WO2021124335A1

WO2021124335A1 - Orthodontic wire manipulation recommendation system

Info

Publication number: WO2021124335A1
Application number: PCT/IL2020/051304
Authority: WO
Inventors: Nir Shvalb; Rachel Sarig; Oded MEDINA; Shai YONA
Original assignee: Ariel Scientific Innovations Ltd.; Ramot At Tel-Aviv University Ltd.
Priority date: 2019-12-18
Filing date: 2020-12-17
Publication date: 2021-06-24

Abstract

A method comprising: receiving, as input, a three-dimensional (3D) scan of a dentition of a subject; estimating, based on the 3D scan, a desired movement path for at least one tooth in the dentition; calculating a force that is required to be applied to the tooth, to cause movement of the tooth along the desired movement path; and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply the force to the at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

Description

ORTHODONTIC WIRE MANIPULATION RECOMMENDATION SYSTEM

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority U.S. Provisional Patent Application Ser. No. 62/949,462 filed December 18, 2019, the content of which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present invention relates generally to the field of computer vision.

BACKGROUND OF THE INVENTION

[0003] In orthodontics, a dental arch wire is typically a metal wire conforming to the alveolar or dental arch, which can be used with dental braces as a source of force in correcting irregularities in the position of the teeth, or as a retentive force.

[0004] Typically, orthodontists rely on their experience to manually bend and shape arch wires to deliver the suitable forces at each point. However, this task is complex, and the forces produced in various areas in the wire are not easily predictable.

[0005] Accordingly, it would be desirable to provide for a process for automatically determining an appropriate shape of a metal wire, which will produce the desired amount of force at each point of the arch.

[0006] The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the figures.

SUMMARY OF THE INVENTION

[0007] The following embodiments and aspects thereof are described and illustrated in conjunction with systems, tools and methods which are meant to be exemplary and illustrative, not limiting in scope. [0008] There is provided, in an embodiment, a system comprising: at least one hardware processor; and a non-transitory computer-readable storage medium having stored thereon program instructions, the program instructions executable by the at least one hardware processor to: receive, as input, a three-dimensional (3D) scan of a dentition of a subject, estimate, based on the 3D scan, a desired movement path for at least one tooth in the dentition, calculate a force that is required to be applied to the tooth, to cause movement of the tooth along the desired movement path, and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply the force to the at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

[0009] There is also provided, in an embodiment, a method comprising: receiving, as input, a three-dimensional (3D) scan of a dentition of a subject; estimating, based on the 3D scan, a desired movement path for at least one tooth in the dentition; calculating a force that is required to be applied to the tooth, to cause movement of the tooth along the desired movement path; and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply the force to the at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

[0010] There is further provided, in an embodiment, a computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions executable by at least one hardware processor to: receive, as input, a three-dimensional (3D) scan of a dentition of a subject; estimate, based on the 3D scan, a desired movement path for at least one tooth in the dentition; calculate a force that is required to be applied to the tooth, to cause movement of the tooth along the desired movement path; and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply the force to the at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

[0011] In some embodiments, the 3D scan is a Dental Cone Beam CT (CBCT).

[0012] In some embodiments, the estimating comprises generating a visual model which calculates a numerical representation of the desired movement path.

[0013] In some embodiments, the desired movement path comprises one or more transformations of the at least one tooth in at least 6 degrees of freedom. [0014] In some embodiments, the system further comprises a user interface, the program instructions are further executable to present, and the method further comprises presenting, the visual model to a user of the system on the user interface, and wherein the desired movement path is determined by the user performing the one or more transformations within the visual model using the user interface.

[0015] In some embodiments, the determining comprises at least: (i) evaluating a force to be applied on the at least one tooth by the portion of the arch wire; and (ii) predicting a direction of a movement of the at least one tooth as a result of the application of the force.

[0016] In some embodiments, the determining is performed by, iteratively: (i) generating a proposed shape of the portion of the arch wire; (ii) evaluating a force to be applied on the at least one tooth by the portion of the arch wire; (iii) predicting a direction of a movement of the at least one tooth as a result of the application of the force; and (iv) repeating steps (i)-(iii) to obtain the optimal wire shape that minimizes a cost function.

[0017] In some embodiments, the program instructions are further executable to generate, and the method further comprises generating, a set of manufacturing instructions for the portion of the arch wire, based on the determining.

[0018] In some embodiments, the manufacturing instructions comprise modification instructions for modifying a shape of a provided portion of an arch wire, based on the determining.

[0019] In some embodiments, the modification instructions are generated based on a comparison between the provided portion of the arch wire and the determined optimal shape.

[0020] In some embodiments, the comparison comprises determining a spatial shape of the provided portion of the arch wire from one or more images of the provided portion of the arch wire.

[0021] In some embodiments, the determining of the spatial shape of the provided portion comprises detecting and segmenting the provided portion of the arch wire in 3D imaging, based, at least in part, on epipolar geometry.

[0022] In some embodiments, the 3D imaging is performed using a time-of-flight imaging device. [0023] In some embodiments, the comparison is presented to the used using the user interface, and wherein the presenting comprises presenting the modification instructions to the user.

