGB or HSV color values. In some implementations, color may be used to describe temperature or impedance, such as with heat maps or maps of resistivity. Examples of HNNFEM are shown in FIG.20 (a pyramid encoder- decoder) and FIG.21 (a U-Net). [00241] FIG.19 shows an example of the feature extraction module for operation on a 3D Representation of the patient’s dentition 1902 (which may optionally contain color, temperature, or tissue impedance information). Optional oral care arguments 1900 may be provided to the NNFEB modules 1908, 1916 or 1930, or to the fully connected layers 1924, to customize the generative outputs of those modules. Color information may, in some implementations, come from color photographs which are integrated with the 3D mesh as textures. Temperature information may, likewise, be captured using a thermal camera and similar applied to the 3D mesh as a color texture. The patient’s dentition 1902 may be provided to mesh element feature module 1904, which may compute one or more of: structural mesh element features, spatial mesh element features, or color mesh element features. [00242] When spatial mesh element features are computed, the spatial mesh element features (e.g., XYZ coordinates of the vertices, among others disclosed herein) 1906 may be provided to NNFEB 1908, which may generate neural network features 1910 (e.g., hierarchical features), which may be provided to pooling module 1912, which may generate outputs which are provided to vector concatenation module 1922. [00243] When color mesh element features are computed, the color mesh element features (e.g., RGB values of the vertices, among others disclosed herein) 1914 may be provided to NNFEB 1916, which may generate neural network features 1918 (e.g., hierarchical features) which may be provided to pooling module 1920, which may generate outputs which are provided to vector concatenation module 1922. [00244] When structural mesh element features are computed, the structural mesh element features (e.g., vertex curvature, among others disclosed herein) 1928 may be provided to NNFEB 1930, which may generate neural network features 1932 (e.g., hierarchical features) which may be provided to pooling module 1934, which may generate outputs which are provided to vector concatenation module 1922. [00245] Vector concatenation module 1922 may generate outputs which are provided to MLP 1924, which may generate refined neural network features (e.g., global, intermediate and/or local neural network features) 1926 which are outputted. Optional oral care arguments may be provided to modules 1908, 1916, 1930, and/or 1924. [00246] The outputs of this feature exaction methods described in FIG.18 and FIG.19 may be used in style transfer. The outputs of the feature extraction methods may include global, intermediate or local information about the stylized point cloud P. The feature extraction module may extract such information about the geometry or color of P. Not all examples of S, C or P involve color, in which cases the techniques of this disclosure may still transfer style information pertaining to spatial or structural geometry. In some implementations, the outputs of the feature extraction module may be used in the calculation of the losses described herein. In some implementations, the loss values may, in some implementations, be used in the calculation of P*_spatial or P^* _structural, which may be iteratively updated until convergence. In other implementations, a style transfer ML model may generate P*. The resulting stylized point cloud P may be outputted and used, for example, in the generation of an oral care appliance (e.g., aligners, fixture model, dental restoration appliance or others disclosed herein). Such an appliance may, in some instances, be 3D printed (e.g., in a clinical environment where the patient is present and waiting for the appliance to be completed). Techniques of this disclosure may, in some instances, be performed in a time-constrained context (e.g., while the patient waits in the clinical environment for an oral care appliance to be generated). That is, systems implementing the techniques described herein may be configured to operate in real- or near-real-time. [00247] Encoder E12206 of FIG.22 may be trained to generate a pre-modification latent representation 2210 for the pre-modification 3D oral care representation 2202 (e.g., a 3D representation such as teeth, or other types of 3D oral care representations). 