WO2023179224A1 - 产生牙龈三维数字模型的方法 - Google Patents

产生牙龈三维数字模型的方法 Download PDF

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Publication number
WO2023179224A1
WO2023179224A1 PCT/CN2023/075000 CN2023075000W WO2023179224A1 WO 2023179224 A1 WO2023179224 A1 WO 2023179224A1 CN 2023075000 W CN2023075000 W CN 2023075000W WO 2023179224 A1 WO2023179224 A1 WO 2023179224A1
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digital model
dimensional digital
state
deformation
control points
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PCT/CN2023/075000
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English (en)
French (fr)
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沈恺迪
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杭州朝厚信息科技有限公司
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Publication of WO2023179224A1 publication Critical patent/WO2023179224A1/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
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/10—Segmentation; Edge detection
    • G06T7/12—Edge-based segmentation

Definitions

  • the present application generally relates to a method of generating a three-dimensional digital model of the gums.
  • the three-dimensional digital model of the tooth includes the crown part and the gingiva part.
  • the crown portion can be obtained by intraoral scanning, or by scanning an impression or physical model of the patient's tooth.
  • the three-dimensional digital model of the gums in the subsequent state is generally based on the three-dimensional digital model of the gums in the initial state or the previous state, based on the same control points on the cavity line in two different states. , perform deformation processing on the three-dimensional digital model of the gums to obtain the three-dimensional digital model of the gums in the subsequent state.
  • the three-dimensional digital model of the gums produced through this method has kinks and mold penetration.
  • One aspect of the present application provides a computer-executed method for generating a three-dimensional gingival digital model, which includes: obtaining a first-state three-dimensional gingival digital model; The method samples to obtain a first set of deformation control points; obtains a second state dental crown three-dimensional digital model; and uses the first method to sample and obtain a second group of deformation control points on the dental cavity line of the second state dental crown three-dimensional digital model. ; And based on the first group and the second group of deformation control points, perform deformation processing on the first state gingival three-dimensional digital model to obtain a second state gingival three-dimensional digital model, wherein the first group The number is equal to the second group of deformation control points.
  • the deformation processing is to use the second set of deformation control points as new positions of the first set of deformation control points, establish a deformation equation based on this, and calculate each element of the second state gingival three-dimensional digital model. The coordinates of the vertex.
  • the method of generating a three-dimensional gingival digital model further includes: sampling on the bottom contour line of the first state gingival three-dimensional digital model to obtain a third set of deformation control points, during the deformation processing, The third group of deformation control points remains unchanged.
  • the deformation processing is based on one of the following deformation methods: TPS deformation method, Laplacian deformation method, and rigid body deformation method.
  • the first state is an initial state.
  • the method of generating a three-dimensional digital model of the gums further includes: obtaining a three-dimensional digital model of the dental crown in the third state; The method samples and obtains a fourth group of deformation control points; and based on the first group and the fourth group of deformation control points, performs deformation processing on the first state gingival three-dimensional digital model to obtain a third state gingival three-dimensional digital model, wherein, The number of the fourth group and the second group of deformation control points is equal, and the first to third states are successive states.
  • the first method includes: dividing the labial and buccal segments and the lingual segments on the dental cavity lines corresponding to each crown, and for the two terminal crowns, dividing the dental cavity lines on the labial
  • the end section between the buccal section and the lingual section is used as the end section; and N 1 deformation control points are respectively sampled on each of the buccal and lingual sections, and on each end N 2 deformation points are sampled on the segment to obtain a set of deformation control points, where N 1 and N 2 are predetermined natural numbers.
  • the sampling is uniform sampling.
  • Another aspect of the present application provides a method for generating a three-dimensional digital model of teeth and jaws, which includes: fusing the three-dimensional digital model of the second state gingiva and the three-dimensional digital model of the second state dental crowns to obtain the second state three-dimensional digital model of the teeth and jaws. 3D digital model.