[0024] In addition to the exemplary aspects and embodiments described above, further aspects and embodiments will become apparent by reference to the figures and by study of the following detailed description.

BRIEF DESCRIPTION OF THE FIGURES

[0025] Exemplary embodiments are illustrated in referenced figures. Dimensions of components and features shown in the figures are generally chosen for convenience and clarity of presentation and are not necessarily shown to scale. The figures are listed below.

[0026] Fig. 1A shows the various planes in which teeth may be moved;

[0027] Fig. IB shows upper and lower arches with reverse curve of Spee.

[0028] Fig. 2 is a flowchart of the functional steps in an automated process for determining a desired orthodontic wire shape targeted for a subject, according to some embodiments of the present disclosure;

[0029] Fig. 3 illustrates a simulation tool, according to some embodiments of the present disclosure;

[0030] Fig. 4 demonstrates a spatial shape reconstruction process using epipolar geometry, according to some embodiments of the present disclosure;

[0031] Figs. 5A-5D illustrate wire imaging, according to some embodiments of the present disclosure;

[0032] Fig. 6 illustrates a moving average operation, according to some embodiments of the present disclosure;

[0033] Figs. 7A-7C illustrate wire segmenting results, according to some embodiments of the present disclosure;

[0034] Fig. 8 illustrates the coordinate frame system of the wire, wherein one of the axes (z) is always tangent to the wire, according to some embodiments of the present disclosure; [0035] Fig. 9 illustrates a virtual spring model, according to some embodiments of the present disclosure;

[0036] Figs. 10A-10C depict the bending and torsion angles of a wire segment, according to some embodiments of the present disclosure;

[0037] Fig. 11 shows the bending angles of 2 wire segments, according to some embodiments of the present disclosure; and

[0038] Fig. 12 shows a spherical joint represented by 3 revolute joints, according to some embodiments of the present disclosure.

DETAILED DESCRIPTION

[0039] Disclosed herein are a system, method, and computer program product for automated calculating of a personalized dental arch wire shape, based on imaging of a subject’s dentition.

[0040] In some embodiments, the present disclosure provides for acquiring imaging data associated with a subject’s dentition. In some embodiments, the present disclosure then analyzes the imaging data to model a desired movement trajectory for at least some of the teeth within the subject’s dentition. In some embodiments, the present disclosure then provides for calculating forces to be applied to each of the teeth by an othodontic wire, to cause the teeth to move overtime in the desired movement trajectory. Finally, in some embodiments, the present disclosure provides for determining a spatial shape of an othodontic wire configured to achieve the calculated forces when applied to the subject’s dentition. In some embodiments, a set of manufacturing instructions may be produced based on the determined shape, to be used in a manufacturing process for producing an othodontic wire having the determined spatial shape. In some embodiments, the manufacturing process comprises bending, by a suitable process, a provided dental arch wire based on the instructions, to obtain the determined shape.

[0041] Abnormal alignment of the teeth and jaws is common, where the treatment can take several months to a few years and may involve the use of an orthodontic archwire to apply a force to move the teeth in the desired direction. The teeth are fixed to the periodontal ligament (PDL) tissue which may show resorption upon teeth movement. When a sufficient force (up to some point) is placed on a tooth, bone is laid down on the tension side of the PDL and resorped on the pressure side, causing tooth movement. However, if the applied forces are too high, cell death can occur and a cell-free area may form, resulting in a much reduced rate of resorption and slower tooth movement with greater pain and discomfort for the patient. Therefore, applying a precise amount of force in a specific direction is imperative for achieving desired results.

[0042] As noted above, precisely-made archwires are crucial to the success of lingual orthodontic treatments. However, proper formation of lingual archwires is complicated by the often irregular shapes found between patients, and the high level of precision required. For instance, lingual archwires require offsets which may, depending on the case, be considerable in number and/or asymmetry. Further, bending archwires for crowded dentitions is often extremely difficult due to the small inter-bracket distances and the mesiodistal width differences. Inaccuracies in the design or manufacture of the archwire can have undesirable clinical consequences. Thus, there is a need for the orthodontist to have strict control over the size and shape of the archwire.

[0043] Typically, lingual archwires are shaped manually with the help of a plaster model of the patient's teeth. An alternative to the formation of a plaster model is to upload a digital photograph of the dental arch into a computer loaded with software and design a virtual lingual arch wire. The orthodontist is presented with a view of the dental arch on a computer screen, and can design a virtual lingual archwire comprising a series of straight sections which fit the screen image of the dental arch. An output may then be a set of instructions describing how to manufacture the archwire designed on the screen. For example, the orthodontist could take a straight section of orthodontic wire, bend an angle of 34° at a distance of 14 mm from one end, bend an angle of 47° in the opposite direction at a distance of 3 mm from the first bend, and so on. In this way, the orthodontist may manually manufacture the archwire designed with the help of the computer program. In practice, the orthodontist bends the arch wire in the direction of the wanted tooth movements. Fig. 1A shows the various planes in which teeth may be moved, e.g., in-out (1st order), up-down (2nd order) and torque (2rd order). Other wire spatial manipulation can be related to arch shape and symmetry. For example, in order to level the height of the teeth, or to intrude the incisors, manual manipulation on the wire can be done (e.g., reverse curve of Spee). Fig. IB shows upper and lower arches with reverse curve of Spee.