3D oral care representations which are 3D representations may comprise one or more mesh elements (as described herein). Encoder E12206 may, in some implementations, use a mesh element feature module (as described elsewhere in this specification) to compute mesh element feature vectors for one or more of the mesh elements. For example, these mesh element features may assist the encoder E12206 in encoding the shape and/or structure of the patient’s dentition, resulting in representations that are more accurate (e.g., representations which may, in some implementations, be reconstructed into facsimiles of the original teeth or gums). Such representations (e.g., latent representations or latent forms) may comprise information-rich or reduced-dimensionality versions of the provided teeth (or gums) from the patient case. In other implementations, the encoder E12206 may be replaced by other latent representation generation ML modules (e.g., one or more U-Nets, one or more transformer encoders, one or more pyramid encoder-decoders, one or more other neural network modules (e.g., pairs of convolution and pooling layers), or other representation-generation models described herein). [00248] Representation learning techniques may be used to train a machine learning model (e.g., a latent representation modification module - LRMM) to modify a latent representation of a 3D oral care representation in a manner that, when the latent representation is reconstructed (e.g., using a decoder), the reconstructed 3D oral care representation includes properties (e.g., shape, structure, etc.) which make that 3D oral care representation suitable for use in generating an oral care appliance. A reconstruction autoencoder (e.g., a variational autoencoder with optional continuous normalizing flows) may be trained to reconstruct 3D oral care representations from a training dataset 2202. The encoder 2206 may be trained to encode the training data 2202 into a latent representation, and then the decoder may be trained to reconstruct that latent representation into a close facsimile 2226 of the original training data 2202. The result is a trained encoder-decoder structure. The latent representation in between the encoder 2206 and decoder 2222 may undergo modification by an LRMM, so that the reconstructed 3D oral care representation 2226 contains modifications relative to the original 3D oral care representation 2202. [00249] In some implementations, the LRMM may be trained to modify latent representations of data from cohort patient cases, such patient dentition (e.g., the patient’s teeth). The training dataset may contain pairs of pre-modification data 2202, post-modification (or target) data 2204. [00250] In some instances, the training data may include one or more 3D representations of the patient’s pre-modification dentition 2202 (e.g., the patient’s pre-restoration teeth), and corresponding 3D representations of the patient’s post-modification (or target) dentition 2204 (e.g., the patient’s post- restoration teeth). [00251] In some instances, the training data may include one or more 3D representations of a pre- modification oral care appliance component 2202 (e.g., prefab library components or generated components – such as parting surfaces, etc.), and one or more corresponding 3D representations of post- modification (or target) oral care appliance components 2204. [00252] In some instances, the training data may include one or more pre-modification dentition and/or pre-modification fixture model components 2202 (e.g., a digital pontic tooth, blockout, interproximal webbing, or others described herein), and one or more corresponding 3D representations of the patient’s post-modification (or target) dentition and/or post-modification (or target) fixture model components 2204 (e.g., the patient’s dentition with interproximal webbing added to the interproximal spaces between some teeth – such as anterior teeth). [00253] In some instances, the training data may include one or more pre-modification transforms 2202, such as transforms to place teeth (or appliance components or fixture model components) into poses which are suitable for oral care appliance generation, and one or more corresponding post- modification (or target) transforms 2204. [00254] In some instances, the training data may include one or more pre-modification mesh element labels (e.g., labels which may be used in mesh segmentation or mesh cleanup), which may be accompanied by one or more corresponding post-modification (or target) mesh element labels. [00255] During the training of the LRMM 2216, a 3D oral care representation of training data 2202 (e.g., pre-modification data) may have a corresponding 3D oral care representation of target data (e.g., post modification data) 2204. LRMM 2216 may contain one or more MLPs, or one or more U-Nets (among other of the architectures disclosed herein). In some implementations, the encoder E12206, the decoder D12222 and the LRMM 2216 may be trained end-to-end. In other implementations, the encoder E12206, the decoder D12222 may be trained separately from the LRMM 2216. [00256] The training data 2202 may undergo latent encoding (e.g., using encoder 2206), which may generate pre-modification latent representation 2210. The corresponding target data 2204 may likewise undergo latent encoding (e.g., using encoder E12208), which may generate a latent representation of the target data 2214. The encoder 2208 may, in some implementations, be the same as encoder 2206. In some implementations, the pre-modification latent representation 2210 may be provided to LRMM 2216. In some implementations, oral care arguments 2200 may be provided to the LRMM 2216. In some implementations, oral care arguments 2200 may undergo latent encoding (2228), before being provided to LRMM 2216. In some implementations, the latent encoding (2228) may use an encoder to encode categorical, Boolean or real valued oral care arguments 2200. In some implementations, the latent encoding (2228) may use