WO2023143461A1 - 产生牙颌三维数字模型的方法 - Google Patents

产生牙颌三维数字模型的方法 Download PDF

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Publication number
WO2023143461A1
WO2023143461A1 PCT/CN2023/073409 CN2023073409W WO2023143461A1 WO 2023143461 A1 WO2023143461 A1 WO 2023143461A1 CN 2023073409 W CN2023073409 W CN 2023073409W WO 2023143461 A1 WO2023143461 A1 WO 2023143461A1
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WIPO (PCT)
Prior art keywords
digital model
dimensional digital
gingiva
tooth
deformation
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PCT/CN2023/073409
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English (en)
French (fr)
Inventor
任远
王明政
冯洋
乔德明
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上海时代天使医疗器械有限公司
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Priority claimed from CN202210089331.1A external-priority patent/CN116543096A/zh
Priority claimed from CN202210089332.6A external-priority patent/CN116531124A/zh
Priority claimed from CN202210128253.1A external-priority patent/CN116630525A/zh
Application filed by 上海时代天使医疗器械有限公司 filed Critical 上海时代天使医疗器械有限公司
Publication of WO2023143461A1 publication Critical patent/WO2023143461A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis

Definitions

  • the present application generally relates to a method of generating a three-dimensional digital model of a tooth and jaw.
  • Shell-shaped dental appliances made of polymer materials are becoming more and more popular due to the advantages of beauty, convenience and cleaning.
  • a manufacturing method of a shell-shaped dental appliance is to place a heat-softened polymer membrane material on the model of the jaw (including the crown and part of the gum) whose crown part matches the target tooth layout of the corresponding orthodontic step.
  • the pressure film forms the shell-shaped dental appliance of this orthodontic step.
  • the jaw model is obtained by making corresponding three-dimensional digital model control equipment (for example, photo-curing molding equipment).
  • corresponding three-dimensional digital models of the gums are consistent, that is, the gums of the patient's original state (the state before orthodontic treatment).
  • the gums will deform as the teeth move, so the gums on these jaw models do not match the real ones. This can lead to underfitting or overfitting (resulting in compression of the gingiva) of the shell-shaped appliance so produced, in areas of the gums, particularly between two adjacent teeth or where teeth are missing.
  • One aspect of the present application provides a computer-executed method for generating a three-dimensional digital model of the gums, which includes: obtaining a three-dimensional digital model of the gums in a first state; and based on the deformation control points and the second Deformation control points of the three-dimensional digital model of the crown in the state, performing deformation processing on the three-dimensional digital model of the gum in the first state, and obtaining the three-dimensional digital model of the gum in the second state, wherein the three-dimensional digital model of the crown and the three-dimensional digital model of the gum in the same state The corresponding deformation control points coincide.
  • the deformation processing is to use the deformation control point of the 3D digital model of the dental crown in the second state as the new position of the corresponding deformation control point of the 3D digital model of the gingiva in the first state, and establish a deformation equation based on this , calculating the coordinates of the vertices of the three-dimensional digital model of the gums in the second state.
  • the deformation control points of the three-dimensional digital model of the gingiva include deformation control points on the cavity line
  • the deformation control points of the three-dimensional digital model of the dental crown include deformation control points on the cavity line
  • the gingiva The deformation control points on the cavity line of the three-dimensional digital model correspond one-to-one to the deformation control points on the cavity line of the three-dimensional digital model of the tooth crown.
  • the deformation control points of the three-dimensional digital model of the gingiva also include deformation control points on the edge line of the bottom surface, and during the deformation process, the deformation control points on the edge line of the bottom surface remain stationary.
  • the deformation treatment is based on the TPS deformation method.
  • the first state is an initial state.
  • the deformation control points are obtained by sampling on the three-dimensional digital model of the teeth and jaws in the initial state.
  • the deformation control points are obtained by uniform sampling in a predetermined number.
  • the three-dimensional digital model of the initial state of the jaw is obtained by scanning one of the following: the patient's jaw, the impression of the jaw, and the solid model of the jaw.
  • the three-dimensional digital model of the gingiva in the first state includes a real gingival part and a base, wherein the real gingival part is in contact with the crown and is located on the base.
  • the real gingival portion is a gingival portion within a predetermined distance from the gum line.
  • the first state is an initial state
  • the method for generating a three-dimensional digital model of the gingiva further includes: acquiring multiple three-dimensional digital models of the crown in successive states; and repeating the above operations to generate multiple successive states
  • Each of the three-dimensional digital models of the gums is generated based on the three-dimensional digital model of the gums in the first state and a corresponding one of the three-dimensional digital models of the tooth crowns in successive states.
  • Yet another aspect of the present application provides a method for generating a three-dimensional digital model of a tooth and jaw, which includes: combining the three-dimensional digital model of the gum in the second state generated by the method for generating a three-dimensional digital model of the gum with the second The three-dimensional digital model of the crown in the state is synthesized to obtain the three-dimensional digital model of the tooth and jaw in the second state.
  • Another aspect of the present application provides a method for manufacturing a shell-shaped dental appliance, which includes: using the second-state tooth and jaw three-dimensional digital model control equipment generated by the method for generating a three-dimensional digital model of the tooth and jaw to produce a shell-shaped Braces.
  • Another aspect of the present application provides a computer system for generating a three-dimensional digital model of the gums, which includes a storage device and a processor, the storage device stores a computer program, and when it is run by the processor, it will execute The method for generating a three-dimensional digital model of gingiva.
  • Another aspect of the present application provides a computer-executed method for generating a three-dimensional digital model of the gums, which includes: obtaining a three-dimensional digital model template of the gums; obtaining a three-dimensional digital model of the crown; and based on the deformation on the three-dimensional digital model template of the gums Control points and deformation control points of the three-dimensional digital model of the tooth crown, perform three-dimensional deformation processing on the three-dimensional digital model template of the gingiva, and obtain a three-dimensional digital model of the gingiva that matches the three-dimensional digital model of the tooth crown.
  • the deformation processing uses the deformation control point of the three-dimensional digital model of the dental crown as the new position of the corresponding deformation control point of the template of the three-dimensional digital model of the gingiva, based on which a three-dimensional deformation equation is established, and the calculated The coordinates of each vertex of the three-dimensional digital model of the gingiva.
  • the deformation control points of the three-dimensional digital model of the gingiva include deformation control points on the cavity line
  • the deformation control points of the three-dimensional digital model of the tooth crown include deformation control points on the cavity line
  • the tooth The deformation control points on the cavity line of the three-dimensional digital model of the crown are in one-to-one correspondence with the deformation control points on the cavity line of the three-dimensional digital model template of the gums.
  • the deformation control points of the three-dimensional digital model of the gingiva also include the deformation control points between every two adjacent tooth positions
  • the deformation control points of the three-dimensional digital model of the dental crown also include the deformation control points between every two adjacent tooth positions.
  • the deformation control points between the crowns, the deformation control points between the adjacent crowns of the three-dimensional digital model of the dental crowns and the deformation control points between the adjacent teeth of the three-dimensional digital model of the gums correspond one-to-one.
  • the deformation control points of the three-dimensional digital model of the gums also include deformation control points on the bottom edge line, and in the three-dimensional deformation process, the deformation control points on the bottom edge line of the three-dimensional digital model template of the gums Point stay still.
  • the three-dimensional deformation processing is based on the TPS deformation method.
  • the method for generating a three-dimensional digital model of the gums further includes: adjusting the number of teeth in the three-dimensional digital model of the gums according to the three-dimensional digital model of the crown, and the three-dimensional deformation processing is based on the adjusted teeth The 3D digital model template of the gingiva after digit quantity.
  • the method for generating a three-dimensional digital model of the gingiva further includes: scaling the three-dimensional digital model template of the gingiva according to the three-dimensional digital model of the crown, so that the three-dimensional digital model template of the gingiva is consistent with the three-dimensional digital model of the tooth
  • the contours of the three-dimensional digital model of the crown are basically coincident, and the three-dimensional deformation processing is based on the scaled three-dimensional digital model template of the gingiva.
  • the method for generating a three-dimensional digital model of the gingiva further includes: adjusting the arch shape of the scaled three-dimensional digital model of the gingiva according to the three-dimensional digital model of the dental crown.
  • the arch adjustment of the gingival three-dimensional digital model template includes: fitting the first spline curve based on the cavity line center of the three-dimensional digital model of the tooth crown, and uniformly sampling N deformations on it control points; the second spline curve is obtained by fitting the center of the tooth position based on the gingiva three-dimensional digital model template, and N deformation control points are uniformly sampled on it; and deformation anchor points based on the first spline curve A deformation equation is established with the deformation anchor point on the second spline curve, and two-dimensional deformation processing is performed on the three-dimensional digital model template of the gingiva and its deformation control points.
  • the two-dimensional warping process is based on a TPS warping method.
  • the method for generating a three-dimensional digital model of gums further includes: performing two-dimensional scaling on the end of the adjusted arch-shaped three-dimensional digital model template of gums.
  • the method for generating a three-dimensional digital model of the gingiva further includes: calculating the three-dimensional digital model of the gingiva based on the mapping of the deformation control points of the three-dimensional digital model template of the gingiva on the texture map, using a harmonic parameter calculation algorithm Mapping of all vertices of the template on the texture map; and performing a texture map operation on the three-dimensional digital model of the gingiva based on the mapping relationship.
  • the three-dimensional digital model of the dental crown is obtained by scanning one of the following: the patient's jaw, the impression of the jaw, and the solid model of the jaw.
  • the method for generating a three-dimensional digital model of the gingiva further includes: acquiring a plurality of successive three-dimensional digital models of dental crowns, respectively representing a plurality of successive tooth layouts; A three-dimensional digital model, performing deformation processing on the three-dimensional digital model template of the dental crown to generate a plurality of successive three-dimensional digital models of the gums.
  • Another aspect of the present application provides a method for generating a three-dimensional digital model of a tooth and jaw, which includes: synthesizing the three-dimensional digital model of the gum and the three-dimensional digital model of the crown to obtain a three-dimensional digital model of the tooth and jaw.
  • Another aspect of the present application provides a method for manufacturing a shell-shaped dental appliance, which includes: using the above-mentioned three-dimensional digital model control device for manufacturing a shell-shaped dental appliance.
  • Another aspect of the present application provides a computer system for generating a three-dimensional digital model of the gums, which includes a storage device and a processor, the storage device stores a computer program, and when it is executed by the processor, it will execute The method for generating a three-dimensional digital model of gingiva.
  • Another aspect of the present application provides a computer-executed method for generating a three-dimensional digital model of a tooth, which includes: obtaining a three-dimensional digital model of a tooth crown; obtaining a template of a three-dimensional digital model of a tooth root; The N deformation control points and the corresponding N deformation control points on the edge line of the three-dimensional digital model of the tooth crown are deformed to the three-dimensional digital model template of the tooth root to obtain a shape that matches the three-dimensional digital model of the tooth crown.
  • the three-dimensional digital model template of the tooth root is obtained by averaging multiple three-dimensional digital models of real tooth roots of the corresponding tooth number.
  • the computer-implemented method for generating a three-dimensional digital tooth model further includes: prior to the deformation processing, making the three-dimensional digital model template of the tooth root and the three-dimensional digital tooth crown template by translation and/or rotation Align so that the mesial and distal directions of the two are consistent and the long axes are parallel.
  • the computer-executed method for generating a three-dimensional digital tooth model further includes: after the alignment, scaling the three-dimensional digital model template of the tooth root so that its size is the same as that of the three-dimensional digital dental crown.
  • the models basically match.
  • the computer-executed method for generating a three-dimensional digital model of a tooth further includes: performing morphological adjustment on a part of the root region adjacent to the crown of the three-dimensional digital model of the tooth, so that the crown and The connection between the roots is more natural.
  • the deformation processing includes: taking the deformation control points of the three-dimensional digital model of the crown as the new positions of the corresponding deformation control points of the three-dimensional digital model template of the tooth root, establishing a three-dimensional deformation equation based on this, and calculating the Describe the new position of each vertex of the tooth root three-dimensional digital model template.
  • the three-dimensional deformation processing is based on the TPS deformation method.
  • the three-dimensional digital model of the dental crown is obtained by scanning one of the following: the patient's jaw, the impression of the jaw, and the solid model of the jaw.
  • the N control points on the edge line of the three-dimensional digital model of the tooth crown are obtained by uniform sampling, and the N control points on the edge line of the three-dimensional digital model template of the tooth root are obtained by uniform sampling.
  • the computer-executed method for generating a three-dimensional digital model of teeth further includes: using the method described in claim 1 to generate a three-dimensional digital model of two adjacent teeth; detecting the two adjacent teeth Whether there is a collision between the tooth roots of the three-dimensional digital model, and if there is a collision, the collision is classified as a mild collision or a severe collision based on a predetermined threshold and a collision depth; if the collision is a mild collision, then all collision points are found and its surrounding adjacent points, move each of these points to the opposite direction of its normal vector by a distance determined according to the collision depth, and perform morphological reconciliation and smoothing operations on all involved points;
  • the collision is a violent collision
  • the distance determined according to the maximum collision depth and carry out the shape reconciliation operation on the other points on the two tooth roots.