[0044] As noted above, orthodontists rely on expertise and experience to shape the wire so as to apply the necessary forces, however, this task is complex, and the forces applied in various areas in the wire are not easily predictable. There are three main difficulties in wire bending: • Evaluating the amount of force applied on a tooth by the wire;

• predicting the direction of movement of teeth as a result of the application of force by the wire; and

• predicting unwanted movement and side effects.

[0045] Fig. 2 is a flowchart of the functional steps in an automated process for determining a desired orthodontic wire shape targeted for a subject, according to some embodiments of the present disclosure.

[0046] In some embodiments, at step 200, a dentition of a subject may be imaged using any suitable imaging and/or scanning method known in the art, e.g., Dental Cone Beam CT (CBCT) or any other suitable imaging methodology. In some embodiments, the imaging provides for a 3D rendition of the dentition that can be used to accurately visualize the dentition, including, e.g., number, type, and arrangement in the mouth of the teeth.

[0047] In some embodiments, at step 202, a 3D model of the dentition is produced based on the imaging. In some embodiments, the 3D model comprises bio-mechanical data pertaining to teeth in the dentition, e.g., surface geometry of the dentition. In some embodiments, the 3D model may comprise, e.g., an STL (STereoLithography) file.

[0048] In some embodiments, at step 204, a 3D simulation may be generated based on the 3D model. In some embodiments, the 3D simulation may be presented to a dental practitioner, e.g., on a display monitor. In some embodiments, the dental practitioner may access a user interface to manipulate individual teeth within the dentition in the 3D simulation, to simulate a desired path or trajectory for each individual tooth. In some embodiments, the simulation may permit a dental practitioner to simulate a desired path or trajectory for an individual tooth using any combination of multiple transformations of the tooth, e.g., any translation and/or rotation. In some embodiments, the present simulation tool allows for simulation of an individual tooth in 6 degrees of freedom (DOF) - 3 in translation and 3 in rotation. In some embodiments, the desired path or trajectory of a tooth may comprise linear or non-linear movement of the tooth. In some embodiments, the simulation tool may be configured to generate a numerical representation of the simulated desired path or trajectory. Fig. 3 illustrates a simulation tool of the present disclosure. [0049] In some embodiments, at step 206, a provided preliminary dental arch wire may be scanned to determine a spatial shape thereof. In some embodiments, in order to obtain a spatial shape of a wire, it may be imaged from two or more different angles, for example, by rotating the wire for imaging by a single camera, or by setting two cameras in a stereo arrangement, wherein fixed relative positions between the cameras are known. In some embodiments, the imaged wire may be detected and segmented in the resulting images, using one or more object detection and segmentation methods known in the art and as further detailed herein. In some embodiments, the detection and segmentation provide for determining a spatial shape off the provided initial orthodontic wire. In some embodiments, the present disclosure may utilize time-of-flight or similar imaging sensors or devices or range finders, e.g., a Lidar device.

[0050] In some embodiments, a wire imaging setup of the present disclosure may comprise a calibrated stereo camera setup. In some embodiments, a dental arch wire may be imaged by each of the two cameras in the stereo setup, and the images may be segmented to detect the wire therein. In some embodiments, image registration and/or matching may be performed between the images, to associated corresponding points of the segmented wire in the stereo images. In some embodiments, the registration process may comprise generating an epipolar line from each wire point in the first image to a line in the second image, then points with a minimum Euclidean distance between the segmented wire in the second image and the epipolar line are determined as potential matching points. By using this approach, wire edges may be first matched, wherein the line may be shifted to intersect the matching point. However, due to the non-straight shape of the wire, there may be more than one possible solution at the various non edge points of the wire. Because the wire is continuous, this may be overcome by applying some weight to previous matched point and selecting the potential point that is closest to the initially-selected point. Finally, triangulation may be used to produce the spatial shape of the wire.

[0051] Fig. 4 demonstrates a spatial shape reconstruction process using epipolar geometry. A real world point A is imaged by a camera and projected at α_L on the left image 302. Because the image provides 2D information, it may be concluded that the real world point corresponding to α_L lies on the C_L — α_L axis (for example points A, A₁, A₂). This axis is, then, projected on the right image 304, yielding an epipolar line. Because the wire is a thin body, it may be referred to as a line with no hidden areas. By segmenting the wire in the images and intersecting with the epipolar line, the corresponding point a_R may be determined. Then, the intersection of the C_L — α_L and C_R — a_R axes will provide the real world point A. By comparing known matching points with the above geometrical constraints, a 3 X 3 fundamental matrix F may be calculated that matches the constraint:

where x_L and x_R are the left and right camera coordinates of the corresponding point. This process is known as calibration. The fundamental matrix relates corresponding points in stereo images and translates any given point in one image to an epipolar line on the other image. Then, the exact matching point in the epipolar should be detected and triangulation is applied to produce the real world spatial location of the selected point.