  • Another aspect of the present application provides a method for making a physical model of the teeth and jaws, which includes: using the three-dimensional digital model control device of the teeth and jaws in the second state to make a physical model of the teeth and jaws in the second state.
  • the apparatus is a stereolithography apparatus.
  • Figure 1 is a schematic flow chart of a method for generating a three-dimensional digital model of gums in one embodiment of the present application
  • Figure 2 is an example of a three-dimensional digital model of the crown of the mandibular dentition shown in an interface of a computer program used to generate a three-dimensional digital model of gums in an embodiment of the present application;
  • Figure 3 is a complete outline of the bottom surface of the three-dimensional digital model of the gums in an example shown in an interface of the computer program;
  • Figure 4 schematically shows the labial and buccal segments, lingual segments, adjacent segments with adjacent teeth, and terminal segments of the cavity line of the last tooth on one side of the dental arch in an example
  • Figure 5 is a side grid of a three-dimensional digital model of the gums in an example shown in an interface of the computer program
  • Figure 6 is a top mesh of a three-dimensional digital model of gums in an example of an interface to the computer program.
  • Figure 7 shows the bottom mesh of a three-dimensional digital model of gums in an example of an interface of the computer program.
  • One aspect of the present application provides a method for generating a three-dimensional digital model of the gums. Based on the projection of the three-dimensional digital model of the dental crown along the height direction of the gums, the outline of the bottom surface of the three-dimensional digital model of the gums is generated. Sampling a first predetermined number of points on the contour line of the hole line and the bottom surface of the gum three-dimensional digital model, obtaining the first predetermined number of point pairs, generating a convex curve based on each of the point pairs, and in each A second predetermined number of points are sampled on the curve, and the dental cavity line, contour line, and sampling points on the curve are sequentially connected to obtain a lateral grid of the three-dimensional digital model of the gums.
  • the cavity line is the edge outline where the crown of the tooth meets the gums.
  • FIG. 1 is a schematic flow chart of a method 100 for generating a three-dimensional digital model of gums in an embodiment of the present application.
  • the method 100 of generating a three-dimensional digital model of gums is performed by a computer.
  • a computer system for generating a three-dimensional digital model of gums which includes a storage device and a processor, wherein the storage device stores a computer program, which when executed by the processor , the method 100 for generating a three-dimensional digital model of gums will be executed.
  • the three-dimensional digital model of the dental crown includes a three-dimensional digital model of the dental crown of the patient's complete dentition (ie, maxillary dentition or mandibular dentition).
  • the three-dimensional digital model of the dental crown can be obtained through intraoral scanning, or by scanning a dental impression or physical model. After scanning a three-dimensional digital model of the crown of the complete tooth row, it can be segmented to make each crown independent of each other, so that any crown can be moved independently.
  • FIG. 2 shows an example of a three-dimensional digital model of the dental crown of the mandibular dentition in an interface of a computer program used to generate a three-dimensional digital model of gums according to an embodiment of the present application.
  • the outline of the bottom of the three-dimensional digital model of the gums is generated based on the three-dimensional digital model of the dental crown.
  • the direction perpendicular to the occlusal surface may be taken as the height direction of the gums.
  • the world coordinate system can be established as follows, using the occlusal surface as the plane where the X-axis and Y-axis are located, and the geometric center of the three-dimensional digital model of the dental crown (that is, the mean of all vertices) as the origin of the world coordinate system. Make the Y-axis approximately parallel to the dental arch axis of symmetry. In light of this application, it will be understood that in addition to this example, any other suitable way can be used to determine the height direction of the gums and establish the world coordinate system.
  • a contour line of the bottom surface of the three-dimensional digital model of the gums can be generated.
  • the inner contour of the bottom surface of the three-dimensional digital model of the gums can be generated first.
  • ⁇ 1 may be 2 mm. It is understood that the value of ⁇ 1 can be adjusted according to specific needs and circumstances.
  • a third-order Bezier curve is generated based on the initial landmark point.