  • Another aspect of the present application provides a computer system for generating a three-dimensional digital model of teeth, which includes a storage device and a processor, the storage device stores a computer program, and when it is executed by the processor, it will execute The method for generating a three-dimensional digital model of teeth.
  • Fig. 1 is a schematic flowchart of a method for generating a three-dimensional digital model of a tooth and jaw in one embodiment of the present application
  • Fig. 2A is an interface of a computer program for generating a three-dimensional digital model of a tooth and jaw in an embodiment of the present application, showing the remaining gingival part of the three-dimensional digital model of the tooth and jaw in the initial state obtained by scanning after the crown part is removed;
  • Fig. 2B is the remaining part of the gingiva three-dimensional digital model shown in Fig. 2A shown in an interface of the computer program after removing unnecessary parts;
  • Fig. 3A schematically shows the projection points in an example and the first curve fitted based on these projection points
  • Fig. 3B schematically shows the complete outline of the bottom surface of the base in an example
  • Fig. 4A is a point cloud for Poisson reconstruction of the first-state gingiva three-dimensional digital model in an example shown by an interface of the computer program;
  • Fig. 4B is a three-dimensional digital model of the gingiva in the first state obtained by performing Poisson reconstruction based on the point cloud shown in Fig. 4A shown in an interface of the computer program;
  • Fig. 5 is the second state dental and jaw three-dimensional digital model synthesized that is shown in an interface of the computer program
  • Fig. 6 is a schematic flowchart of a method for generating a three-dimensional digital model of a tooth and jaw in another embodiment of the present application
  • Fig. 7 is a three-dimensional digital model template of gingiva in an example shown in an interface of a computer program for generating a three-dimensional digital model of teeth in an embodiment of the present application;
  • Fig. 8 shows some deformation control points on the gingiva three-dimensional digital model template in an example shown by an interface of the computer program
  • Fig. 9 is the mapping of some deformation control points on the texture map (right side) on the gingiva three-dimensional digital model template (left side) in an example shown by an interface of the computer program;
  • Fig. 10A is a three-dimensional digital model template of gingiva in an example shown in an interface of the computer program
  • Fig. 10B is a three-dimensional digital model template of the gingiva shown in Fig. 10A shown in an interface of the computer program after removing a tooth position form at the ends of both sides;
  • Fig. 11A shows the three-dimensional digital model of the dental crown, the first spline curve and its deformation anchor point in an example shown in an interface of the computer program
  • Fig. 11B shows a scaled three-dimensional digital model template of gingiva, a second spline curve and its deformation anchor point in an example shown in an interface of the computer program;
  • Fig. 12A is a 3D digital model template of the gingiva before 2D scaling of the extremities in an example shown in an interface of the computer program;
  • Fig. 12B is an interface of the computer program showing a three-dimensional digital model template of the gums obtained after 2D scaling the end of the three-dimensional digital model template of the gums shown in Fig. 12A.
  • Fig. 13A is a three-dimensional digital model template of the gingiva and a three-dimensional digital model of the crown before deformation processing in an example shown on an interface of the computer program;
  • Fig. 13B is a 3D digital model of gingiva obtained after deformation processing of the 3D digital model template of the gingiva shown in Fig. 13A displayed on an interface of the computer program and a 3D digital model of the jaw synthesized by the 3D digital model of the crown;
  • Fig. 13C is the rendered effect of the three-dimensional digital model of the tooth and jaw shown in Fig. 13B displayed on an interface of the computer program;
  • Fig. 14 is a schematic flowchart of a method for generating a three-dimensional digital model of teeth in another embodiment of the present application.
  • Fig. 15 is a three-dimensional digital model of a dental crown in an example shown by an interface of a computer program for generating a three-dimensional digital model of teeth in an embodiment of the present application;
  • Fig. 16 is a three-dimensional digital model template of the tooth root of No. 1-8 teeth of the maxillary dentition in an example shown by an interface of the computer program;
  • FIG. 17A an example of an aligned three-dimensional digital model of the crown and a scaled template of the three-dimensional digital model of the root shown in an interface of the computer program;
  • Fig. 17B is a three-dimensional digital model of the tooth root obtained after deformation processing of the three-dimensional digital model of the tooth root shown in Fig. 17A displayed on an interface of the computer program and a three-dimensional digital model of the tooth crown shown in Fig. 17A;
  • Fig. 17C is a three-dimensional digital model of teeth obtained after stitching the three-dimensional digital model of the crown and the three-dimensional digital model of the tooth root shown in Fig. 17B on an interface of the computer program;
  • Fig. 17D is a three-dimensional digital model of the tooth shown in Fig. 17C shown in an interface of the computer program after the part of the root region adjacent to the crown is reconciled;
  • Figure 18A a three-dimensional digital model of two adjacent teeth with a collision between the roots in an example shown by an interface of the computer program
  • Fig. 18B is an interface of the computer program showing the three-dimensional digital models of the two teeth shown in Fig. 18A after the collision is resolved.
  • One aspect of the present application provides a method for generating a three-dimensional digital model of a jaw, which can generate a three-dimensional digital model of the jaw that changes with the movement of the teeth.
  • the method for generating a three-dimensional digital model of a tooth and jaw of the present application will be described below by taking the generation of a three-dimensional digital model of a tooth and jaw for making a shell-shaped dental appliance as an example.
  • Orthodontic treatment utilizing shell appliances is the wearing of a series of successive shell appliances one at a time to gradually reposition the patient's teeth from their original layout to a first intermediate layout, a second intermediate layout...and finally an intermediate Layout until the target layout.
  • this series of successive shell-shaped dental appliances it is necessary to generate a corresponding series of successive three-dimensional digital models of the teeth and jaws.
  • FIG. 1 is a schematic flowchart of a method 100 for generating a three-dimensional digital model of a tooth and jaw in an embodiment of the present application.
  • the method 100 for generating a three-dimensional digital model of a tooth and jaw is executed by a computer.
  • a computer system for generating a three-dimensional digital model of a tooth and jaw which includes a storage device and a processor, wherein the storage device stores a computer program that, when executed by the processor, will The method 100 for generating a three-dimensional digital model of a tooth and jaw is executed.
  • a three-dimensional digital model of gingiva in a first state is acquired.
  • the 3D digital model of the gums and the 3D digital model of the crown that match each other are referred to as the 3D digital model of the gums and the 3D digital model of the crown in the same state, for example, the 3D digital model of the gums in the first state and the 3D digital model of the crown in the first state
  • the digital model is matched, the 3D digital model of the gingiva in the second state is matched with the 3D digital model of the crown in the second state, and so on.
  • the 3D mesh model is the most commonly used 3D digital model. Therefore, in the following description, in most cases, the 3D digital model and the 3D mesh model can be replaced with each other.
  • the three-dimensional mesh model of the teeth and jaws in the initial state can be obtained by intraoral scanning, or by scanning an impression or a solid model of the teeth and jaws. Then, the crown part and the gingiva part are segmented to obtain the three-dimensional mesh model of the crown and the three-dimensional mesh model of the gingiva in the initial state.
  • FIG. 2A is an interface of a computer program for generating a three-dimensional digital model of a tooth and jaw in an embodiment of the present application.
  • the initial state of the three-dimensional digital model of the tooth and jaw obtained by scanning is the remaining gingiva after the crown part is removed. part.
  • FIG. 2B is an interface of the computer program showing the remaining part of the three-dimensional digital model of the gum shown in FIG. 2A after removing unnecessary parts.
  • the jaw model used for hot-pressing film to make shell-shaped dental appliances also needs a base with a certain height. Therefore, a three-dimensional digital model of the gingiva in the first state including the required gingival part and the base can be generated. In one embodiment, the following method may be used to generate the three-dimensional digital model of the gums in the first state.
  • FIG. 3A schematically shows projected points in an example and a first curve fitted based on these projected points.
  • a predetermined number of sampling points may be uniformly sampled on the first curve, for example, 10 sampling points. Then these sampling points are shifted by a predetermined distance r along the normal direction of the first curve to obtain the first group of points, and then use the first group of points as the control points of the cubic spline curve to pass through the cubic spline curve
  • the outer contour of the bottom surface of the base is obtained by interpolation.
  • the sampling points are shifted by a predetermined distance r along the negative direction of the normal direction of the first curve to obtain a second group of points, and then the second group of points are used as the control points of the cubic spline curve, through the cubic spline curve
  • the inner contour line of the bottom surface of the base is obtained by means of curve interpolation.
  • the ends of the inner and outer contour lines are connected by a semicircle with a radius of r to obtain a complete contour line of the bottom surface of the base.
  • FIG. 3B schematically shows the complete outline of the bottom surface of the base in an example.
  • FIG. 4A is an interface of the computer program, which schematically shows the point cloud on which the Poisson reconstruction is based in an example.
  • FIG. 4B is an interface of the computer program, which schematically shows the three-dimensional digital model of the gingiva in the first state obtained by performing Poisson reconstruction based on the point cloud shown in FIG. 4A .
  • the generated three-dimensional digital model of the gingiva in the first state may have some defects, including air bubbles and roughness of the edge line of the bottom surface of the base, and these defects can be dealt with accordingly.
  • an AO value (Ambient Occlusion) can be calculated for each vertex. If the AO value is less than a predetermined threshold (for example, 0.2), it is considered that there is a bubble at the vertex, and it is eliminated by performing Laplacian smoothing on the vertex. bubble. Since these processing means are well known to those skilled in the art, they will not be described in detail here.
  • a deformation control point is selected on the three-dimensional digital model of the gum in the first state.
  • the deformation control points can be selected as follows: control points are sampled at predetermined intervals on the edge of the bottom surface of the base; , 5 sampling points) as the deformation control points; for each crown, select a point on both sides of the dental cavity line along the arch curve (that is, close to the adjacent teeth) as the deformation control points; and for each tooth For the crown, select the center of gravity of the tooth cavity as the deformation control point. In the original state, the crown fits perfectly with the gingiva, so the deformation control points on the crown coincide with the corresponding deformation control points on the gingiva.
  • the deformation process is performed on the 3D digital model of the gingiva in the first state to obtain the second state 3D digital model of gingiva.
  • the deformation process can use any applicable deformation method for the grid model, including but not limited to TPS (Thin-Plate Splines) deformation method, Laplace deformation method, rigid body deformation method, etc.
  • TPS Thin-Plate Splines
  • Laplace deformation method Laplace deformation method
  • rigid body deformation method rigid body deformation method
  • the deformation processing of the three-dimensional digital model of the gums in the first state may be carried out using a TPS deformation method.
  • TPS deformation method The specific implementation of the TPS deformation method can be found in "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations" published by Fred L. Bookstein in IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11, No.6, June 1989, and "Thin-Plate Spline Approximation for Image Registration” by Rolf Sprengel, Karl Rohr and H. Siegfried Stiehl in Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.
  • control points of the 3D digital model of the crown in the second state can be used as the new positions of the corresponding control points of the 3D digital model of the gingiva in the first state, and the control points on the edge of the bottom surface of the base can be kept
  • the TPS deformation equation is established based on this, and the coordinates of the vertices of the three-dimensional digital model of the gums in the second state are calculated by using the deformation equation, and the three-dimensional digital model of the gums in the second state is reconstructed.
  • the three-dimensional digital model of the dental crown in the second state is different from the pose of at least one crown of the three-dimensional digital model of the dental crown in the first state.
  • the three-dimensional digital model of the dental crown in the second state may be the orthodontic The 3D digital model of the crown under the target tooth layout of any orthodontic step of treatment.
  • the cavity line of the crown of the three-dimensional digital model of the crown in the second state that has not changed in pose relative to the three-dimensional digital model of the crown in the first state is the same as the three-dimensional digital model of the gingiva in the first state.
  • the corresponding cavity lines of the model coincide.
  • the 3D digital model of the gingiva in the second state and the 3D digital model of the crown in the second state are synthesized to obtain a 3D digital model of the jaw in the second state.
  • the deformation control points of the 3D digital model of the gingiva in the second state obtained after the deformation processing coincide with the deformation control points of the 3D digital model of the crown in the second state, and the two are synthesized to obtain the 3D digital model of the jaw in the second state.
  • the corresponding deformation control points of the three-dimensional digital model of the gingiva in the second state obtained through deformation processing coincide with the deformation control points of the three-dimensional digital model of the crown in the second state.
  • the two can be combined by Boolean operations Fusion to obtain the 3D digital model of the jaw in the second state.
  • FIG. 5 is a synthesized three-dimensional digital model of the jaw in the second state displayed on an interface of the computer program.