a CLIP encoder (or a GPT transformer encoder or GPT transformer decoder) to generate latent representation for textual oral care arguments 2200 (e.g., textual descriptions of modifications which are to be performed). [00257] In some implementations, (optional) oral care metrics (or other dimensional measurements or calculations) may be computed (2212) on the target data 2204, and subsequently be provided to LRMM 2216. These oral care metrics (or other dimensional measurements) may specify to the LRMM 2216 aspects of the target shape and/or structure for the reconstructed 3D oral care representation 2226. The LRMM may be trained to generate a post-modification latent representation 2220, which may be provided to decoder 2222, which may generate a reconstructed 3D oral care representation 2226 with a shape, structure, dimensions, numerical values or other values which are suitable for use in oral care appliance generation. [00258] The LRMM 2216 may be trained, at least in part, by a latent loss function (e.g., for comparing latent vectors – such as cross-entropy or others described herein) or by a non-latent loss function (e.g., for comparing data structures which are in their original, non-latent forms). Examples of non-latent losses include reconstruction loss or KL-Divergence loss (e.g., for 3D representations – such as point clouds, or other data structures described herein), L1 or L2 losses (e.g., for transforms, or other data structures described herein), cross-entropy loss (e.g., for mesh element labels, or other data structures described herein), or others described herein. The latent loss may be computed (2218) between the latent representation of the target data 2214, and the generated post-modification latent representation 2220. The non-latent loss may be computed (2224) between the target 3D oral care representation 2204, and the reconstructed 3D oral care representation 2226. [00259] In deployment, the input 2300 of FIG.23 is not intended to represent training data, but rather specifies one or more 3D oral care representations which are to be modified (e.g., a pre-restoration tooth mesh, a mold parting surface to be modified, a patient dentition which is to receive interproximal webbing or blockout, or others described herein) may be provided to encoder E12304. The encoder 2304 may generate a pre-modification latent representation 2306. The pre-modification latent representation 2210 may be provided to the LRMM 2308, which may generate a post-modification latent representation 2310. Post-modification latent representation 2310 may be provided to decoder D12312, which may reconstruct post-modification latent representation 2310 into post-modification 3D oral care representation 2314. In some implementations, oral care arguments 2302 may be provided to the LRMM 2308, providing specification for the intended modification(s) which is to be applied to latent representation 2306. Such oral care arguments may include, for example, specifications for the shape and/or structure of an intended post-modification 3D oral care representation 2314 (e.g., dimensional measurements that describe the intended shape and/or structure). In some implementations, one or more oral care metrics, which may measure (or quantify aspects of) the shape and/or structure of an intended 3D oral care representation (e.g., a 3D representation of a tooth, a fixture model component, an appliance component, set of orthodontic setup transforms, or other 3D representation which is to be modified), may be provided to the LRMM 2308. In some instances, oral care arguments 2302 may contain text, which may undergo latent encoding (2314) (e.g., using a CLIP text encoder, or a GPT transformer encoder), before being provided to the LRMM 2308. [00260] In some implementations, a genetic algorithm can be used to generate (or modify) a 3D oral care representation (e.g., a tooth restoration design, an appliance component, a fixture model component, tooth transforms for setups, tooth coordinate systems, a set of mesh element labels for segmentation or mesh cleanup, or others described herein). A population of chromosomes (e.g., data structures which describe a particular type of 3D oral care representation) may undergo fitness determination. One or more of the most-fit chromosomes (e.g., the top half most-fit chromosomes) may be set aside for reproduction and duplicated. The duplicates may undergo one or more variation operations. Variation operations include mutation and/or crossover. The remaining least-fit chromosomes (e.g., the bottom half least-fit chromosomes) may be deleted. The new population may comprise one or more fit chromosomes from the prior population, and one or more new individuals which have been generated through mutation and/or crossover, based upon the genetics of the highly-fit parents. Once again, the fitness of the population may be determined, and the method iterates. In some implementations, a population may comprise latent representations (e.g., latent vectors) of 3D oral care representations. [00261] In some examples, a population may contain 100 chromosomes (among other possible population sizes). For example, the chromosomes may comprise latent representations of tooth restoration