[0052] In some embodiments, to obtain a reference frame of the wire, a predefined shape may be rigidly attached to the wire for imaging. In some embodiments, a rotation matrix of the wire may be obtained by using an orientation sensor, e.g., by coupling an IMU sensor to a ball shaped object which provide coarse distance estimation.

[0053] In some embodiments, the wire may be segmented in the acquired images, e.g., based on background subtraction. For example, in some embodiments, a reference image may be acquired of the background without the wire, as shown in Fig. 5(A), and an image of the othodontic wire over the background, 5(B). The reference image may be subtracted from the othodontic wire image, 5(C), then edge detection or thresholding is applied to produce the segmented wire, 5(D).

[0054] In some embodiments, the wire has iso-thickness properties, which may be of assistance when determining the 3D shape of the wire and calculating the forces it applies. In order to refer to the wire as a line with a single dimension, it should be reduced to a thickness of a single pixel. This may be achieved by applying a moving average in polar coordinates, as shown in Fig. 6, the segmented wire points are averaged in their r values for each Q. where P₀ is the center of gravity of the segmented wire, 5(D), r is the distance between P₀ and the segmented point, and Q is the angle of the moving measure of the distance. For each value of Q. the P₀-segmented point distance is averaged and then transformed back to Cartesian coordinates to produce a single pixel thickness segmented wire. The result of the 1-pixel width segmented wire is displayed in Fig. 7, which illustrates moving average applied over the segmented wire. 7(A) shows the overlaid mask of the wire. 7(B) shows the result of the moving average process is laid on the mask. 7(C) shows the result of the moving average is laid on the original wire image.

[0055] With continued reference to step 206 in Fig. 2, in some embodiments, the present disclosure provides for spatial reconstruction of this objects. When an object is imaged by a single camera, the object position in space cannot be determined in absolute terms, because the distance to each point in the object us unknown. A possible approach to overcome this is to set a beam starting at the camera position and passing through each wire detected point on the image plain. The 3D location of this wire lies on this beam. Applying this for all the tire detected points will produce a cone like shape. Then by using the calculated rotation matrix as detailed above and the known position of reference points, such as the edges of the wire, cones obtained from different images may be rotated and translated to intersect and produce the 3D representation of the wire.

[0056] In some embodiments, at step 208, the present disclosure provides for modeling mechanical force interactions between a provided wire shape and a dentition of a subject. In some embodiments, the present modeling approach may utilize one or more force modeling techniques know in the art and as may be detailed herein, e.g., thin beam force analysis.

[0057] In some embodiments, the present disclosure may employ any known method of calculating a wire (e.g., the ELASTICA method, spring and torque spring simulation modeling, Timoshenko beam method, chain algorithm, Cosserat rod theory, etc.). In some embodiments, the generalized forces which are of interest are those that are located in the anchoring points, e.g., the brackets attached to the subject’s teeth, whose exact positions may be ascertained, e.g., manually and/or via any imaging technique.

[0058] In some embodiments, the present disclosure utilizes an elastic energy model, wherein the wire is represented by N segments. The elastic energy of the harnessed wire may then be calculated, wherein a gradient of the energy determines the direction of the force, and an energy difference from a resting initial position determines the size of the force.

[0059] The movement of individual teeth under forces applied by an othodontic wire depends on the structure and connection to the periodontal ligament (PDL) tissue and the acting forces of the orthodontic wire. Accordingly, once the 3D shape of the wire is obtained and the position and desired trajectory of the teeth is known, one can compute the acting forces by the wire. Due to the slow movement of the teeth, the process can be considered as quasistatic up to some duration with no need to calculate the dynamic process.

[0060] In some embodiments, the present disclosure may use Strain Energy Method (Castigliano’s Theorem). Strain energy is the internal energy in the structure due to its deformation. Therefore the principle of conservation of energy:

where U denotes the strain energy and

represents the work done by internal forces. For linearly elastic structures, the partial derivative of the strain energy with respect to an applied force (or couple) is equal to the displacement (or rotation) of the force (or couple) along its line of action. This results in

where d is the deflection at the point of application of the force P. Q is the rotation at the point application of the couple M. The strain energy of the beam is

where E is Young’s Modulus and / is the second moment of the area of the cross-section. There are many types of orthodontic wires with different alloys and different cross section shapes such as round or rectangle. The Young’s Modulus E is affected by the material of the wire and the second moment of the area / is affected by the measurements of the cross section.

[0061 ] By applying a partial derivative we can conclude the deflection and rotation of beams:

[0062] Fig. 8 illustrates the coordinate frame system of the wire, wherein one of the axes (z) is always tangent to the wire. In some embodiments, the configuration of a wire shown in Fig. 8 is presented by a space curve r (s) and a coordinate frame of "directors" axes x, y, z attached to each point on the curve. Therefore, the space curve and the frame can be assembled to a representation of E(s) = (x(s), y(s), z(s),r(s)), where s

[0, L] is the position on the curve and L is the length of the curve. The frame is always oriented to the curve, for example a specific reference vector is always tangent to the curve. Accordingly, there may be found a close analogy between, e.g., the Cosserat rod model in space and describing the motion of a rigid body in time.