  • Another aspect of the present application provides a method for manufacturing a shell-shaped dental appliance, using a series of successive three-dimensional digital model control equipment obtained by the above method to produce a series of successive positive molds, and then using the hot-pressed film forming process in the A series of successive shell-shaped appliances are obtained by laminating the film on the series of successive male molds.
  • the shell-shaped dental appliance produced by the method of the present application is more suitable for the fit of the gums, and it is not easy to compress the gums or not fit the gums, especially two The gums between adjacent teeth.
  • the method of this application can also be used to generate three-dimensional digital models of dental jaws for other purposes, for example, dental jaws used to demonstrate the effect of orthodontic treatment 3D digital model.
  • the required three-dimensional digital model of the gingiva may be different from the above examples, for example, more real gingiva parts are reserved, or no base is required.
  • Another aspect of the present application provides a method for generating a three-dimensional digital model of a tooth and jaw.
  • the three-dimensional digital model template of the gum is subjected to deformation processing, and then the three-dimensional digital model of the dental crown and the deformed
  • the three-dimensional digital model of the gingiva was synthesized to obtain the three-dimensional digital model of the jaw.
  • FIG. 6 is a schematic flowchart of a method 200 for generating a three-dimensional digital model of a tooth and jaw in an embodiment of the present application.
  • the method 200 for generating a three-dimensional digital model of a tooth and jaw is executed by a computer.
  • a computer system for generating a three-dimensional digital model of a tooth and jaw which includes a storage device and a processor, wherein the storage device stores a computer program that, when executed by the processor, will Execute the method 200 for generating a three-dimensional digital model of a tooth and jaw.
  • a three-dimensional digital model template of the gingiva is obtained.
  • CAD software can be used to make a mesh model with the basic shape of the gingiva as a template for the three-dimensional digital model of the gingiva.
  • the number of vertices of the gingiva three-dimensional digital model template can be determined according to specific requirements. The more vertices there are, the more details the model can have, but the calculation speed of deformation processing is slower, and vice versa.
  • the model can be a left-right symmetrical model, therefore, only the left half or the right half can be selected, and the other half can be obtained by mirroring.
  • the upper and lower jaws can use the same base template.
  • a different template can be made for the upper and lower jaws (eg, the thickness of the template for the upper jaw is greater than the thickness of the template for the lower jaw).
  • FIG. 7 is an example of a three-dimensional digital model template of gingiva shown in an interface of a computer program for generating a three-dimensional digital model of teeth and jaws in an embodiment of the present application.
  • a deformation control point is selected on the three-dimensional digital model template of the gum.
  • deformation control points After obtaining the gingiva 3D digital model template, some deformation control points need to be selected on it as anchor points for subsequent deformation processing. Similarly, these deformation control points can also be symmetrical on the left and right planes. Therefore, it is only necessary to select the deformation control points on the left half or the right half of the gingiva 3D digital model template, and the other half of the deformation control points can be obtained by mirroring .
  • the following points can be selected as deformation control points on the three-dimensional digital model template of the gingiva: (1) points on the edge contour of the bottom surface of the three-dimensional digital model template of the gingiva, for example, sampling deformation at predetermined intervals or uniformly Control points; (2) points at the junction of the gingiva and crown, for example, points on the buccal and lingual sides of the cavity line, for example, 5 points are selected for each side; (3) points between adjacent teeth, such as , selecting a deformation control point between every two adjacent crowns on the three-dimensional digital model template of the gingiva.
  • FIG. 8 shows the partial deformation control points on the three-dimensional digital model template of the gingiva in an example shown on the interface of the computer program.
  • the deformation control points may be manually selected. In yet another embodiment, the deformation control points may also be automatically selected by a computer.
  • the vertices of the three-dimensional digital model template of the gums are mapped to a texture coordinate system.
  • FIG. 9 shows the mapping of some deformation control points on the texture map (right side) on the gingiva three-dimensional digital model template (left side) in an example of an interface of the computer program.
  • the position of the deformation control point in the texture map (that is, the coordinates in the texture coordinate system) can be manually calibrated.
  • the texture map can be artificially produced by using Photoshop software.
  • the texture coordinates of the remaining vertices can be calculated using a Harmonic Map algorithm.
  • the harmonic parameter seeking algorithm can be found in "Multiresolution Analysis of Arbitrary Meshes" published in SIGGRAPH'95: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques September 1995.
  • OpenGL can be used to render the texture map on the three-dimensional digital model template of the gingiva or the three-dimensional digital gingiva obtained after deformation processing.
  • the surface of the model to obtain a 3D digital model of the gingiva that resembles the appearance of real gingiva.
  • step 207 deformation processing is performed on the three-dimensional digital model template of the gingiva according to the three-dimensional digital model of the crown to obtain a three-dimensional digital model of the gingiva.
  • the three-dimensional digital model template of the gum can be deformed according to the arrangement of the three-dimensional digital model of the crown, so as to obtain a three-dimensional digital model of the gum matching the three-dimensional digital model of the crown, In this way, the two can be synthesized to obtain a three-dimensional digital model of the jaw.
  • the three-dimensional digital model of the dental crown includes a plurality of dental crowns.
  • the three-dimensional digital model of the dental crown in the initial state can be obtained by means of intraoral scanning or scanning an impression or a solid model.
  • three-dimensional digital models of the dental crown with different tooth layouts can be obtained.
  • Each quadrant of the gingiva 3D digital model template has 8 positions to form a concave shape suitable for the corresponding crown. However, not all cases have 8 teeth in each quadrant. Therefore, the 3D gingiva digital model needs to be modified. Model templates to eliminate the recessed form of redundant tooth positions. For the case where there are only 7 teeth in each quadrant, in one embodiment, the excess part at the end of the three-dimensional digital model template of the gingiva can be calculated as a harmonious form, so that it becomes a round and smooth shape that is continuous with the non-end part In this way, the redundant tooth shape is removed.
  • the algorithm of the harmonic shape can adopt the algorithm disclosed in "An Intuitive Framework for Real-Time Freeform Modeling" published by Mario Botsch and Leif Kobbelt in SIGGRAPH'04:ACM SIGGRAPH 2004Papers August 2004Pages 630-634, Especially k is the second-order energy equation (ie Thin Plate Surface).
  • Fig. 10A the three-dimensional digital model template of the gums in an example shown in the interface of the computer program; please refer to Fig. 3D digital model template of gingiva after bit morphology.
  • the length and width of the three-dimensional digital model of the crown can be calculated, and based on this, the template of the three-dimensional digital model of the gingiva is scaled, so that the changed template of the three-dimensional digital model of the gum basically coincides with the outline of the three-dimensional digital model of the crown .
  • the arch shape of the three-dimensional digital model template of the gum can be changed.
  • the first spline curve can be fitted based on the tooth position center of the three-dimensional digital model of the dental crown, and a predetermined number of sampling points (for example, 10 sampling points) are evenly sampled on it as deformation anchors point.
  • a second spline curve can be fitted based on the tooth position center of the three-dimensional digital model template of the gingiva, and the same number of sampling points can be evenly sampled on it as deformation anchor points.
  • a 2D TPS deformation equation is established, and the scaled three-dimensional digital model template and deformation control points of the gingiva are subjected to 2D TPS deformation processing, so that the arch of the three-dimensional digital model template of the gingiva is consistent with the three-dimensional shape of the crown.
  • the bow shape of the digital model matches.
  • FIG. 11A shows a three-dimensional digital model of a dental crown, a first spline curve and its deformation anchor points in an example shown on the interface of the computer program.
  • FIG. 11B which is an example of the zoomed three-dimensional digital model template of the gingiva, the second spline curve and its deformation anchor point shown in the interface of the computer program.
  • FIG. 12A is an example of the 3D digital model template of the gingiva before 2D scaling of the end in the interface of the computer program.
  • FIG. 12B shows the 3D digital model template of the gingiva obtained after 2D scaling the end of the 3D digital model template of the gingiva shown in FIG. 12A , as shown on the interface of the computer program.
  • deformation control points can be selected on the three-dimensional digital model of the dental crown.
  • the deformation control points on the three-dimensional digital model of the dental crown can be selected as follows: (1) select a predetermined number of deformation control points (the predetermined number It is the same as the number of deformation control points on the corresponding part of the three-dimensional digital model template of the gingiva, so that the deformation control points of the two form a one-to-one correspondence);
  • the midpoint corresponds to the deformation control point between corresponding adjacent tooth positions on the three-dimensional digital model template of the gingiva.
  • the cavity line is the outline where the crown margin meets the gum.
  • the average value of the z-coordinates of the center points of the cavity lines of the three-dimensional digital model of the tooth crown and each tooth of the three-dimensional digital model template of the gingiva can be used.
  • the average value of the z coordinates of the center point of the hole line is used to determine the relative position of the two along the z axis.
  • the deformation process can use any applicable deformation method for the grid model, including but not limited to TPS (Thin-Plate Splines) deformation method, Laplace deformation method, rigid body deformation method, etc.
  • TPS Thin-Plate Splines
  • Laplace deformation method Laplace deformation method
  • rigid body deformation method rigid body deformation method
  • the deformation processing of the three-dimensional digital model template of the gums may be performed by using a TPS deformation method.
  • TPS deformation method The specific implementation of the TPS deformation method can be found in "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations" published by Fred L. Bookstein in IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11, No.6, June 1989, and "Thin-Plate Spline Approximation for Image Registration” by Rolf Sprengel, Karl Rohr and H. Siegfried Stiehl in Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.
  • the corresponding deformation control points of the three-dimensional digital model of the gingiva obtained through deformation processing coincide with the deformation control points of the three-dimensional digital model of the crown.
  • the two can be fused by Boolean operations to obtain a complete 3D digital model of teeth and jaws.
  • FIG. 13A shows the 3D digital model template of the gingiva and the 3D digital model of the crown before deformation processing in an example shown on the interface of the computer program.
  • Fig. 13B shows the three-dimensional digital model of the gums obtained after deformation processing of the three-dimensional digital model template of the gingiva shown in Fig. 13A shown in the interface of the computer program and the three-dimensional digital model of the jaw synthesized by the three-dimensional digital model of the crown .
  • the texture map can be directly rendered on the surface of the 3D digital model of the gingiva with OpenGL to obtain a 3D figure close to the real gingiva. Model.
  • FIG. 13C shows the rendered effect of the three-dimensional digital model of the tooth and jaw shown in FIG. 13B displayed on the interface of the computer program.
  • Orthodontic treatment utilizing shell appliances is the wearing of a series of successive shell appliances one at a time to gradually reposition the patient's teeth from their original layout to a first intermediate layout, a second intermediate layout...and finally an intermediate Layout until the target layout.
  • a series of successive three-dimensional digital models of dental crowns are obtained, respectively representing a series of successive tooth layouts.
  • repeat step 207 to generate a matching gingiva three-dimensional digital model for each of the three-dimensional digital models of the crown.
  • the matched three-dimensional digital model of the crown and the three-dimensional digital model of the gum are synthesized into a three-dimensional digital model of the jaw.
  • use these three-dimensional digital model control equipment to make positive models.
  • a series of successive shell-shaped tooth aligners are formed by pressing films on these positive molds with a hot pressing film forming process.
  • Yet another aspect of the present application provides a method for generating a three-dimensional digital model of a tooth.
  • the three-dimensional digital model template of the tooth root is basically aligned with the three-dimensional digital model of the crown, and then, the three-dimensional digital model template of the tooth root is Deformation processing is performed to make the edges fit the edges of the three-dimensional digital model of the crown, and then the three-dimensional digital model of the crown and the deformed three-dimensional digital model of the root are fused to obtain a closed and complete three-dimensional digital model of the tooth.
  • FIG. 14 is a schematic flowchart of a method 300 for generating a three-dimensional digital model of teeth in one embodiment of the present application.
  • a three-dimensional digital model of a dental crown is acquired.
  • the three-dimensional digital model of the dental crown can be obtained through intraoral scanning, or scanning impressions or tooth solid models.
  • a 3D digital model of the entire dentition that is, the maxillary dentition or the mandibular dentition
  • a 3D digital model of a single crown is segmented to obtain a 3D digital model of a single crown.
  • FIG. 15 is an example of a three-dimensional digital model of a tooth crown shown in an interface of a computer program for generating a three-dimensional digital model of teeth in an embodiment of the present application.
  • a tooth root three-dimensional digital model template is acquired.
  • cone beam computed tomography Cone Beam Computed Tomography, referred to as CBCT
  • CBCT cone beam computed tomography
  • FIG. 16 is an example of a three-dimensional digital model template of the roots of No. 1-8 teeth in the maxillary dentition shown by an interface of the computer program.
  • a corresponding three-dimensional digital model template of the tooth root is selected to generate a complete three-dimensional digital model of the tooth.
  • the template of the three-dimensional digital model of the tooth root is scaled according to the size of the three-dimensional digital model of the tooth crown.
  • the size of the three-dimensional digital model template of the tooth root does not necessarily match the size of the crown.