  • the third-order Bezier curve can be generated as follows: the last two landmark points are used as the two control points of the third-order Bezier curve, and the other two control points are calculated based on all landmark points. , so that the sum of the distances between the Bezier curve generated based on the four control points and all landmark points is the smallest.
  • k may be 2.
  • the k value may not be set, and the iteration may be continued until the landmark point is no longer updated.
  • the purpose of the iteration is to make the inner contour line as close as possible to the dental arch, and to make the projection of the dental crown on the XY plane as far as possible outside the inner contour line.
  • the final third-order Bezier curve was used as the inner contour of the bottom surface of the gingival three-dimensional digital model.
  • a third-order Bezier curve is generated based on the initial landmark point.
  • the third-order Bezier curve can be generated as follows: the last two landmark points are used as the two control points of the third-order Bezier curve, and the other two control points are calculated based on all landmark points. , so that the sum of the distances between the Bezier curve generated based on the four control points and all landmark points is the smallest.
  • ⁇ 2 and ⁇ 3 may be 2 mm. It is understood that the values of ⁇ 2 and ⁇ 3 can be adjusted according to specific needs and circumstances.
  • the final third-order Bezier curve is used as the outer contour of the bottom surface of the gingival three-dimensional digital model.
  • a connecting line between the inner and outer contours can be generated to obtain a complete contour of the bottom surface of the three-dimensional digital model of the gums.
  • the following method can be used to generate the connecting line of the inner and outer contours. Move the midpoint of the endpoints on the same side of the inner and outer contours along the Y-axis toward the dental arch opening direction by a predetermined distance, for example, 2 mm. Then, using this point and the corresponding two endpoints as control points, a second-order Bezier curve is generated as the connecting line between the inner and outer contours on this side.
  • a predetermined distance for example, 2 mm.
  • Figure 3 shows the complete contour line of the bottom surface of the three-dimensional digital model of the gums in an example shown in an interface of the computer program, and the control points a 1 , b 1 , c 1 and d 1 corresponding to the inner contour line.
  • the control points a 2 , b 2 , c 2 and d 2 corresponding to the outer contour line, the control points a 1 , a 2 and e 1 of the left connecting line, and the control points d 1 , d 2 and e of the right connecting line 2 .
  • each crown can be projected onto the XY plane, and the point closest to the origin of the coordinate system can be used as the initial landmark point for generating the inner contour, and the point farthest from the origin of the coordinate system can be used as the initial landmark point. Points serve as initial landmark points for generating outer contours.
  • a three-dimensional digital model of the gums is generated based on the cavity line of the three-dimensional dental crown digital model and the contour line of the bottom surface of the three-dimensional gum three-dimensional digital model.
  • a labial and buccal segment and a lingual segment can be divided on the cavity line based on the positional relationship between the crown and the adjacent teeth, and the labial segment of the cavity line of these crowns can be divided into two segments.
  • the contour lines of the buccal segment and the lingual segment and the bottom surface of the three-dimensional digital model of the gums generate a grid on the side of the three-dimensional digital model of the gums.
  • a distance threshold can be defined first. For a crown with adjacent teeth on both sides, find a point on the cavity line where the distance from the adjacent teeth is less than the distance threshold. Based on this, the cavity line is divided into four segments, namely the labial and buccal segments, and the lingual segment. The lateral segment and the two adjacent segments adjacent to the adjacent teeth on both sides. For the crown at both ends, find points on the cavity line whose distance from the adjacent teeth is less than the distance threshold, and a predetermined number (can be determined according to the specific situation and needs, for example, 8-12 points) with the adjacent teeth. Based on this point, the tooth cavity line is divided into four segments, namely the labial and buccal segment, the lingual segment, the adjacent segment with adjacent teeth, and the terminal segment.
  • Figure 4 schematically shows the labial and buccal segments, the lingual segments, the adjacent segments with adjacent teeth, and the terminal segment of the cavity line of the two most distal teeth on one side of the dental arch in an example.