[0063] Previously, a model for steering a flexible needle in soft tissue under real-time fluoroscopic guidance was presented, wherein, given a target and possible obstacle locations, the computer calculates the flexible needle-tip trajectory that avoids the obstacle and hits the target. Using an inverse kinematics algorithm, the needle base maneuvers required for a tip to follow this trajectory are calculated, enabling a robot to perform controlled needle insertion. Assuming small displacements, the flexible needle is modeled as a linear beam supported by virtual springs, where the stiffness coefficients of the springs can vary along the needle. A quasi-static motion may be assumed, wherein it is denoted that there is no physical meaning for the free length of the virtual springs but only to the stiffness coefficient that expresses the force of the tissue on the needle as a function of local displacement.

where is the virtual spring coefficient and w_i is the relative displacement of the spring for is resting position at point i. The needle is sectioned into n beam elements that can be represented by slope and position, therefore, the displacement of the needle has 4 coefficients for each beam segment, the displacement and slope at the beginning and at the end of each beam. This may be expressed in equations representing the 4 constraints of the model:

• The boundary conditions at rest of the starting point in the first beam,

• the continuity between elements,

• the negligible bending moment of the last element, and

• the displacement of the node from initial penetration position.

[0064] This results in a 4xn equations. Finally, the optimum shape may be determined as the minimum displacement from resting state.

[0065] This model may allow an analytical solution wherein, in the case of an othodontic wire, the connections between the wire and the teeth may act as virtual springs, as schematically illustrated in Fig. 9. There are many similarities between the needle and the wire cases, both are thin deformable objects subject to lateral forces either by tissue or by the connections to the teeth. Both objects act in a quasi-static environment and there is no constraints to the slope of the edges. While in the needle model, the tip is required for a specific target position, the orthodontic wire is not. However we wish to apply a specific force on specific (teeth) locations in the wire, where at the needle model the acting forces are a given values.

[0066] Accordingly, in some embodiments, the present disclosure may provide for approximating an othodontic wire as a set of beams, wherein at each joint, the force applied by a virtual spring is proportional to the displacement of the spring from its initial position. The wire and the beam are both deformable thin objects and both share the constraints of continuity of shape and slope between the segmented beams. In both cases the bending moment at the last element (the ending edge of the wire) is negligible, which allows to solve for a minimal displacement of the wire from its resting state. However, in contrast with the needle model noted above, in the case of the wire there is no demand for a specific position to the ending edge.

[0067] In some embodiments, hyper-elastic beam energy may be determined based on a model representing aNitinol rectangle cross section wire. However, because the types of alloy used determine the values of the Young’s Modulus E, and the cross section shape determines the second moment of the area /, the proposed solution is applicable for different materials and cross sections. Fig. 10 depicts the bending and torsion angles of a segment. Fig. 10(A) shows bending angle over X axis. Fig. 10(B) shows bending angle over the Y axis, and Fig. 10(C) shows torsion angle over the Z axis.

[0068] Denote

as rotation angles of axes x, y, z in frame i with respect to frame i — 1. For N segments the state configuration c is described by the 3 (/V — 1) dimensional vector presented in equation 7.

[0069] Determine the configuration of the minimum energy (i.e. the shape of the wire without harness constraints) as:

where is the zero energy angle of segment i in one of the three rotation axes j. Therefore the relative elastic energy (compared to the minimum energy) of any given configuration c with respect to the minimum energy configuration c₀ is:

where k_j is the bending or torsion coefficients. The deflection angle for a rod of Length L is given by:

where P is the force, E is the Young’s modulus, and / is the second moment of the area for rotations about the x and y axes. Therefore we can conclude the bending coefficient k_b from the elastic bending energy:

[0070] And the second moment of the area / is:

where A is the cross section area. In the same way we can solve for the torsion coefficient k_t :

where T is the torsion, f is the angle of twist, G is the shear modulus and J is the torsion constant given by:

[0071] In some embodiments, the force applied by the wire on each tooth in the harness points, depends on the rotation angles between the wire segments, the measurements of the wire and it’s properties. The total bending angle of a segment is accumulated by the bending angles of previous segments. Fig. 11 shows the bending angles of 2 segments. [0072] From the spatial shape of the initial wire as reconstructed in step 206 above, the deflection angles of each section may be determined. The coefficients of the bending and the torsion were determined in equations 11 and 12. This allows to express the Lagrangian and solve for the minimum elastic energy constraint. Equations 13-16 demonstrate this for 2 segments of length l in 2 dimensions, as depict in Fig. 11.

[0073] Accordingly, set:

to produce the set of equations:

where a, b, c, d, k, θ₁, θ₂ are known. Finally, this can be solved for λ_x, λ_y that represent the acting forces in axes x, y. Note that a, b, c, d have length units (for example meters ) and the 2k9 part is in moment units (such as Newton x meters), therefore λ_x, λ_y should be in force units (for example Newton ) as expected.