  • the three-dimensional digital model template of the tooth root can be scaled so that its size matches the size of the crown. In order to ensure that the shape of the complete three-dimensional digital model of teeth generated subsequently is more natural.
  • scaling can be determined by projecting the crown edge onto the XY plane and computing the diagonal length of the bounding box, similarly projecting the root edge onto the XY plane and computing the bounding box diagonal Line length, the ratio obtained by dividing the diagonal length of the crown projection bounding box by the diagonal length of the root bounding box is used as the three-dimensional scaling ratio of the tooth root.
  • the three-dimensional digital model template of the tooth root before scaling the three-dimensional digital model template of the tooth root, it can be aligned with the three-dimensional digital model of the crown by translation and rotation, so that the long axes of the two are parallel, the mesial and distal directions are consistent, and The centers of the edges basically coincide.
  • FIG. 17A is an example of an interface of the computer program showing the aligned 3D digital model of the crown and the scaled 3D digital model template of the root.
  • deformation processing is performed on the scaled three-dimensional digital root model template based on the edge of the three-dimensional digital model of the dental crown.
  • a plurality of deformation control points can be selected on the edge of the three-dimensional digital model of the tooth crown (that is, the cavity line), and corresponding points can be selected on the edge of the scaled three-dimensional digital model template of the tooth root. Then, use the deformation control points of the three-dimensional digital model of the tooth crown as the new positions of the corresponding deformation control points of the template of the three-dimensional digital model of the tooth root, and establish a deformation equation based on this, and the three-dimensional digital model of the tooth root The template is deformed to obtain a three-dimensional digital model of the tooth root that matches the three-dimensional digital model of the crown.
  • the deformation control points on the three-dimensional digital model of the dental crown and the three-dimensional digital model of the root can be selected as follows: uniformly sample N (for example, 30) on the edge line of the three-dimensional digital model of the dental crown Points are used as the deformation control points of the three-dimensional digital model of the tooth crown, and N points are uniformly sampled correspondingly on the edge lines of the three three-dimensional digital model templates as the deformation control points of the three-dimensional digital model template of the tooth root.
  • the deformation process can use any applicable deformation method for the grid model, including but not limited to TPS (Thin-Plate Splines) deformation method, Laplace deformation method, rigid body deformation method, etc.
  • TPS Thin-Plate Splines
  • Laplace deformation method Laplace deformation method
  • rigid body deformation method rigid body deformation method
  • the deformation processing of the three-dimensional digital model of the gums in the first state may be carried out using a TPS deformation method.
  • TPS deformation method The specific implementation of the TPS deformation method can be found in "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations" published by Fred L. Bookstein in IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11, No.6, June 1989, and "Thin-Plate Spline Approximation for Image Registration” by Rolf Sprengel, Karl Rohr and H. Siegfried Stiehl in Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.
  • FIG. 17B shows the three-dimensional digital model of the tooth root obtained after deformation processing of the three-dimensional digital model of the tooth root shown in FIG. 17A shown in an interface of the computer program and the three-dimensional digital model of the crown shown in FIG. 17A .
  • the three-dimensional digital model of the crown and the three-dimensional digital model of the tooth root are stitched together.
  • the edges of the three-dimensional digital model of the tooth root obtained through deformation processing and the three-dimensional digital model of the crown basically coincide, other points on the edges of the two may not coincide except for the deformation control points. Therefore, the two can be stitched together by mesh model stitching to obtain a complete closed three-dimensional digital model of teeth.
  • FIG. 17C is a three-dimensional digital tooth model obtained by stitching the three-dimensional digital model of the crown and the three-dimensional digital model of the tooth root shown in FIG. 17B as shown in an interface of the computer program.
  • the morphological adjustment is performed on the area adjacent to the tooth root and the crown of the three-dimensional digital model of the tooth.
  • the shape of the area adjacent to the crown on the root may be blended.
  • the form blending may be performed on the area at a predetermined distance below the crown edge line, for example, the area 2 mm below the crown edge line. It can be understood that the predetermined distance can be determined according to specific requirements and conditions.
  • the algorithm of the harmonic shape can adopt the algorithm disclosed in "An Intuitive Framework for Real-Time Freeform Modeling" published by Mario Botsch and Leif Kobbelt in SIGGRAPH'04:ACM SIGGRAPH 2004Papers, especially k is the second order The energy equation (ie Thin Plate Surface).
  • FIG. 17D is a 3D digital model of the tooth shown in FIG. 17C , which is displayed on an interface of the computer program, after the part of the root area adjacent to the crown is morphologically reconciled.
  • the above-mentioned method 300 for generating a three-dimensional digital model of a tooth is for a single tooth. After the method is used to generate the three-dimensional digital models of multiple teeth in a dentition, there may be collisions between the roots of the three-dimensional digital models of adjacent teeth. At this time, the collisions can be processed to eliminate the collisions.
  • the above-mentioned method 300 for generating a three-dimensional digital model of teeth may further include an operation of collision resolution. In one embodiment, the following method can be used to eliminate the collision between the tooth roots.
  • the point in the root that needs to be moved is determined based on the height of the point of maximum collision.