  • the points on the cavity line of a crown that are closer to the adjacent teeth than the distance threshold can be calculated. For each point on the cavity line of the current crown, the distance between the adjacent tooth cavity line and the distance between the adjacent teeth is calculated. most recently point, if the distance between the two is less than the distance threshold, then the point on the cavity line of the current crown is regarded as the point whose distance from the adjacent tooth is less than the distance threshold.
  • the distance threshold can be given according to specific circumstances and needs, for example, the distance threshold can range from 0.5 mm to 1/3 of the mesial and distal length of the crown, for example, 1 mm.
  • the contour line can be segmented as follows: for a crown, the points on the cavity line closest to the cavity lines of the adjacent tooth crowns on both sides are respectively calculated, and then, within the Find the closest points to the two points on the contour line, and use the section of the inner contour line between the two points as the section corresponding to the lingual section of the cavity line of the dental crown; similarly , respectively find the two closest points to the adjacent teeth on the outer contour line, and use the section of the outer contour line between the two points as the labial and cheek line with the dental cavity line of the dental crown.
  • the section between the distal endpoints of the segments on the inner and outer contours corresponding to the lingual and labial sections of the cavity line of the terminal crown can be used as The segment corresponding to the distal segment of the cavity line of the distal crown.
  • any other suitable method may be used to segment the bottom surface contour line.
  • the labial and buccal segments and the lingual segments of the cavity line of each crown can be projected onto the XY plane, and the intersections of the normals of their endpoints and the inner and outer contours of the base contour can be Segmentation.
  • the base contour line and the cavity line can be located respectively.
  • a predetermined number of points are sampled on each segment, wherein the same number of points are sampled on two corresponding segments.
  • N 1 points can be sampled on each buccal and lingual segment
  • N 1 points can also be sampled on the corresponding segment on the base contour line
  • N 2 points can be sampled on each end segment.
  • N 2 points are also sampled on the corresponding segment on the bottom contour line.
  • the sampling may be uniform sampling.
  • sampling points on the dental cavity line and the corresponding number of sampling points on the bottom contour line form a one-to-one corresponding point pair in sequence.
  • the upper edge of the labial and buccal side of the dental cavity line clockwise
  • the third sampling point and the third sampling point in the clockwise direction on the section of the bottom surface contour corresponding to the lip and buccal section form a point pair.
  • a convex curve is generated.
  • a control point can be obtained by moving the bottom point of a point pair (that is, the point located on the bottom contour line) along its normal vector toward the outside of the gum by a predetermined distance, and then moving the control point along the Z axis. Move the average Z coordinate of the bottom point and the top point toward the top point of the point pair (ie, the point located on the cavity line) to obtain another control point.
  • the predetermined distance can be determined according to specific conditions and needs, for example, 2 mm.
  • the top point, bottom point and two calculated control points are used as four control points to generate a third-order Bezier curve.
  • FIG. 5 is a side mesh of a three-dimensional digital model of the gums in an example shown in an interface of the computer program.
  • N 1 , N 2 and N 3 can be determined according to the mesh accuracy requirements for the three-dimensional digital model of the gums.
  • a top mesh can be created for the three-dimensional digital model of the gingiva.
  • N 2 points can be sampled respectively on the adjacent segments/terminal segments on both sides of the cavity line.
  • N 1 points on the labial and buccal segments and the lingual segment of the dental cavity line are connected in one-to-one correspondence, and N 2 points are sampled on each connecting line.
  • the adjacent segments/terminal segments, labial and buccal segments, lingual segments and sampling points on the connecting lines are connected in order to form the top grid of the three-dimensional digital model of the gums.
  • FIG. 6 is a top mesh of a three-dimensional digital model of gums in an example shown in an interface of the computer program.
  • a base mesh can be created for the 3D digital model of the gums.
  • the sampling points on the bottom contour line can be divided into equal numbers of inner and outer parts of the dental arch, and then these sampling points are connected in sequence to form the bottom grid of the three-dimensional digital model of the gums.