[0074] In the 3 dimensional problem with m constraints (i.e. wire-teeth harness points), the (x_t, y_t, z_t) position of the harness point t may be calculated in world coordinates using the forward kinematics. The produced Lagrangian is:

where W (c) is the corresponding 3D X m constrains for the energy calculated in equations 11 and 12 and

is the resting state harness point t position in world coordinates. By applying the Lagrange multipliers method, this may be solved for the 3 x m values of l and calculate the forces that the wire exerts on the teeth.

[0075] In some embodiments, at step 210, an optimized dental arch wire shape may be determined for the subject, based on the desired path or trajectory for one or more individual teeth in the dentition of the subject. In some embodiments, the optimized wire shape may be determined by calculating the required forces to be applied on each tooth to produce the desired movement path or trajectory, based, at least in part on the mechanical model generated at step 208 and calculated teeth trajectories under these forces. In some embodiments, step 210 is an iterative step wherein a shape of a provided initial wire may be iteratively adjusted, by calculating differential teeth movements based on adjusted shapes, while minimizing a cost or optimization function.

[0076] In some embodiments, any suitable model, such as a Denavit-Hartenberg (DH) method, may be used to adjust wire shape. The wire may be represented as a serial configuration of spherical joints, with a segment between each pair of joints. In turn, each spherical joint is represented by adjacent 3 revolute joints with 0 distance and length l between the spherical joints. Fig. 12 shows a spherical joint represented by 3 revolute joints. Distance between revolute joints is 0, the length of each segment between the spherical joints is determined as 1.

[0077] Equations 17a represent the matrices of the revolute joints in a spherical wrist configuration:

where Q is the rotation angle, l is the length of a segment between 2 spehri cal joints and

is the homogeneous matrix of the spherical wrist.

[0078] In some embodiments, at step 212, a set of the instructions may be determined to produce the optimized dental arch wire shape calculated at step 210, by modifying a shape of a provided initial arch wire. In some embodiments, the instructions may be provided to a dental practitioner, which may adjust the wire shape manually or semi -manually. In some embodiments, the instructions may be provided to an automated manufacturing process, e.g., a wire-bending robotic apparatus, which may adjust the wire shape based on the instructions.

Othodontic wire Object Detection and Segmentation

[0079] In some embodiments, the present disclosure provides for orthodontic wire detection and segmentation in images, by rigidly attaching it to a cube. In some embodiments, the present disclosure thus provides for determining a spatial shape of an othodontic wire by obtaining the orientation of an attached object from different angles, wherein the attached object is, e.g., a cube having different face colors.

[0080] In some embodiments, the present disclosure provides for the segmentation process of 3 orthogonal edges of the cube, as required to determine the cube orientation. The faces of the cube may be detected and segmented in images by applying thresholding based on face color values. A slight morphological opening may be applied to remove small tails that could be introduced due to various light conditions. In some embodiments, the thresholding may be performed in, e.g., the RGB color space. In some embodiments, the present disclosure then provides for applying a Sobel edge detection for each surface to find the edges of the squares and morphologically dilating each edge to ensure intersection between the edges of adjacent surfaces. The adjacent edges are then intersected, wherein a center point of the intersection of these edges is determined as the cube’s center comer. 2D vectors presenting the orientation edges are set as lines starting from this comer and end at the furthest pixel of each edge.

[0081] Once 3 spatial vectors are obtained, their orientation may be calcuated relative to a reference view, e.g., from the Y negative axis:

[0082] Thus, real world vectors may be represented in equation 19, where l_1y, l_2y, I_3y are unknown parameters to be calculated:

[0083] The length of the physical edges of the cube are known and equal, as well as the angle between them (90 degrees). This data enables calculating the orientation based on the 3 cube edges vectors obtained in the segmentation process (equations 20-21):

[0084] From equations 20 and 21 it may be concluded:

[0085] Since L₁ and L₂ are orthogonal:

[0086] From equations 20 and 24 C may be found:

[0087] Since C represent a physical length (equation 20), only the real positive solution obtained from the quadratic equation 25 may be used. Thus, L₂ and L₃ may be normalized:

and denoted:

[0088] Finally, the rotation matrix that represent the cube’s orientation may be calculated:

[0089] The camera-cube distance may be obtained from the orientation and projection of cube edges calculated above. Since the rotation matrix is known, the length in pixels of each edge of the cube may be calculated by using equation 29 and the projection members in the rotation matrix (equation 28).

where V_k is the length in pixels of the projection of the k’th vector (figure 29) and are

the projections x and z members of each column in the normalized rotation matrix (equation 28). Next, a fit model may be computed based on linear regression fit from results and measurements in various distances. Since equation 29 reflects the length of the cube edge in pixels, and the actual measurements of the designed cube are known, the spatial resolution of the pixel length in the cube image plain can be calculated. However this calculation will not apply to other image plains.

[0090] A known object can assist in segmenting the wire in a noisy environment by setting a region of interest (ROI) in the image. Since the physical size of the cube and the wire are known, their relative position is also known, as they are firmly attached. Therefore, an ROI based on the directions of the cube edges parallel and perpendicular to the wire cube connection line may be determined. Next, the ROI is applied over the detected edges of the difference image. Then, morphological closing is applied over the binary difference image to connect nearby objects and select the largest detected object to produce the wire mask.