  • the tooth root can be divided into the root neck area, the root middle area and the root tip area along the height direction, each accounting for 1/3 of the total height. Which points need to be moved can be determined in the apical area according to the ratio of the vertical distance from the maximum collision point to the apex to the total root height (in this embodiment, only points in the apical area will be selected as moving points).
  • the moving distance of the point to be moved is determined according to the collision depth of the maximum collision point (for example, the moving distance can be the maximum collision depth), and the displacement direction of the point to be moved is determined according to the position of the maximum collision point (for example, The displacement direction may be along the line connecting the maximum collision point), and operations such as grid deformation (for example, Laplace deformation) are performed on the grid.
  • FIG. 18A is an example of an interface of the computer program showing the three-dimensional digital model of two adjacent teeth with collision between tooth roots.
  • FIG. 18B is an interface of the computer program showing the three-dimensional digital models of the two teeth shown in FIG. 18A after the collision is released.
  • all the operations of the above method can be executed by a computer.
  • Another aspect of the present application provides a computer system for generating a three-dimensional digital model of a tooth and jaw, which includes a storage device and a processor, wherein the storage device stores a computer program, and when it is executed by the processor, The method 300 of generating a three-dimensional digital model of a tooth will be performed.

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Abstract

本申请的一方面提供了一种计算机执行的产生牙龈三维数字模型的方法，其包括：获取第一状态牙龈三维数字模型；以及基于所述第一状态牙龈三维数字模型的形变控制点和第二状态牙冠三维数字模型的形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第二状态牙龈三维数字模型，其中，同一状态的牙冠三维数字模型和牙龈三维数字模型的对应形变控制点重合。

Description

产生牙颌三维数字模型的方法 技术领域
本申请总体上涉及一种产生牙颌三维数字模型的方法。
 背景技术
由于美观、便捷以及利于清洁等优点，以高分子材料制成的壳状牙齿矫治器越来越受欢迎。
壳状牙齿矫治器的一种制作方法是，在牙冠部分与对应矫治步的目标牙齿布局相吻合的牙颌(包括牙冠和部分牙龈)模型上，将经加热软化的高分子膜片材料压膜形成该矫治步的壳状牙齿矫治器。
在现有的方案中，牙颌模型是以对应的三维数字模型控制设备(例如，光固化成型设备)制作获得。对于一组一系列逐次的壳状牙齿矫治器，所对应的一系列逐次的牙颌三维数字模型的牙龈部分是一致的，即患者原始状态(进行正畸治疗之前的状态)的牙龈。
在正畸治疗过程中，牙龈将随着牙齿的移动而发生形变，因此，这些牙颌模型上的牙龈与真实牙龈并不一致。这可能导致如此制作获得的壳状牙齿矫治器不够贴合或过度贴合(导致压迫牙龈)一些区域的牙龈，特别是两颗相邻牙齿之间的牙龈或缺牙处的牙龈。
另外，在正畸治疗之前，医生有向患者展示正畸治疗过程中牙颌的变化的需求。然而，在现有的方案中，一组一系列逐次的牙颌的三维数字模型的牙龈保持不变，与原始状态的牙龈一致，无法展示正畸治疗对牙龈造成的变化。
基于以上原因，有必要提供一种新的产生牙颌三维数字模型的方法，以产生牙龈更接近真实情况的牙颌三维数字模型。
发明内容
本申请的一方面提供了一种计算机执行的产生牙龈三维数字模型的方法，其包括：获取第一状态牙龈三维数字模型；以及基于所述第一状态牙龈三维数字模型的形变控制点和第二状态牙冠三维数字模型的形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第二状态牙龈三维数字模型，其中，同一状态的牙冠三维数字模型和牙龈三维数字模型的对应形变控制点重合。
在一些实施方式中，所述形变处理是将所述第二状态牙冠三维数字模型的形变控制点作为所述第一状态牙龈三维数字模型的对应形变控制点的新位置，基于此建立形变方程，计算所述第二状态牙龈三维数字模型各顶点的坐标。
在一些实施方式中，所述牙龈三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙龈三维数字模型牙洞线上的形变控制点与所述牙冠三维数字模型牙洞线上的形变控制点一一对应。
在一些实施方式中，所述牙龈三维数字模型的形变控制点还包括底面边缘线上的形变控制点，在所述形变处理中，所述底面边缘线上的形变控制点保持不动。
在一些实施方式中，所述形变处理是基于TPS形变方法。
在一些实施方式中，所述第一状态是初始状态。
在一些实施方式中，所述形变控制点是在初始状态牙颌三维数字模型上采样获得。
在一些实施方式中，所述形变控制点是按预定数量均匀采样获得。
在一些实施方式中，所述初始状态牙颌三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
在一些实施方式中，所述第一状态牙龈三维数字模型包括真实牙龈部分和底座，其中，所述真实牙龈部分与牙冠相接，位于所述底座之上。
在一些实施方式中，所述真实牙龈部分是自牙龈线预定距离内的牙龈部分。
在一些实施方式中，所述第一状态是初始状态，所述产生牙龈三维数字模型的方法还包括：获取多个逐次状态的牙冠三维数字模型；以及重复上述操作，产生多个逐次状态的牙龈三维数字模型，其每一个是基于所述第一状态牙龈三维数字模型以及所述多个逐次状态的牙冠三维数字模型中相对应的一个而产生。
本申请的又一方面提供了一种产生牙颌三维数字模型的方法，其包括：将所述的产生牙龈三维数字模型的方法所产生的所述第二状态牙龈三维数字模型和所述第二状态牙冠三维数字模型合成得到第二状态牙颌三维数字模型。
本申请的又一方面提供了一种壳状牙齿矫治器的制作方法，其包括：利用所述的产生牙颌三维数字模型的方法所产生的第二状态牙颌三维数字模型控制设备制作壳状牙齿矫治器。
本申请的又一方面提供了一种用于产生牙龈三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器运行后，将执行所述的产生牙龈三维数字模型的方法。
本申请的又一方面提供了一种计算机执行的产生牙龈三维数字模型的方法，其包括：获取牙龈三维数字模型模板；获取牙冠三维数字模型；以及基于所述牙龈三维数字模型模板上的形变控制点和所述牙冠三维数字模型的形变控制点，对所述牙龈三维数字模型模板进行三维形变处理，得到与所述牙冠三维数字模型相匹配的牙龈三维数字模型。
在一些实施方式中，所述形变处理是以所述牙冠三维数字模型的形变控制点作为所述牙龈三维数字模型模板的对应形变控制点的新的位置，基于此建立三维形变方程，计算所述牙龈三维数字模型各顶点的坐标。
在一些实施方式中，所述牙龈三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的牙洞线上的形变控制点与所述牙龈三维数字模型模板的牙洞线上的形变控制点一一对应。
在一些实施方式中，所述牙龈三维数字模型的形变控制点还包括每两个相邻牙位之间的形变控制点，所述牙冠三维数字模型的形变控制点还包括每两个相邻牙冠之间的形变控制点，所述牙冠三维数字模型的相邻牙冠间的形变控制点与所述牙龈三维数字模型的相邻牙位之间的形变控制点一一对应。
在一些实施方式中，所述牙龈三维数字模型的形变控制点还包括其底面边缘线上的形变控制点，在所述三维形变处理中，所述牙龈三维数字模型模板底面边缘线上的形变控制点保持不动。
在一些实施方式中，所述三维形变处理是基于TPS形变方法。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：根据所述牙冠三维数字模型调整所述牙龈三维数字模型模板的牙位数量，所述三维形变处理是基于经调整牙位数量后的牙龈三维数字模型模板。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：根据所述牙冠三维数字模型对所述牙龈三维数字模型模板进行缩放，使所述牙龈三维数字模型模板与所述牙冠三维数字模型的轮廓基本重合，所述三维形变处理是基于经缩放的牙龈三维数字模型模板。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：根据所述牙冠三维数字模型，调整所述经缩放的牙龈三维数字模型模板的弓形。
在一些实施方式中，对所述牙龈三维数字模型模板的弓形调整包括：基于所述牙冠三维数字模型的牙洞线中心拟合得到第一样条曲线，并在其上均匀采样N个形变控制点；基于所述牙龈三维数字模型模板的牙位中心拟合得到第二样条曲线，并在其上均匀采样N个形变控制点；以及基于所述第一样条曲线上的形变锚点和所述第二样条曲线上的形变锚点建立形变方程，对所述牙龈三维数字模型模板及其形变控制点进行二维形变处理。
在一些实施方式中，所述二维形变处理是基于TPS形变方法。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：对所述经调整弓形的牙龈三维数字模型模板的末端进行二维缩放。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：基于所述牙龈三维数字模型模板的形变控制点在纹理贴图上的映射，以调和求参算法计算所述牙龈三维数字模型模板所有顶点在所述纹理贴图上的映射；以及基于所述映射关系，对所述牙龈三维数字模型进行纹理贴图操作。
在一些实施方式中，所述牙冠三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
在一些实施方式中，所述的产生牙龈三维数字模型的方法还包括：获取多个逐次的牙冠三维数字模型，分别代表多个逐次的牙齿布局；以及分别基于所述多个逐次的牙冠三维数字模型，对所述牙冠三维数字模型模板进行形变处理，产生多个逐次的牙龈三维数字模型。
本申请的又一方面提供了一种产生牙颌三维数字模型的方法，其包括：将所述的牙龈三维数字模型和牙冠三维数字模型合成得到牙颌三维数字模型。
本申请的又一方面提供了一种壳状牙齿矫治器的制作方法，其包括：利用所述的牙颌三维数字模型控制设备制作壳状牙齿矫治器。
本申请的又一方面提供了一种用于产生牙龈三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行所述的产生牙龈三维数字模型的方法。
本申请的又一方面提供了一种计算机执行的产生牙齿三维数字模型的方法，其包括：获取牙冠三维数字模型；获取牙根三维数字模型模板；基于所述牙根三维数字模型模板的边缘线上的N个形变控制点和所述牙冠三维数字模型的边缘线上对应的N个形变控制点，对所述牙根三维数字模型模板进行形变处理，得到与所述牙冠三维数字模型相匹配的牙根三维数字模型；以及将所述牙冠三维数字模型和所述牙根三维数字模型的边缘进行缝合，得到完整的牙齿三维数字模型，其中，所述N是自然数。
在一些实施方式中，所述牙根三维数字模型模板是对相应牙号的多个真实牙根的三维数字模型求平均获得。
在一些实施方式中，所述的计算机执行的产生牙齿三维数字模型的方法还包括：在所述形变处理之前，通过平移和/或旋转使所述牙根三维数字模型模板与所述牙冠三维数字对准，使两者近远中方向一致，并且长轴平行。
在一些实施方式中，所述的计算机执行的产生牙齿三维数字模型的方法还包括：在所述对准之后，对所述牙根三维数字模型模板进行缩放，使其尺寸与所述牙冠三维数字模型基本匹配。
在一些实施方式中，所述的计算机执行的产生牙齿三维数字模型的方法还包括：对所述牙齿三维数字模型的与所述牙冠邻接的部分牙根区域进行形态调和，使得所述牙冠和牙根之间的衔接更自然。
在一些实施方式中，所述形变处理包括：以所述牙冠三维数字模型的形变控制点作为所述牙根三维数字模型模板的对应形变控制点的新位置，基于此建立三维形变方程，计算所述牙根三维数字模型模板各顶点的新的位置。
在一些实施方式中，所述三维形变处理是基于TPS形变方法。
在一些实施方式中，所述牙冠三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
在一些实施方式中，所述牙冠三维数字模型的边缘线上的N个控制点是均匀采样获得，所述牙根三维数字模型模板的边缘线上的N个控制点是均匀采样获得。
在一些实施方式中，所述的计算机执行的产生牙齿三维数字模型的方法还包括：利用权利要求1所述的方法产生两颗相邻牙齿的三维数字模型；检测所述两颗相邻牙齿的三维数字模型的牙根之间是否存在碰撞，若存在碰撞，则基于预定的阈值和碰撞深度，将该碰撞归类为温和碰撞或剧烈碰撞；若所述碰撞为温和碰撞，那么，找到所有碰撞点及其周围邻接点，将每个这些点向其法向量的反方向移动根据所述碰撞深度确定的距离，并对所有涉及的点进行形态调和及平滑操作；