  • FIG. 7 is a bottom mesh of a three-dimensional digital model of gums in an example displayed on an interface of the computer program.
  • the three-dimensional digital model of the dental crowns shown in Figure 2 is the three-dimensional digital model of the dental crowns in the first state, that is, these crowns are in the first tooth layout.
  • the generated corresponding three-dimensional digital model of the gums is the three-dimensional digital model of the gums in the first state.
  • the patient wears a series of successive shell appliances to gradually reposition the teeth from their original layout to a first intermediate layout, a second intermediate layout... ...and finally the intermediate layout up to the target layout.
  • dental professionals may show the effect of orthodontic treatment to patients.
  • One way is to use animation to show the teeth from the initial state to the first intermediate state, the second intermediate state... and finally the intermediate state. If the state changes to the target state, then it is necessary to generate corresponding gingival three-dimensional digital models for the three-dimensional digital model of the crown from the initial layout of the teeth to the first intermediate layout, the second intermediate layout, and finally the intermediate layout to the target layout. , to obtain these three-dimensional digital models of teeth and jaws.
  • a three-dimensional digital model of the gums in the second state is generated.
  • each of the second state gingival digital model to the last state gingival three-dimensional digital model can be directly generated based on the first state gingival digital model.
  • the first state is an initial state
  • the second state may be any state in the series of successive states except the first state. .
  • a three-dimensional digital model of the gums in the current state can also be generated based on the three-dimensional digital model of the gums in the previous state.
  • the first state is a state preceding the second state in a series of successive states.
  • This application is based on the cavity line of the three-dimensional digital model of the dental crown in the second state, and deforms the side grid of the three-dimensional gingival digital model in the first state to obtain the side grid of the three-dimensional gingival digital model in the second state.
  • the first state gingival three-dimensional digital model and the first state dental crown three-dimensional digital model correspond to the labial and buccal segments and lingual segments of the cavity line of each tooth and the end segment of the cavity line corresponding to the end teeth.
  • a predetermined number of sampling points have been obtained through sampling. If the sampling points on the three-dimensional digital model of the gingiva in the first state and the same sampling points on the three-dimensional digital model of the dental crown in the second state are used as control points, and the deformation process is performed on the three-dimensional digital model of the gingiva in the first state, in In some cases, especially when the teeth twist around their long axes, mesh kinking or molding can easily occur.
  • This deformation processing method is based on the assumption that the relative position of the gingival edge and the teeth remains unchanged.
  • the inventor of the present application found that although the gingiva deforms with the movement of the teeth, during the tooth movement, the edge of the gingiva and the teeth The relative position of the teeth may change, for example, when the teeth twist.
  • the inventor of the present application has designed a new deformation method by resampling control points on the cavity line of the three-dimensional digital model of the second state dental crown, and using the control points obtained by resampling as the first
  • the new position of the corresponding control point on the three-dimensional digital model of the gums in the first state is deformed to obtain a three-dimensional digital model of the gums in the second state.
  • the three-dimensional digital model of the gums in the second state obtained in this way is closer to reality. Condition.
  • the tooth cavity in the three-dimensional digital model of the dental crown in the first state in step 105 can be used.
  • the sampling points obtained by sampling on the line and the bottom contour line are used as the control points of the three-dimensional digital model of the gums in the first state.
  • the same method can be used on the cavity line of the three-dimensional digital model of the dental crown in the second state.
  • the corresponding control points are obtained by sampling.
  • the same method can also be used to resample the cavity lines of the three-dimensional digital model of the gums in the first state and the cavity lines of the three-dimensional digital model of the dental crown in the second state to obtain corresponding values. control points.
  • the position of at least one crown of the second state three-dimensional digital model of the dental crown has changed, and the control point corresponding to the two crowns is at the The position of the crown along the cavity line may vary.