designs. The fitness of each of the 100 chromosomes may be determined, the least-fit half of chromosomes may be eliminated, and the most-fit half may be duplicated. The duplicates may be grouped into random pairs and undergo crossover. Crossover between latent vectors of a consistent length may involve the selection of a random index, and the exchange of all latent vector dimensions (e.g., genetic material) between the two chromosomes, either before or after that index. Mutation of the duplicates may involve adding random noise to one or more dimensions of the latent vector, among other approaches. The fitness of the 100 chromosomes may again be computed, and the method may iterate until a stopping criterion is met. In some implementations, the stopping criterion may involve the average population fitness exceeding a predetermined threshold. The following pseudocode illustrates this method. Start: ^ Determine fitness of each chromosome in the population ^ Set aside the most-fit half of the population for reproduction (discard the other half). ^ Duplicate the most-fit half, and then vary those copies: apply mutation operations (to create random variations within each individual) and/or cross-over operations (to combine genetic material between two or more parents). ^ Iterate until stopping criterion is met [00262] Mutation would be bounded at some distance from the mean of that dimension of the latent vector to prevent low-probability latent vectors being generated, resulting in anomalous tooth geometries being generated in the population. [00263] The following are descriptions of data structures that can be used to describe chromosomes. [00264] Mesh element labels for one or more meshes – A mesh may be described by lists of mesh elements (e.g., a list of vertices containing XYZ coordinates, a list of faces that specifies the indices of the vertices are in each face, and a list of edges that specifies the indices of the vertices that are in each edge). For one or more of those lists, there may be a list of associated mesh element labels. In some examples of this disclosure, a genetic algorithm may be used to segment a mesh (e.g., a mesh of the patient’s dentition that was generated by an intraoral scanner). The structure may be fixed, but a population may be generated which comprises lists of mesh element labels. Such a list of mesh element labels may correspond in a 1-to-1 manner with the list of vertices (e.g., each vertex may have an associated mesh element label). A population of 100 chromosomes may comprise 100 lists of mesh element labels. Each list of mesh element label may describe a different way of segmenting the same mesh. [00265] Coordinate systems of one or more teeth – One or more transforms (e.g., 4x4 matrix, etc.) for respective teeth. [00266] Setup transforms for one or more teeth – One or more transforms (e.g., 4x4 matrix, etc.) for respective teeth. [00267] Tooth restoration design – 3D representation comprising one or more mesh elements. [00268] Fixture model component – 3D representation comprising one or more mesh elements. [00269] Appliance components (e.g., parting surface for Lego) – 3D representation comprising one or more mesh elements. [00270] Fitness determination may, in some implementations, involve reconstructing a latent vector into the source data structure. For example, when a latent vector of a chromosome represents a 3D mesh or a tooth (or a fixture model component, or appliance component), that latent vector may be reconstructed using a decoder into a reconstructed 3D mesh of a tooth restoration design (or of a fixture model component, or appliance component). In other examples, when the latent vector represents one or more transforms (e.g., that describe setups poses for the teeth, or local coordinate systems for the teeth), the latent vector may be reconstructed into respective one or more reconstructed transforms. Furthermore, when the latent vector represents one or more mesh element labels, the latent vector may be reconstructed into a list of respective mesh element labels. That reconstructed representation(s) can then undergo fitness evaluation, according to the particulars of the relevant technique (e.g., setups prediction, appliance component generation or placement, fixture model component generation or placement, local coordinate system prediction, tooth restoration design generation, or others described herein). [00271] In some implementations, the reconstructed representation may be compared to one or more corresponding reference (or ground truth) representations. In such examples, fitness may be computed, at least in part, by quantifying the difference through L1, L2, MSE, cross-entropy or another of the methods used for loss calculation herein. [00272] In some implementations, fitness may be determined, at least in part, using oral care metrics. One or more oral care metrics may be computed (e.g., “Alignment” – in the case of setups prediction, or others described herein) to quantify the fitness of the reconstructed representation. A highly fit reconstructed representation may have oral care metric values which are within a threshold of the mean of corresponding oral care metrics which have been computed for ground