若所述碰撞为剧烈碰撞，那么，根据最大碰撞点的高度确定所述两个牙根中需要移动的点，将这些需要移动的点沿最大碰撞点连线的方向移动根据最大碰撞深度确定的距离，并对所述两个牙根上的其他点进行形态调和操作。
本申请的又一方面提供了一种用于产生牙齿三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行所述的产生牙齿三维数字模型的方法。
 附图说明
以下将结合附图及其详细描述对本申请的上述及其他特征作进一步说明。应当理解的是，这些附图仅示出了根据本申请的若干示例性的实施方式，因此不应被视为是对本申请保护范围的限制。除非特别指出，附图不必是成比例的，并且其中类似的标号表示类似的部件。
图1为本申请一个实施例中的产生牙颌三维数字模型的方法的示意性流程图；
图2A，为本申请一个实施例中用于产生牙颌三维数字模型的计算机程序的一个界面所展示的扫描获得的初始状态的牙颌三维数字模型在去除了牙冠部分后剩余的牙龈部分；
图2B，为所述计算机程序的一个界面所展示的图2A所示的牙龈三维数字模型在去除不需要的部分之后所剩余的部分；
图3A，示意性地展示了一个例子中的投影点以及基于这些投影点拟合得到的第一曲线；
图3B，示意性地展示了一个例子中的底座底面的完整轮廓线；
图4A，为所述计算机程序的一个界面所展示的一个例子中的用于泊松重建第一状态牙龈三维数字模型的点云；
图4B，为所述计算机程序的一个界面所展示的基于图4A所示点云进行泊松重建得到的第一状态牙龈三维数字模型；
图5为所述计算机程序的一个界面所展示的合成得到的第二状态牙颌三维数字模型；
图6为本申请又一实施例中的产生牙颌三维数字模型的方法的示意性流程图；
图7，为本申请一个实施例中用于产生牙颌三维数字模型的计算机程序的一个界面所展示的一个例子中的牙龈三维数字模型模板；
图8，为所述计算机程序的一个界面所展示的一个例子中的牙龈三维数字模型模板上的部分形变控制点；
图9，为所述计算机程序的一个界面所展示的一个例子中的牙龈三维数字模型模板(左侧)上的部分形变控制点在纹理贴图(右侧)上的映射；
图10A，为所述计算机程序的一个界面所展示的一个例子中的牙龈三维数字模型模板；
图10B，为所述计算机程序的一个界面所展示的图10A所示牙龈三维数字模型模板在两侧末端分别去除了一个牙位形态后的牙龈三维数字模型模板；
图11A，为所述计算机程序的一个界面所展示的一个例子中的牙冠三维数字模型、第一样条曲线及其形变锚点；
图11B，为所述计算机程序的一个界面所展示的一个例子中经缩放的牙龈三维数字模型模板、第二样条曲线及其形变锚点；
图12A，为所述计算机程序的一个界面所展示的一个例子中在对末端进行2D缩放前的牙龈三维数字模型模板；
图12B，为所述计算机程序的一个界面所展示的对图12A所示牙龈三维数字模型模板末端进行2D缩放后获得的牙龈三维数字模型模板。
图13A，为所述计算机程序的一个界面所展示的一个例子中进行形变处理前的牙龈三维数字模型模板和牙冠三维数字模型；
图13B，为所述计算机程序的一个界面所展示的图13A所示的牙龈三维数字模型模板经形变处理后得到的牙龈三维数字模型和所述牙冠三维数字模型合成的牙颌三维数字模型；
[根据细则91更正 10.03.2023]
图13C，为所述计算机程序的一个界面所展示的图13B所示牙颌三维数字模型经渲染后的效果；
图14为本申请又一实施例中的产生牙齿三维数字模型的方法的示意性流程图；
图15，为本申请一个实施例中用于产生牙齿三维数字模型的计算机程序的一个界面所展示的一个例子中的牙冠三维数字模型；
图16，为所述计算机程序的一个界面所展示的一个例子中上颌牙列的1-8号牙的牙根三维数字模型模板；
图17A，为所述计算机程序的一个界面所展示的一个例子中对准的牙冠三维数字模型和经缩放的牙根三维数字模型模板；
图17B，为所述计算机程序的一个界面所展示的图17A所示牙根三维数字模型经形变处理后得到的牙根三维数字模型与图17A所示的牙冠三维数字模型；
图17C，为所述计算机程序的一个界面所展示的图17B所示的牙冠三维数字模型和牙根三维数字模型缝合后得到的牙齿三维数字模型；
图17D，为所述计算机程序的一个界面所展示的图17C所示牙齿三维数字模型的与牙冠邻接的部分牙根区域经形态调和后得到的牙齿三维数字模型；
图18A，为所述计算机程序的一个界面所展示的一个例子中牙根之间存在碰撞的两颗相邻牙齿的三维数字模型；以及
图18B，为所述计算机程序的一个界面所展示的图18A所示两颗牙齿的三维数字模型经碰撞解除后的样子。
 具体实施方式
以下的详细描述中引用了构成本说明书一部分的附图。说明书和附图所提及的示意性实施方式仅仅出于是说明性之目的，并非意图限制本申请的保护范围。在本申请的启示下，本领域技术人员能够理解，可以采用许多其他实施方式，并且可以对所描述实施方式做出各种改变，而不背离本申请的主旨和保护范围。应当理解的是，在此说明并图示的本申请的各个方面可以按照很多不同的配置来布置、替换、组合、分离和设计，这些不同配置都在本申请的保护范围之内。
本申请的一方面提供了一种产生牙颌三维数字模型的方法，能够产生牙龈随牙齿移动而变化的牙颌三维数字模型。下面以产生用于制作壳状牙齿矫治器的牙颌三维数字模型为例，对本申请的产生牙颌三维数字模型的方法进行说明。
利用壳状牙齿矫治器的牙科正畸治疗，是逐次佩戴一系列逐次的壳状牙齿矫治器，以将患者牙齿从原始布局逐渐地重新定位到第一中间布局、第二中间布局……最后中间布局直至目标布局。为了制作这一系列逐次的壳状牙齿矫治器，需要产生对应的一系列逐次的牙颌三维数字模型。
请参图1，为本申请一个实施例中的产生牙颌三维数字模型的方法100的示意性流程图。
在一个实施例中，所述产生牙颌三维数字模型的方法100由计算机执行。本申请又一方面提供了一种用于产生牙颌三维数字模型计算机系统，其包括存储装置和处理器，其中，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行所述产生牙颌三维数字模型的方法100。
在101中，获取第一状态牙龈三维数字模型。
为了便于说明，将相互匹配的牙龈三维数字模型和牙冠三维数字模型称为同一状态的牙龈三维数字模型和牙冠三维数字模型，例如，第一状态牙龈三维数字模型和第一状态牙冠三维数字模型相匹配，第二状态牙龈三维数字模型和第二状态牙冠三维数字模型相匹配，以此类推。在本领域的实际操作中，三维网格模型是最常用的三维数字模型，因此，在以下描述中，大多数情况下，三维数字模型和三维网格模型可相互替换。
在一个实施例中，可以通过口内扫描，或者扫描印模或牙颌实体模型等方式，获得初始状态的牙颌三维网格模型。然后，将牙冠部分和牙龈部分进行分割，获得初始状态的牙冠三维网格模型和牙龈三维网格模型。
请参图2A，为本申请一个实施例中用于产生牙颌三维数字模型的计算机程序的一个界面所展示的扫描获得的初始状态的牙颌三维数字模型在去除了牙冠部分后剩余的牙龈部分。
壳状牙齿矫治器的制造并不需要完整的牙龈的三维数字模型，而且扫描获得的牙颌三维数字模型的牙龈部分靠近边缘处质量通常不太理想，因此，可以只保留需要的牙龈部分。例如，对于壳状牙齿矫治器的制造而言，一般只需要牙龈线2mm之内的牙龈部分。请参图2B，为所述计算机程序的一个界面所展示的图2A所示的牙龈三维数字模型在去除不需要的部分之后所剩余的部分。
用于热压膜制作壳状牙齿矫治器的牙颌模型除了牙冠和所需牙龈部分之外，还需要具有一定高度的底座。因此，可以产生一个包括所述需要的牙龈部分和底座的第一状态牙龈三维数字模型。在一个实施例中，可以采用以下方法产生该第一状态牙龈三维数字模型。
首先，找到每颗牙冠的牙洞(牙冠与牙龈的边缘)的几何中心点(其坐标为牙洞线上各顶点坐标的平均值)，并将其投影到底座底面所在的平面。然后，基于这些投影的点拟合出第一曲线。请参图3A，示意性地展示了一个例子中的投影点以及基于这些投影点拟合得到的第一曲线。
接着，可以在所述第一曲线上均匀采样预定数量的采样点，例如，10个采样点。再将这些采样点沿所述第一曲线的法向的正向偏移预定的距离r，得到第一组点，再以该第一组点作为三次样条曲线控制点，通过三次样条曲线插值的方式得到底座底面的外轮廓线。然后，将所述采样点沿所述第一曲线的法向的负向偏移预定的距离r，得到第二组点，再以该第二组点作为三次样条曲线控制点，通过三次样条曲线插值的方式得到底座底面的内轮廓线。最后，以半径为r的半圆将所述内外轮廓线的末端相连，得到底座底面的完整轮廓线。请参图3B，示意性地展示了一个例子中的底座底面的完整轮廓线。
然后，在牙洞内部、底座底面轮廓线内以及牙龈和底座底面轮廓线之间插入点，再基于这些插入的点和所述需要的牙龈部分的顶点进行泊松重建，得到包括原始状态的需要牙龈部分和底座的封闭的第一状态牙龈三维数字模型。请参图4A，为所述计算机程序的一个界面，其示意性地展示了一个例子中所述泊松重建所基于的点云。请参图4B，为所述计算机程序的一个界面，其示意性地展示了基于图4A所示点云进行泊松重建得到的第一状态牙龈三维数字模型。
在一些情况下，产生的第一状态牙龈三维数字模型可能存在一些瑕疵，包括气泡和底座底面边缘线的不光滑，此时可以针对这些瑕疵进行相应处理。在一个实施例中，可以对每个顶点计算AO值(Ambient Occlusion)，若AO值小于预定的阈值(例如0.2)，则认为该处存在气泡，通过对该顶点进行拉普拉斯平滑处理消除气泡。由于这些处理手段为业界一般技术人员所熟知，此处不再详述。
可以理解，除了以上的方法之外，也可以采用其他合适的方法产生所述第一状态牙龈三维数字模型的底座部分。
在103中，在所述第一状态牙龈三维数字模型上选取形变控制点。
为了使得所述第一状态牙龈三维数字模型的牙龈部分能够随牙冠的移动而相应地发生形变，需要在所述第一状态牙龈三维数字模型的牙龈部分与牙冠邻接处选取一组形变控制点。
在一个实施例中，可以如此选取形变控制点：在所述底座底面的边缘以预定间隔采样控制点；对于每一牙冠，在牙洞线唇舌两侧分别均匀采样预定数量的采样点(例如，5个采样点)作为形变控制点；对于每一牙冠，在牙洞线上沿牙弓曲线的两侧(即靠近邻牙处)分别选取一个点作为形变控制点；以及对于每一牙冠，选取其牙洞重心作为形变控制点。在原始状态下，牙冠与牙龈完全吻合，因此，此时牙冠上的形变控制点和牙龈上的对应形变控制点重合。
在105中，基于所述第一状态牙龈三维数字模型的形变控制点和第二状态牙冠三维数字模型的形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第二状态牙龈三维数字模型。
所述形变处理可以采用任何适用的针对网格模型的形变方法，包括但不限于TPS(Thin-Plate Splines)形变方法、拉普拉斯形变方法、刚体形变方法等。
在一个实施例中，可以采用TPS形变方法对所述第一状态牙龈三维数字模型进行形变处理。
TPS形变方法的具体实现可参由Fred L.Bookstein发表于IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11,No.6,June 1989的《Principal Warps:Thin-Plate Splines and the Decomposition of Deformations》，以及由Rolf Sprengel、Karl Rohr和H.Siegfried Stiehl发表于Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society的《Thin-Plate Spline Approximation for Image Registration》。
在一个实施例中，可以用所述第二状态牙冠三维数字模型的控制点作为所述第一状态牙龈三维数字模型的对应控制点的新的位置，保持所述底座底面边缘上的控制点固定不动，基于此建立TPS形变方程，并利用该形变方程计算所述第二状态牙龈三维数字模型各顶点的坐标，重建得到所述第二状态牙龈三维数字模型。
所述第二状态牙冠三维数字模型与所述第一状态牙冠三维数字模型的至少一个牙冠的位姿不同，例如，所述第二状态牙冠三维数字模型可以是所述牙齿正畸治疗的任一矫治步的目标牙齿布局下的牙冠三维数字模型。
在进行形变处理时，所述第二状态牙冠三维数字模型中相对于所述第一状态牙冠三维数字模型位姿未发生变化的牙冠的牙洞线与所述第一状态牙龈三维数字模型的对应牙洞线重合。
在107中，将所述第二状态牙龈三维数字模型和第二状态牙冠三维数字模型合成得到第二状态牙颌三维数字模型。
经形变处理后得到的第二状态牙龈三维数字模型与第二状态牙冠三维数字模型的形变控制点重合，将两者合成即得到第二状态牙颌三维数字模型。
所述经形变处理得到的第二状态牙龈三维数字模型的相应形变控制点和所述第二状态牙冠三维数字模型的形变控制点重合，在一个实施例中，可以通过布尔运算将两者进行融合，以得到第二状态牙颌三维数字模型。
请参图5，为所述计算机程序的一个界面所展示的合成得到的第二状态牙颌三维数字模型。
本申请又一方面提供了一种壳状牙齿矫治器的制造方法，利用以上方法获得的一系列逐次的牙颌三维数字模型控制设备制作一系列逐次的阳模，然后以热压膜成型工艺在这一系列逐次的阳模上压膜获得一系列逐次的壳状矫治器。与传统方法制作获得的壳状牙齿矫治器相比，利用本申请的方法制作获得的壳状牙齿矫治器对于牙龈的贴合更加合适，不容易发生压迫牙龈或不贴合牙龈，尤其是两颗相邻牙齿间的牙龈。
在本申请的启示下，可以理解，除了用于制作壳状牙齿矫治器，本申请的方法还能用于产生其他用途的牙颌三维数字模型，例如，用于展示正畸治疗效果的牙颌三维数字模型。可以理解，对于不同的应用，所需的牙龈三维数字模型可能与以上的例子不同，例如，保留更多的真实牙龈部分，或者无需底座等。
本申请的又一方面提供了一种产生牙颌三维数字模型的方法，根据牙冠三维数字模型，对牙龈三维数字模型模板进行形变处理，然后，将所述牙冠三维数字模型和经形变处理的牙龈三维数字模型合成得到牙颌三维数字模型。以下结合附图对本申请一个实施例中的产生牙颌三维数字模型的方法进行详细说明。
请参图6，为本申请一个实施例中的产生牙颌三维数字模型的方法200的示意性流程图。
在一个实施例中，所述产生牙颌三维数字模型的方法200由计算机执行。本申请又一方面提供了一种用于产生牙颌三维数字模型计算机系统，其包括存储装置和处理器，其中，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行所述产生牙颌三维数字模型的方法200。
在201中，获取牙龈三维数字模型模板。
在一个实施例中，可以利用CAD软件制作一个具有牙龈基本形态的网格模型作为牙龈三维数字模型模板。该牙龈三维数字模型模板的顶点数量可以根据具体需求确定，顶点数量越多，模型可以拥有更多的细节，但形变处理的计算速度更慢，顶点数量越少反之。
在一个实施例中，该模型可以是左右面对称模型，因此，可以选只制作其中的左半部分或右半部分，另一半可以通过镜像的方式得到。
在一个实施例中，上、下颌即可以使用同一个基础模板。在又一实施例中，可以为上、下颌分别制作一个不同的模板(例如，上颌模板的厚度大于下颌模板的厚度)。
请参图7，为本申请一个实施例中用于产生牙颌三维数字模型的计算机程序的界面所展示的一个例子中的牙龈三维数字模型模板。
在203中，在所述牙龈三维数字模型模板上选取形变控制点。
在获取牙龈三维数字模型模板后，需要在其上选取一些形变控制点，作为后续形变处理的锚点。类似的，这些形变控制点也可以是左右面对称的，因此，只需要选取所述牙龈三维数字模型模板左半边或右半边的形变控制点，另一半的形变控制点可以通过镜像的方式得到。