[0091] In some embodiments, the present disclosure provides for attaching to the orthdontic wire an object, e.g., a ball, comprising an IMU sensor, which may then provide the rotation matrix calculated in Equation 28. In this method, there is only the need to segment the ball while the wire is segmented in the same way as described above. In some embodiments, the ball may be segmented by acquitring background and wire images. A difference HSV image may be generated by subtracting the background image from the wire image and converting the color space to HSV. Then, thresholding may be applied over the difference image, resulting in a binary image. Morphological opening may also be applied, followed by closing action and fdling holes to restore areas removed by the opening action. Since it is known the ball should be imaged as a large circle, the largest detected object may be selected. Finally, the center of mass and the major axis of the segmented object are determined as the center and diameter of the generated circle. Once the ball is detected, pixels per cm ratio in the ball image plain may be calculated by the length of the major axis and the known diameter of the ball (equation 31). The distance to the image plain was calculated using a model generated by measurements of several images in various distances.

[0092] In some embodiments, the present disclosure provides for determining the 3D shape of an orthodontic wire in images. The possible configuration of the wire in space represented as a cone like shape. When a rotated object is imaged from different views, the location of the object in space cannot be strictly determined since the camera-object distance is not known. In the present case, the distance from a reference object such as the cube or the ball can be calculated and determine the image plain and spatial resolution, however the distance to the various points on the wire can be different. Therefore, each point on the wire may be located on a beam that starts from the camera towards the points of the wire on the image plain and beyond. The overall collection sets of camera wire beams is observed as a cone like shape. Cones from different images may be relatively positioned and intersected to determine the 3D shape of the wire. This is possible since the wire is a thin object. The coarse positioning of the cones is done based on the known rotation matrix (from equation 28 or a layout sensor) and a known reference point in the images such as the edge of the wire or center of the ball/segmented center comer of the cube. Part of the wire can be beyond the image plane (determined as the ball distance), in this case the cones will not fully intersect as demonstrated, therefore the cone beams are stretched to a sufficient length. Next, gradient descent (GD) may be applied to translate the cone in order to find a minimum Euclidean distance between 3 known camera- image vectors: (i) camera-center of the ball or cube center comer; (ii) camera - close wire edge to the ball cube, and (iii) camera - the distant wire edge to the ball cube. [0093] Once the cones are positioned, the spatial shape of the wire may be produced by determining a wire 3D point as a point over beam in cone A with minimum distance to the closest beam in cone B. The wire is not a straight line, therefore using a minimum beams distance criteria solely, may produce multiple solutions and discontinuity in the determined shape this may be overcome by considering the distance to the previous detected point.

[0094] The present invention may be a system, a method, and/or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention.

[0095] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. Rather, the computer readable storage medium is a non-transient (i.e., not-volatile) medium.

[0096] Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.

[0097] Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, statesetting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.

[0098] Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions.

[0099] These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.

[0100] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.

[0101 ] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical fiinction(s). It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware -based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0102] The description of a numerical range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range. [0103] The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

CLAIMS What is claimed is:

1. A system comprising: at least one hardware processor; and a non-transitory computer-readable storage medium having stored thereon program instructions, the program instructions executable by the at least one hardware processor to: receive, as input, a three-dimensional (3D) scan of a dentition of a subject, estimate, based on said 3D scan, a desired movement path for at least one tooth in said dentition, calculate a force that is required to be applied to said tooth, to cause movement of said tooth along said desired movement path, and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply said force to said at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

2. The system of claim 1, wherein said 3D scan is a Dental Cone Beam CT (CBCT).

3. The system of any one of claims 1 or 2, wherein said estimating comprises generating a visual model which calculates a numerical representation of said desired movement path.

4. The system of claim 3, wherein said desired movement path comprises one or more transformations of said at least one tooth in at least 6 degrees of freedom.

5. The system of any one of claims 3 or 4, wherein said system further comprises a user interface, wherein said program instructions are further executable to present said visual model to a user of said system on said user interface, and wherein said desired movement path is determined by said user performing said one or more transformations within said visual model using said user interface.

6. The system of any one of claims 1-5, wherein said determining comprises at least:

(i) evaluating a force to be applied on said at least one tooth by said portion of said arch wire; and (ii) predicting a direction of a movement of said at least one tooth as a result of said application of said force.

7. The system of any one of claims 1-6, wherein said determining is performed by, iteratively:

(i) generating a proposed shape of said portion of said arch wire;

(ii) evaluating a force to be applied on said at least one tooth by said portion of said arch wire;

(iii) predicting a direction of a movement of said at least one tooth as a result of said application of said force; and

(iv) repeating steps (i)-(iii) to obtain said optimal wire shape that minimizes a cost function.

8. The method of any one of claims 1-7, wherein said program instructions are further executable to generate a set of manufacturing instructions for said portion of said arch wire, based on said determining.

9. The system of claim 8, wherein said manufacturing instructions comprise modification instructions for modifying a shape of a provided portion of an arch wire, based on said determining.

10. The system of claim 9, wherein said modification instructions are generated based on a comparison between said provided portion of said arch wire and said determined optimal shape.