truth examples. Stated another way, ground truth examples which are known to be correct or otherwise have high fitness (e.g., ground truth setups, ground truth tooth restoration designs, or other ground truth oral care meshes) may undergo oral care metrics calculation. The oral care metrics for the reconstructed representation may be compared to the oral care metrics for the set of ground truth examples, as a part of fitness calculation. [00273] In some implementations, fitness may be determined, at least in part, through collision qualification between 3D representations. For example, collision detection may be performed as a part of fitness evaluation. For example, a fitness function may compute a number of collisions between a reconstructed mesh of a tooth and the tooth of the corresponding tooth mesh in the opposing arch (or neighboring teeth). Fitness function could also be augmented to include the typical distances of various parts of the teeth from each other, such as distances of opposing cusps, curvature of the cusps, etc. A collision-based fitness may determine how well a reconstructed tooth crown interfaces with the corresponds one or more crowns in the opposing arch. For example, collisions in occlusal contacts or interproximal contacts can be measured. [00274] An example fitness function can be computed for an orthodontic final setup. A final setup may comprise tooth transforms for the teeth of the patient’s arches. Each transform may place a tooth into a pose that corresponds to the final state of occlusion at the completion of orthodontic treatment. Fitness function may compute oral care metrics, including metrics which characterize occlusal contacts or interproximal contacts. The fitness function may compute collisions between teeth (e.g., in occlusal contacts or interproximal contacts). The fitness function could also be developed as a standalone AI model that would approximate the distribution of an "acceptable" or ground truth final setup. In some implementations, the discriminator of a GAN can be adapted for use in such an ML model. The discriminator may be trained to classify a setup as either “real” (e.g., acceptable and representative of good dentition) or "fake" (e.g., unlikely to occur in a human population with good healthy dentitions). The GAN discriminator could be used to calculate the fitness of an orthodontic setup. That fitness may be used in accordance with the selection process of the genetic algorithms described herein, to support the selection process for determining the parents of the next generation. [00275] In some implementations, ML models of this disclosure (e.g., encoder-decoder structures, such as U-Nets, transformers or autoencoders) may be trained according to Population-Based Optimization (PBO). Population-Based Optimization can be utilized for training neural networks. PBO may use the principals of genetic algorithms where a 'population' of neural network configurations, including variations to the architecture, or to the training method are evolved over time by selecting the best-performers from populations and choosing optimal attributes from those best performers. PBO can also operate during training. A population of models may be trained with different optimization schedules (LR schedule, gradient decay, gradient clipping, etc.) for a fixed duration of time, e.g., 1 epoch. At the end of the epoch, the best performers are selected. For the next epoch, the best performers are selected, and are trained with another set of schedules. This process is repeated across all the epochs of training and yields models that can outperform models trained with only 1 of these training schedules. [00276] A 3D oral care representation with high fitness is highly suitable for use in generating an oral care appliance (e.g., customized to the treatment needs of the patient). A 3D oral care representation with low fitness is poorly suited for use in generating an oral care appliance (e.g., not customized to the treatment needs of the patient). In some implementations, fitness may be defined as a quantitative measure of the extent to which a generated 3D oral care representation conforms to distribution of one or more ground truth or reference 3D oral care representations. In some implementations, fitness can be determined, at least in part by computing one or more oral care metrics. For example, when a genetic algorithm is used to generate an orthodontic setup, the fitness function may include the calculation of one or more orthodontic metrics. A setup with orthodontic metric values that lie within one or more pre- computed thresholds (e.g., thresholds which describe the distribution of one or more ground truth or reference setups examples) may be considered to be highly fit. Furthermore, when a genetic algorithm is used to generate a 3D representation (e.g., a tooth restoration design, appliance component, fixture model component, or archform, among others), the fitness function can include one or more oral care metrics. For example, restoration design metrics may be computed for a tooth restoration design. A generated tooth restoration design with metric values within one or more pre-computed thresholds may be considered to be highly fit.