在一个实施例中，可以在所述牙龈三维数字模型模板上选取以下点作为形变控制点：(一)所述牙龈三维数字模型模板底面边缘轮廓上的点，例如，以预定间隔或均匀采样形变控制点；(二)牙龈牙冠交接处的点，例如，在牙洞线上唇颊侧和舌侧的点，例如，每侧选取5个点；(三)相邻牙齿之间的点，例如，在所述牙龈三维数字模型模板上每两颗相邻牙冠之间选取一个形变控制点。
请参图8，为所述计算机程序的界面所展示的一个例子中的牙龈三维数字模型模板上的部分形变控制点。
在一个实施例中，可以人工选定所述形变控制点。在又一实施例中，也可以利用计算机自动选定所述形变控制点。
在205中，将所述牙龈三维数字模型模板的顶点映射至贴图坐标系。
为了给牙龈三维数字模型着色，使其外观接近真实牙龈，需要对其进行纹理贴图操作。
首先，需要制作纹理贴图。请参图9，为所述计算机程序的一个界面所展示的一个例子中的牙龈三维数字模型模板(左侧)上的部分形变控制点在纹理贴图(右侧)上的映射。
在一个实施例中，可以人工标定形变控制点在纹理贴图中的位置(即贴图坐标系中的坐标)。
在一个实施例中，可以利用Photoshop软件人工制作纹理贴图。
在一个实施例中，在标定了所述牙龈三维数字模型模板的形变控制点在贴图坐标系中的坐标之后，可以利用调和求参算法(Harmonic Map)计算出其余顶点的贴图坐标。其中，调和求参算法可参发表于SIGGRAPH'95:Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques September 1995的《Multiresolution Analysis of Arbitrary Meshes》。
在获得所述牙龈三维数字模型模板的所有顶点在所述贴图坐标系中的坐标之后，就能够利用OpenGL将所述贴图渲染在所述牙龈三维数字模型模板或经形变处理后得到的牙龈三维数字模型的表面，以获得与真实牙龈外观相似的牙龈三维数字模型。
在207中，根据牙冠三维数字模型对所述牙龈三维数字模型模板进行形变处理，得到牙龈三维数字模型。
在获得牙冠三维数字模型后，可以根据该牙冠三维数字模型的排列，对所述牙龈三维数字模型模板进行形变处理，以获得与所述牙冠三维数字模型相匹配的牙龈三维数字模型，这样，就能将两者合成得到牙颌三维数字模型。在一个实施例中，所述牙冠三维数字模型包括多个牙冠。
在一个实施例中，可以通过口内扫描或扫描印模或实体模型等方式，获得初始状态的牙冠三维数字模型。通过对所述初始状态的牙冠三维数字模型进行操作，以移动一颗或以上牙冠，可以获得不同牙齿布局的牙冠三维数字模型。
牙龈三维数字模型模板的每个象限有8个位置分别形成与对应牙冠相适应的凹入形态，然而，并非所有病例的每个象限都具有8颗牙齿，因此，需要修改所述牙龈三维数字模型模板，以消除掉多余的牙齿位置的凹入形态。对于每一象限只有7颗牙的情况，在一个实施例中，可以将所述牙龈三维数字模型模板末端多出的部分进行调和形态的计算，使得其变成一个圆润光滑且与非末端部分连续的形态，这样就去除了多余的牙位形态。
在一个实施例中，调和形态的算法可采用由Mario Botsch和Leif Kobbelt发表于SIGGRAPH'04:ACM SIGGRAPH 2004Papers August 2004Pages 630–634的《An Intuitive Framework for Real-Time Freeform Modeling》中所披露的算法，尤其是k为2阶的能量方程(即Thin Plate Surface)。
请参图10A，为所述计算机程序的界面所展示的一个例子中的牙龈三维数字模型模板；请再参图10B，展示了图10A的牙龈三维数字模型模板在两侧末端分别去除了一个牙位形态后的牙龈三维数字模型模板。
接着，可以计算牙冠三维数字模型的长和宽，并基于此，对所述牙龈三维数字模型模板进行缩放，使得变化后的牙龈三维数字模型模板与所述牙冠三维数字模型的轮廓基本重合。
然后，可以根据所述牙冠三维数字模型，改变所述牙龈三维数字模型模板的弓形。在一个实施例中，可以基于所述牙冠三维数字模型的牙位中心拟合出第一样条曲线，并在其上均匀采样预定数量的采样点(例如，10个采样点)作为形变锚点。同样，可以基于所述牙龈三维数字模型模板的牙位中心拟合出第二样条曲线，并在其上均匀采样同样数量的采样点作为形变锚点。再基于这两组形变锚点建立一个2D的TPS形变方程，把经缩放的牙龈三维数字模型模板和形变控制点进行2D的TPS形变处理，使得牙龈三维数字模型模板的弓形与所述牙冠三维数字模型的弓形相匹配。
请参图11A，为所述计算机程序的界面所展示的一个例子中的牙冠三维数字模型、第一样条曲线及其形变锚点。请参图11B，为所述计算机程序的界面所展示的一个例子中经缩放的牙龈三维数字模型模板、第二样条曲线及其形变锚点。
接着，可以对经弓形匹配的牙龈三维数字模型模板末端的多余部分进行2D缩放。请参图12A，为所述计算机程序的界面所展示的一个例子中在对末端进行2D缩放前的牙龈三维数字模型模板。请参图12B，为所述计算机程序的界面所展示的对图12A所示牙龈三维数字模型模板末端进行2D缩放后获得的牙龈三维数字模型模板。
然后，可以在所述牙冠三维数字模型上选取形变控制点。在一个实施例中，可以如此选取牙冠三维数字模型上的形变控制点：(一)在每一牙冠的牙洞线唇颊侧和舌侧分别选取预定数量的形变控制点(该预定数量与所述牙龈三维数字模型模板上对应部分的形变控制点数量相同，使得两者的形变控制点成一一对应关系)；(二)取每两颗邻牙牙洞线的最近点的连线的中点作为与所述牙龈三维数字模型模板上对应的相邻牙位之间的形变控制点相对应。牙洞线是牙冠边缘与牙龈交接处的轮廓线。
接着，以所述牙冠三维数字模型的形变控制点作为所述牙龈三维数字模型模板的对应形变控制点的新位置，保持所述牙龈三维数字模型模板底面边缘上的形变控制点不变，基于此建立形变方程，计算牙龈三维数字模型各顶点的坐标，得到与所述牙冠三维数字模型相匹配的牙龈三维数字模型。
在一个实施例中，在对所述牙龈三维数字模型模板进行形变处理时，可以基于所述牙冠三维数字模型各牙洞线中心点z坐标的平均值和所述牙龈三维数字模型模板各牙洞线中心点z坐标的平均值，来确定两者沿z轴的相对位置。
所述形变处理可以采用任何适用的针对网格模型的形变方法，包括但不限于TPS(Thin-Plate Splines)形变方法、拉普拉斯形变方法、刚体形变方法等。
在一个实施例中，可以采用TPS形变方法对所述牙龈三维数字模型模板进行形变处理。
TPS形变方法的具体实现可参由Fred L.Bookstein发表于IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11,No.6,June 1989的《Principal Warps:Thin-Plate Splines and the Decomposition of Deformations》，以及由Rolf Sprengel、Karl Rohr和H.Siegfried Stiehl发表于Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society的《Thin-Plate Spline Approximation for Image Registration》。
所述经形变处理得到的牙龈三维数字模型的相应形变控制点和所述牙冠三维数字模型的形变控制点重合，在一个实施例中，可以通过布尔运算将两者进行融合，以得到完整的牙颌三维数字模型。
[根据细则91更正 10.03.2023]
请参图13A，为所述计算机程序的界面所展示的一个例子中进行形变处理前的牙龈三维数字模型模板和牙冠三维数字模型。请参图13B，为所述计算机程序的界面所展示的图13A所示的牙龈三维数字模型模板经形变处理后得到的牙龈三维数字模型和所述牙冠三维数字模型合成的牙颌三维数字模型。
由于之前已经将所述牙龈三维数字模型模板上的顶点已经映射至贴图坐标系，因此，可以直接用OpenGL将所述纹理贴图渲染在所述牙龈三维数字模型表面，得到与真实牙龈接近的三维数字模型。
[根据细则91更正 10.03.2023]
请参图13C，为所述计算机程序的界面所展示的图13B所示牙颌三维数字模型经渲染后的效果。
可以理解，为不同的牙冠三维数字模型产生与之匹配的牙龈三维数字模型，只需要重复207即可，而无需重复201-205。
以制作壳状牙齿矫治器为例。利用壳状牙齿矫治器的牙科正畸治疗，是逐次佩戴一系列逐次的壳状牙齿矫治器，以将患者牙齿从原始布局逐渐地重新定位到第一中间布局、第二中间布局……最后中间布局直至目标布局。首先，获取一系列逐次的牙冠三维数字模型，分别表示一系列逐次的牙齿布局。然后，重复207，分别为这些牙冠三维数字模型的每一个产生一个与之匹配的牙龈三维数字模型。再将相匹配的牙冠三维数字模型和牙龈三维数字模型合成为牙颌三维数字模型。然后，利用这些牙颌三维数字模型控制设备制作阳模。最后，以热压膜成型工艺在这些阳模上压膜形成一系列逐次的壳状牙齿矫治器。
本申请的又一方面提供了一种产生牙齿三维数字模型的方法，通过平移、旋转以及缩放，使牙根三维数字模型模板与牙冠三维数字模型基本对齐，接着，对所述牙根三维数字模型模板进行形变处理，使其边缘贴合所述牙冠三维数字模型的边缘，再将所述牙冠三维数字模型和经形变处理的牙根三维数字模型融合得到封闭的完整的牙齿三维数字模型。以下结合附图对本申请一个实施例中的产生牙齿三维数字模型的方法进行详细说明。
请参图14，为本申请一个实施例中的产生牙齿三维数字模型的方法300的示意性流程图。
在301中，获取牙冠三维数字模型。
在一个实施例中，可以通过口内扫描，或扫描印模或牙齿实体模型等方式，获得牙冠三维数字模型。通常，扫描得到的是整个牙列的三维数字模型(即上颌牙列或下颌牙列)，通过对其进行分割得到单颗牙冠的三维数字模型。
请参图15，为本申请一个实施例中用于产生牙齿三维数字模型的计算机程序的一个界面所展示的一个例子中的牙冠三维数字模型。
在303中，获取牙根三维数字模型模板。
在一个实施例中，可以利用锥形束计算机X线体层摄影(Cone Beam Computed Tomography，简称CBCT)对大量真实牙根进行扫描获得相应的牙根三维数字模型，然后，对对应牙号的牙根三维数字模型求平均，得到该对应牙号牙根三维数字模型模板。
在不缺牙的情况下，上、下颌牙列分别有16颗牙齿，由于左右对称，只需要为上、下颌分别建立8个牙根三维数字模型模板即可。
请参图16，为所述计算机程序的一个界面所展示的一个例子中上颌牙列的1-8号牙的牙根三维数字模型模板。
根据所述牙冠的牙号，选择对应的牙根三维数字模型模板，用于产生完整的牙齿三维数字模型。
在305中，根据所述牙冠三维数字模型的尺寸，对所述牙根三维数字模型模板进行缩放。
在一些情况下，所述牙根三维数字模型模板的尺寸不一定与所述牙冠的尺寸相符，此时，可以对牙根三维数字模型模板进行缩放，使其尺寸与所述牙冠的尺寸相符，以保证后续产生的完整的牙齿三维数字模型的形态比较自然。
在一个实施例中，可以通过以下方法确定缩放比例，将牙冠边缘投影到XY平面并计算包围盒的对角线长度，同样地，将牙根的边缘也投影到XY平面并计算包围盒对角线长度，将牙冠投影包围盒的对角线长度除以牙根包围盒的对角线长度得到的比值作为牙根三维缩放的比例。
在一个实施例中，在对所述牙根三维数字模型模板进行缩放之前，可以通过平移和旋转使其对准所述牙冠三维数字模型，使得两者长轴平行，近远中方向一致，并且边缘的中心基本重合。
请参图17A，为所述计算机程序的一个界面所展示的一个例子中对准的牙冠三维数字模型和经缩放的牙根三维数字模型模板。
在307中，基于所述牙冠三维数字模型的边缘，对所述经缩放的牙根三维数字模型模板进行形变处理。
在一个实施例中，可以在所述牙冠三维数字模型的边缘(即牙洞线)上选定多个形变控制点，并在所述经缩放的牙根三维数字模型模板的边缘上选定对应的形变控制点，然后，以所述牙冠三维数字模型的形变控制点作为所述牙根三维数字模型模板的对应形变控制点的新位置，并基于此建立形变方程，对所述牙根三维数字模型模板进行形变处理，得到与所述牙冠三维数字模型相匹配的牙根三维数字模型。
在一个实施例中，可以如此选取所述牙冠三维数字模型和牙根三维数字模型模板上的形变控制点：在所述牙冠三维数字模型的边缘线上均匀采样N个(例如，30个)点作为所述牙冠三维数字模型的形变控制点，在所述三根三维数字模型模板的边缘线上也相应地均匀采样N个点作为所述牙根三维数字模型模板的形变控制点。
所述形变处理可以采用任何适用的针对网格模型的形变方法，包括但不限于TPS(Thin-Plate Splines)形变方法、拉普拉斯形变方法、刚体形变方法等。
在一个实施例中，可以采用TPS形变方法对所述第一状态牙龈三维数字模型进行形变处理。
TPS形变方法的具体实现可参由Fred L.Bookstein发表于IEEE Transactions On Pattern Analysis and Machine Intelligence.Vol.11,No.6,June 1989的《Principal Warps:Thin-Plate Splines and the Decomposition of Deformations》，以及由Rolf Sprengel、Karl Rohr和H.Siegfried Stiehl发表于Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society的《Thin-Plate Spline Approximation for Image Registration》。
请参图17B，为所述计算机程序的一个界面所展示的图17A所示牙根三维数字模型经形变处理后得到的牙根三维数字模型与图17A所示的牙冠三维数字模型。
在309中，将所述牙冠三维数字模型和所述牙根三维数字模型进行缝合。
虽然，所述经形变处理得到的牙根三维数字模型的边缘和所述牙冠三维数字模型的边缘基本重合，但两者边缘上除形变控制点之外的其他点可能并不重合。因此，可以通过网格模型缝合的方式将两者进行缝合，以得到完整的封闭的牙齿三维数字模型。
请参图17C，为所述计算机程序的一个界面所展示的图17B所示的牙冠三维数字模型和牙根三维数字模型缝合后得到的牙齿三维数字模型。
在311中，对所述牙齿三维数字模型牙根与牙冠邻接的区域进行形态调和。
为了使得所述牙齿三维数字模型的牙根和牙冠之间的衔接更加自然，在一个实施例中，可以对牙根上与牙冠邻接的区域进行形态调和。在一个实施例中，可以对牙冠边缘线以下预定距离的区域进行形态调和，例如，牙冠边缘线以下2mm的区域。可以理解，这个预定距离可以根据具体需求和情况确定。
在一个实施例中，调和形态的算法可采用由Mario Botsch和Leif Kobbelt发表于SIGGRAPH'04:ACM SIGGRAPH 2004Papers的《An Intuitive Framework for Real-Time Freeform Modeling》所披露的算法，尤其是k为2阶的能量方程(即Thin Plate Surface)。
请参图17D，为所述计算机程序的一个界面所展示的图17C所示牙齿三维数字模型的与牙冠邻接的部分牙根区域经形态调和后得到的牙齿三维数字模型。
上述产生牙齿三维数字模型的方法300是针对单颗牙齿。在利用该方法产生一个牙列的多颗牙齿的三维数字模型之后，相邻牙齿三维数字模型的牙根之间可能存在碰撞，此时，可以对存在碰撞的牙根进行处理，以消除碰撞。在一个实施例中，上述产生牙齿三维数字模型的方法300可以进一步包括碰撞解除的操作。在一个实施例中，可以采用以下方法消除牙根之间的碰撞。
对于每一对相邻牙齿，首先，检测它们之间是否存在碰撞关系，若存在碰撞，则计算它们之间的最大碰撞深度，并根据该最大碰撞深度和预定的阈值，将该碰撞归类为温和碰撞(最大碰撞深度小于所述阈值)或剧烈碰撞(最大碰撞深度大于所述阈值)。