11. The system of claim 10, wherein said comparison comprises determining a spatial shape of said provided portion of said arch wire from one or more images of said provided portion of said arch wire.

12. The system of claim 11, wherein said determining of said spatial shape of said provided portion comprises detecting and segmenting said provided portion of said arch wire in 3D imaging, based, at least in part, on epipolar geometry.

13. The system of claim 12, wherein said 3D imaging is performed using a time-of-flight imaging device.

14. The system of any one of claims 9-13, wherein said comparison is presented to said used using said user interface, and wherein said presenting comprises presenting said modification instructions to said user.

15. A method comprising: receiving, as input, a three-dimensional (3D) scan of a dentition of a subject; estimating, based on said 3D scan, a desired movement path for at least one tooth in said dentition; calculating a force that is required to be applied to said tooth, to cause movement of said tooth along said desired movement path; and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply said force to said at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

16. The method of claim 15, wherein said 3D scan is a Dental Cone Beam CT (CBCT).

17. The method of any one of claims 15 or 16, wherein said estimating comprises generating a visual model which calculates a numerical representation of said desired movement path.

18. The method of claim 17, wherein said desired movement path comprises one or more transformations of said at least one tooth in at least 6 degrees of freedom.

19. The method of any one of claims 17 or 18, wherein said visual model is presented to a user on a user interface, and wherein said desired movement path is determined by said user performing said one or more transformations within said visual model using said user interface.

20. The method of any one of claims 15-19, wherein said determining comprises at least:

(i) evaluating a force to be applied on said at least one tooth by said portion of said arch wire; and

(ii) predicting a direction of a movement of said at least one tooth as a result of said application of said force.

21. The method of any one of claims 15-20, wherein said determining is performed by, iteratively:

(i) generating a proposed shape of said portion of said arch wire;

22. The method of any one of claims 15-21, further comprising generating a set of manufacturing instructions for said portion of said arch wire, based on said determining.

23. The method of claim 22, wherein said manufacturing instructions comprise modification instructions for modifying a shape of a provided portion of an arch wire, based on said determining.

24. The method of claim 23, wherein said modification instructions are generated based on a comparison between said provided portion of said arch wire and said determined optimal shape.

25. The method of claim 24, wherein said comparison comprises determining a spatial shape of said provided portion of said arch wire from one or more images of said provided portion of said arch wire.

26. The method of claim 25, wherein said determining of said spatial shape of said provided portion comprises detecting and segmenting said provided portion of said arch wire in 3D imaging, based, at least in part, on epipolar geometry.

27. The method of claim 26, wherein said 3D imaging is performed using a time-of-flight imaging device.

28. The method of any one of claims 23-27, wherein said comparison is presented to said used using said user interface, and wherein said presenting comprises instructions to said user for manipulating said provided portion of said arch wire, based on said comparison.

29. A computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions executable by at least one hardware processor to: receive, as input, a three-dimensional (3D) scan of a dentition of a subject; estimate, based on said 3D scan, a desired movement path for at least one tooth in said dentition; calculate a force that is required to be applied to said tooth, to cause movement of said tooth along said desired movement path; and determining an optimal shape of a portion of an orthodontic arch wire to be positioned so as to apply said force to said at least one tooth, based, at least in part, on a model which represents mechanical force interactions between a provided arch wire shape and a dentition.

30. The computer program product of claim 29, wherein said 3D scan is a Dental Cone Beam CT (CBCT).

31. The computer program product of any one of claims 29 or 30, wherein said estimating comprises generating a visual model which calculates a numerical representation of said desired movement path.

32. The computer program product of claim 31, wherein said desired movement path comprises one or more transformations of said at least one tooth in at least 6 degrees of freedom.

33. The computer program product of any one of claims 31 or 32, wherein said program instructions are further executable to present said visual model to a user on a user interface, and wherein said desired movement path is determined by said user performing said one or more transformations within said visual model using said user interface.

34. The computer program product of any one of claims 29-33, wherein said determining comprises at least:

35. The computer program product of any one of claims 29-34, wherein said determining is performed by, iteratively:

(i) generating a proposed shape of said portion of said arch wire;

36. The method of any one of claims 29-35, wherein said program instructions are further executable to generate a set of manufacturing instructions for said portion of said arch wire, based on said determining.

37. The computer program product of claim 36, wherein said manufacturing instructions comprise modification instructions for modifying a shape of a provided portion of an arch wire, based on said determining.

38. The computer program product of claim 37, wherein said modification instructions are generated based on a comparison between said provided portion of said arch wire and said determined optimal shape.

39. The computer program product of claim 38, wherein said comparison comprises determining a spatial shape of said provided portion of said arch wire from one or more images of said provided portion of said arch wire.

40. The computer program product of claim 39, wherein said determining of said spatial shape of said provided portion comprises detecting and segmenting said provided portion of said arch wire in 3D imaging, based, at least in part, on epipolar geometry.

41. The computer program product of claim 40, wherein said 3D imaging is performed using a time-of-flight imaging device.

42. The computer program product of any one of claims 37-41, wherein said comparison is presented to said used using said user interface, and wherein said presenting comprises presenting said modification instructions to said user.