Claims

CLAIMS WHAT IS CLAIMED IS: 1. A method of generating a dental restoration tooth design, the method comprising: receiving, by processing circuitry of a computing device, a three-dimensional (3D) pre- restoration tooth representation; providing, by the processing circuitry, the 3D pre-restoration tooth representation, as execution- phase input, to a trained encoder of a reconstruction autoencoder; outputting, using the trained encoder of the reconstruction autoencoder, a latent space representation of the 3D pre-restoration tooth representation having a lower order of dimensionality than the 3D pre-restoration tooth representation; modifying at least a portion of the latent space representation of the 3D pre-restoration tooth representation; providing, by the processing circuitry, the modified latent space representation, as execution- phase input, to a trained decoder of a reconstruction autoencoder; reconstructing, using the trained decoder of the reconstruction autoencoder and the modified latent space representation of the 3D pre-restoration tooth representation, a reconstructed 3D tooth representation that defines a post-restoration version of the 3D pre-restoration tooth representation; and generating, using the reconstructed 3D tooth representation, at least one oral care appliance.

2. The method of claim 1, further comprising: receiving, by the processing circuitry, at least one template representation including one or more mesh elements ordered in a manner consistent with an arrangement that was used in training the autoencoder; and computing, by the processing circuitry, at least one correspondence between one or more mesh elements of the 3D pre-restoration tooth representation and the template representation before the 3D pre- restoration tooth representation is provided as the execution-phase input to the trained reconstruction autoencoder.

3. The method of claim 1, wherein the trained reconstruction autoencoder is pretrained, at least in part, using a continuous normalizing flow.

4. The method of claim 2, wherein the one or more mesh elements represent one or more of a point, a vertex, a face, or an edge associated with a tooth represented in the 3D pre-restoration tooth representation.

5. The method of claim 2, wherein the one or more mesh elements comprise a voxel.

6. The method of claim 1, wherein the 3D pre-restoration tooth representation comprises at least one of a tooth mesh, a 3D point cloud, or a voxelized tooth representation.

7. The method of claim 1, further comprising: receiving, by the processing circuitry, one or more reference 3D representation of a tooth; and assigning, by the processing circuitry, one or more aspects of a style of a reference 3D representation of a tooth to the reconstructed 3D tooth representation.

8. The method of claim 7, wherein the one or more aspects of the style comprise at least one of one or more aspects of the shape and one or more aspects of the structure of the reference 3D representation of a tooth.

9. The method of claim 1, wherein the reconstructed 3D tooth representation is used to generate a veneer design.

10. The method of claim 9, wherein the veneer design is associated with a design for a zirconia veneer.

11. The method of claim 1, further comprising influencing, using the latent space representation, one or more aspects of the reconstructed tooth representation including a tooth silhouette, one or more mamelon grooves, one or more perikymata, one or more fossae, or one or more vertical striation.

12. The method of claim 1, wherein the at least one oral care appliance is an orthodontic aligner tray.

13. The method of claim 1, wherein the at least one oral care appliance is a dental restoration appliance.

14. The method of claim 13, wherein the dental restoration appliance is 3D printed.

15. The method of claim 13, further comprising: shaping, using the dental restoration appliance, dental composite; and curing the dental composite to form one or more veneers.

16. The method of claim 1, further comprising: receiving, by the processing circuitry of a computing device, one or more oral care arguments; influencing, by the one or more oral care arguments, the modifying.

17. The method of claim 1, further comprising: executing, by the processing circuitry, a trained latent representation modification module (LRMM); modifying, by the LRMM, one or more aspects of the latent space representation; and generating, using the one or more modified aspects of the latent space representation, the reconstructed 3D tooth representation.

18. The method of claim 17, further comprising: receiving, by the processing circuitry of a computing device, the one or more oral care arguments; generating, by the LRMM, the modified latent representation based at least in part on one or more aspects of the one or more oral care arguments.

19. The method of claim 1, wherein the computing device is deployed at a clinical context, and wherein the method is performed in near real-time during an encounter with a patient.

20. A computing device for generating a dental restoration tooth design, the computing device comprising: interface hardware configured to receive an input three-dimensional (3D) pre-restoration tooth representation; processing circuitry configured to: provide, by the processing circuitry, the 3D pre-restoration tooth representation, as execution-phase input, to a trained encoder of a reconstruction autoencoder; output, using the trained encoder of the reconstruction autoencoder, a latent space representation of the 3D pre-restoration tooth representation having a lower order of dimensionality than the 3D pre-restoration tooth representation; modify at least a portion of the latent space representation of the 3D pre-restoration tooth representation; provide, by the processing circuitry, the modified latent space representation, as execution- phase input, to a trained decoder of a reconstruction autoencoder; reconstruct, using the trained decoder of the reconstruction autoencoder and the modified latent space representation of the 3D pre-restoration tooth representation, a reconstructed 3D tooth representation that defines a post-restoration version of the 3D pre-restoration tooth representation; and generate, using the reconstructed 3D tooth representation, at least one oral care appliance.