对于温和碰撞，找到所有的碰撞点以及周围邻接点(例如，一阶邻接点或二阶邻接点)，然后，将每个这些点向其法向量的反方向移动一定距离(该距离根据碰撞深度决定，例如，碰撞深度的0.6倍)。最后，对所有涉及到的点进行调和以及平滑操作。
对于剧烈碰撞，根据最大碰撞点的高度确定牙根中需要移动的点。在一个实施例中，可以将牙根沿高度方向分为根颈区域、根中区域以及根尖区域，各占总高度的1/3。可以根据最大碰撞点到根尖的垂直距离占牙根总高度的比例在根尖区域确定哪些是需要移动的点(在该实施例中，只有根尖区域的点才会被选为移动点)。例如，当所述比例为1/5时，那么，根尖区域底部1/5区域的所有点为移动点，其他根尖区域的点、根中区域和根颈区域的点为随动点，牙冠上的点为不动点。也就是说，最大碰撞点距离牙根尖越远，需要移动的点越多。最后，根据最大碰撞点的碰撞深度决定所述需要移动的点的移动距离(例如，移动距离可以是最大碰撞深度)，根据最大碰撞点的位置决定所述需要移动的点的位移方向(例如，位移方向可以是沿最大碰撞点连线的方向)，并对该网格进行网格形变(例如，拉普拉斯形变)等操作。
上述操作之后，并不能保证完全解决碰撞，因为可能存在碰撞关系由剧烈碰撞转为温和碰撞的情况，或产生新的碰撞关系。因此，可以进行迭代操作，直至消除所有碰撞。
请参图18A，为所述计算机程序的一个界面所展示的一个例子中的牙根之间存在碰撞的两颗相邻牙齿的三维数字模型。
请参图18B，为所述计算机程序的一个界面所展示的图18A所示两颗牙齿的三维数字模型经碰撞解除后的样子。
在一个实施例中，上述方法的所有操作可以由计算机执行。
本申请又一方面提供了一种用于产生牙颌三维数字模型的计算机系统，其包括存储装置和处理器，其中，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行所述产生牙齿三维数字模型的方法300。
尽管在此公开了本申请的多个方面和实施例，但在本申请的启发下，本申请的其他方面和实施例对于本领域技术人员而言也是显而易见的。在此公开的各个方面和实施例仅用于说明目的，而非限制目的。本申请的保护范围和主旨仅通过后附的权利要求书来确定。
同样，各个图表可以示出所公开的方法和系统的示例性架构或其他配置，其有助于理解可包含在所公开的方法和系统中的特征和功能。要求保护的内容并不限于所示的示例性架构或配置，而所希望的特征可以用各种替代架构和配置来实现。除此之外，对于流程图、功能性描述和方法权利要求，这里所给出的方框顺序不应限于以同样的顺序实施以执行所述功能的各种实施例，除非在上下文中明确指出。
除非另外明确指出，本文中所使用的术语和短语及其变体均应解释为开放式的，而不是限制性的。在一些实例中，诸如“一个或多个”、“至少”、“但不限于”这样的扩展性词汇和短语或者其他类似用语的出现不应理解为在可能没有这种扩展性用语的示例中意图或者需要表示缩窄的情况。

Claims (44)

  1. 一种计算机执行的产生牙龈三维数字模型的方法，其包括：
    获取第一状态牙龈三维数字模型；以及
    基于所述第一状态牙龈三维数字模型的形变控制点和第二状态牙冠三维数字模型的形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第二状态牙龈三维数字模型，
    其中，同一状态的牙冠三维数字模型和牙龈三维数字模型的对应形变控制点重合。
  2. 如权利要求1所述的产生牙龈三维数字模型的方法，其特征在于，所述形变处理是将所述第二状态牙冠三维数字模型的形变控制点作为所述第一状态牙龈三维数字模型的对应形变控制点的新位置，基于此建立形变方程，计算所述第二状态牙龈三维数字模型各顶点的坐标。
  3. 如权利要求2所述的产生牙龈三维数字模型的方法，其特征在于，所述牙龈三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙龈三维数字模型牙洞线上的形变控制点与所述牙冠三维数字模型牙洞线上的形变控制点一一对应。
  4. 如权利要求3所述的产生牙龈三维数字模型的方法，其特征在于，所述牙龈三维数字模型的形变控制点还包括底面边缘线上的形变控制点，在所述形变处理中，所述底面边缘线上的形变控制点保持不动。
  5. 如权利要求1所述的产生牙龈三维数字模型的方法，其特征在于，所述形变处理是基于TPS形变方法。
  6. 如权利要求1所述的产生牙龈三维数字模型的方法，其特征在于，所述第一状态是初始状态。
  7. 如权利要求6所述的产生牙龈三维数字模型的方法，其特征在于，所述形变控制点是在初始状态牙颌三维数字模型上采样获得。
  8. 如权利要求7所述的产生牙龈三维数字模型的方法，其特征在于，所述形变控制点是按预定数量均匀采样获得。
  9. 如权利要求7所述的产生牙龈三维数字模型的方法，其特征在于，所述初始状态牙颌三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
  10. 如权利要求6所述的产生牙龈三维数字模型的方法，其特征在于，所述第一状态牙龈三维数字模型包括真实牙龈部分和底座，其中，所述真实牙龈部分与牙冠相接，位于所述底座之上。
  11. 如权利要求10所述的产生牙龈三维数字模型的方法，其特征在于，所述真实牙龈部分是自牙龈线预定距离内的牙龈部分。
  12. 如权利要求1所述的产生牙龈三维数字模型的方法，其特征在于，所述第一状态是初始状态，所述方法还包括：
    获取多个逐次状态的牙冠三维数字模型；以及
    重复上述操作，产生多个逐次状态的牙龈三维数字模型，其每一个是基于所述第一状态牙龈三维数字模型以及所述多个逐次状态的牙冠三维数字模型中相对应的一个而产生。
  13. 一种产生牙颌三维数字模型的方法，其包括：将权利要求1所述的产生牙龈三维数字模型的方法所产生的所述第二状态牙龈三维数字模型和所述第二状态牙冠三维数字模型合成得到第二状态牙颌三维数字模型。
  14. 一种壳状牙齿矫治器的制作方法，其包括：利用权利要求13所述的产生牙颌三维数字模型的方法所产生的第二状态牙颌三维数字模型控制设备制作壳状牙齿矫治器。
  15. 一种用于产生牙龈三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器运行后，将执行如权利要求1所述的产生牙龈三维数字模型的方法。
  16. 一种计算机执行的产生牙龈三维数字模型的方法，其包括：
    获取牙龈三维数字模型模板；
    获取牙冠三维数字模型；以及
    基于所述牙龈三维数字模型模板上的形变控制点和所述牙冠三维数字模型的形变控制点，对所述牙龈三维数字模型模板进行三维形变处理，得到与所述牙冠三维数字模型相匹配的牙龈三维数字模型。
  17. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，所述形变处理是以所述牙冠三维数字模型的形变控制点作为所述牙龈三维数字模型模板的对应形变控制点的新的位置，基于此建立三维形变方程，计算所述牙龈三维数字模型各顶点的坐标。
  18. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，所述牙龈三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的形变控制点包括牙洞线上的形变控制点，所述牙冠三维数字模型的牙洞线上的形变控制点与所述牙龈三维数字模型模板的牙洞线上的形变控制点一一对应。
  19. 如权利要求18所述的产生牙龈三维数字模型的方法，其特征在于，所述牙龈三维数字模型的形变控制点还包括每两个相邻牙位之间的形变控制点，所述牙冠三维数字模型的形变控制点还包括每两个相邻牙冠之间的形变控制点，所述牙冠三维数字模型的相邻牙冠间的形变控制点与所述牙龈三维数字模型的相邻牙位之间的形变控制点一一对应。
  20. 如权利要求18所述的产生牙龈三维数字模型的方法，其特征在于，所述牙龈三维数字模型的形变控制点还包括其底面边缘线上的形变控制点，在所述三维形变处理中，所述牙龈三维数字模型模板底面边缘线上的形变控制点保持不动。
  21. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，所述三维形变处理是基于TPS形变方法。
  22. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，它还包括：根据所述牙冠三维数字模型调整所述牙龈三维数字模型模板的牙位数量，所述三维形变处理是基于经调整牙位数量后的牙龈三维数字模型模板。
  23. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，它还 包括：根据所述牙冠三维数字模型对所述牙龈三维数字模型模板进行缩放，使所述牙龈三维数字模型模板与所述牙冠三维数字模型的轮廓基本重合，所述三维形变处理是基于经缩放的牙龈三维数字模型模板。
  24. 如权利要求20所述的产生牙龈三维数字模型的方法，其特征在于，它还包括：根据所述牙冠三维数字模型，调整所述经缩放的牙龈三维数字模型模板的弓形。
  25. 如权利要求24所述的产生牙龈三维数字模型的方法，其特征在于，对所述牙龈三维数字模型模板的弓形调整包括：
    基于所述牙冠三维数字模型的牙洞线中心拟合得到第一样条曲线，并在其上均匀采样N个形变控制点；
    基于所述牙龈三维数字模型模板的牙位中心拟合得到第二样条曲线，并在其上均匀采样N个形变控制点；以及
    基于所述第一样条曲线上的形变锚点和所述第二样条曲线上的形变锚点建立形变方程，对所述牙龈三维数字模型模板及其形变控制点进行二维形变处理。
  26. 如权利要求25所述的产生牙龈三维数字模型的方法，其特征在于，所述二维形变处理是基于TPS形变方法。
  27. 如权利要求24所述的产生牙龈三维数字模型的方法，其特征在于，它还包括：对所述经调整弓形的牙龈三维数字模型模板的末端进行二维缩放。
  28. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，它还包括：
    基于所述牙龈三维数字模型模板的形变控制点在纹理贴图上的映射，以调和求参算法计算所述牙龈三维数字模型模板所有顶点在所述纹理贴图上的映射；以及
    基于所述映射关系，对所述牙龈三维数字模型进行纹理贴图操作。
  29. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，所述牙冠三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
  30. 如权利要求16所述的产生牙龈三维数字模型的方法，其特征在于，它还包括：
    获取多个逐次的牙冠三维数字模型，分别代表多个逐次的牙齿布局；以及
    分别基于所述多个逐次的牙冠三维数字模型，对所述牙冠三维数字模型模板进行形变处理，产生多个逐次的牙龈三维数字模型。
  31. 一种产生牙颌三维数字模型的方法，其包括：将权利要求16所述的牙龈三维数字模型和牙冠三维数字模型合成得到牙颌三维数字模型。
  32. 一种壳状牙齿矫治器的制作方法，其包括：利用权利要求31所述的牙颌三维数字模型控制设备制作壳状牙齿矫治器。
  33. 一种用于产生牙龈三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行如权利要求16所述的产生牙龈三维数字模型的方法。
  34. 一种计算机执行的产生牙齿三维数字模型的方法，其包括：
    获取牙冠三维数字模型；
    获取牙根三维数字模型模板；
    基于所述牙根三维数字模型模板的边缘线上的N个形变控制点和所述牙冠三维数字模型的边缘线上对应的N个形变控制点，对所述牙根三维数字模型模板进行形变处理，得到与所述牙冠三维数字模型相匹配的牙根三维数字模型；以及
    将所述牙冠三维数字模型和所述牙根三维数字模型的边缘进行缝合，得到完整的牙齿三维数字模型，其中，所述N是自然数。
  35. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，所述牙根三维数字模型模板是对相应牙号的多个真实牙根的三维数字模型求平均获得。
  36. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，它还包括：在所述形变处理之前，通过平移和/或旋转使所述牙根三维数字模型模板与所述牙冠三维数字对准，使两者近远中方向一致，并且长轴平行。
  37. 如权利要求36所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，它还包括：在所述对准之后，对所述牙根三维数字模型模板进行缩放，使其尺寸与所述牙冠三维数字模型基本匹配。
  38. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，它还包括：对所述牙齿三维数字模型的与所述牙冠邻接的部分牙根区域进行形态调和，使得所述牙冠和牙根之间的衔接更自然。
  39. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，所述形变处理包括：以所述牙冠三维数字模型的形变控制点作为所述牙根三维数字模型模板的对应形变控制点的新位置，基于此建立三维形变方程，计算所述牙根三维数字模型模板各顶点的新的位置。
  40. 如权利要求39所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，所述三维形变处理是基于TPS形变方法。
  41. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，所述牙冠三维数字模型是通过扫描以下之一获得：患者的牙颌、牙颌印模以及牙颌实体模型。
  42. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，所述牙冠三维数字模型的边缘线上的N个控制点是均匀采样获得，所述牙根三维数字模型模板的边缘线上的N个控制点是均匀采样获得。
  43. 如权利要求34所述的计算机执行的产生牙齿三维数字模型的方法，其特征在于，它还包括：
    利用如权利要求34所述的方法产生两颗相邻牙齿的三维数字模型；
    检测所述两颗相邻牙齿的三维数字模型的牙根之间是否存在碰撞，若存在碰撞，则基于预定的阈值和碰撞深度，将该碰撞归类为温和碰撞或剧烈碰撞；
    若所述碰撞为温和碰撞，那么，找到所有碰撞点及其周围邻接点，将每个这些点向其法向量的反方向移动根据所述碰撞深度确定的距离，并对所有涉及的点进行形态调和及平滑操作；
    若所述碰撞为剧烈碰撞，那么，根据最大碰撞点的高度确定所述两个牙根中需要移动的点，将这些需要移动的点沿最大碰撞点连线的方向移动根据最大碰撞深度确定的距离，并对所述两个牙根上的其他点进行形态调和操作。
  44. 一种用于产生牙齿三维数字模型的计算机系统，其包括存储装置和处理器，所述存储装置存储有一计算机程序，当其被所述处理器执行后，将执行如权利要求34所述的产生牙齿三维数字模型的方法。
PCT/CN2023/073409 2022-01-25 2023-01-20 产生牙颌三维数字模型的方法 WO2023143461A1 (zh)

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