  • the deformation process is to use the control points on the cavity line of the three-dimensional digital crown model of the second state as the new positions of the corresponding control points on the cavity line of the three-dimensional gingival digital model of the first state. , keep the control points on the bottom contour line of the first state gingival three-dimensional digital model unchanged, establish a deformation equation based on this, and calculate the coordinates of each vertex of the second state gingival three-dimensional digital model.
  • the method when performing deformation processing on the first state gingival three-dimensional digital model template, can be based on the average Z coordinate of the center point of each cavity line of the second state dental crown three-dimensional digital model and the first The average Z coordinate of the center point of each tooth cavity line in the three-dimensional gingival digital model template of the first state is used to determine the relative position of the two along the Z axis.
  • the deformation processing can adopt any applicable deformation method for the mesh model, including but not limited to TPS (Thin-Plate Splines) deformation method, Laplacian deformation method, rigid body deformation method, etc.
  • TPS Thin-Plate Splines
  • Laplacian deformation method Laplacian deformation method
  • rigid body deformation method etc.
  • a three-dimensional digital model of the dental crown and a three-dimensional digital model of the gums in the same state can be fused through Boolean operations to obtain a three-dimensional digital model of the teeth in the corresponding state.
  • dental three-dimensional digital model control equipment (stereolithography equipment) can be used to produce dental physical models.

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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；在所述第一状态牙龈三维数字模型的牙洞线上以第一方法采样得到第一组形变控制点；获取第二状态牙冠三维数字模型；在所述第二状态牙冠三维数字模型的牙洞线上以所述第一方法采样得到第二组形变控制点；以及基于所述第一组和第二组形变控制点，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，所述第一组和第二组形变控制点数量相等。

Description

产生牙龈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龈三维数字模型的方法。
背景技术
现在，越来越多的牙科领域场景需要用到牙颌三维数字模型，例如，展示患者牙齿正畸治疗过程中某个状态下的牙颌，或者制作壳状牙科器械(例如，壳状牙齿矫治器和保持器等)。
牙颌三维数字模型包括牙冠部分和牙龈部分。牙冠部分可以通过口内扫描，或扫描印模或患者牙齿的实体模型获得。产生初始状态牙龈三维数字模型的方法有多种，对于后续状态的牙龈三维数字模型，一般是基于初始状态或前一状态牙龈三维数字模型，基于两个不同状态的牙洞线上的相同控制点，对所基于的牙龈三维数字模型进行形变处理得到后续状态的牙龈三维数字模型。然而，在一些情况下，通过这种方法产生的牙龈三维数字模型存在扭结和穿模的情况。
因此，有必要提供一种新的产生牙龈三维数字模型的方法。
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；在所述第一状态牙龈三维数字模型的牙洞线上以第一方法采样得到第一组形变控制点；获取第二状态牙冠三维数字模型；在所述第二状态牙冠三维数字模型的牙洞线上以所述第一方法采样得到第二组形变控制点；以及基于所述第一组和第二组形变控制点，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，所述第一组 和第二组形变控制点数量相等。
在一些实施方式中，所述形变处理是将所述第二组形变控制点作为所述第一组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，所述的产生牙龈三维数字模型的方法还包括：在所述第一状态牙龈三维数字模型的底面轮廓线上采样得到第三组形变控制点，在所述形变处理中，所述第三组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以下形变方法之一：TPS形变方法、拉普拉斯形变方法以及刚体形变方法。
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，所述的产生牙龈三维数字模型的方法还包括：获取第三状态牙冠三维数字模型；在所述第三状态牙冠三维数字模型的牙洞线上以所述第一方法采样得到第四组形变控制点；以及基于所述第一组和第四组形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第三状态牙龈三维数字模型，其中，所述第四组和第二组形变控制点数量相等，所述第一状态至第三状态是逐次的状态。
在一些实施方式中，所述第一方法包括：在对应各牙冠的牙洞线上分割出唇颊侧段和舌侧段，对于两个末端牙冠，将其牙洞线在所述唇颊侧段和舌侧段之间靠末端的一段作为末端段；以及在每一所述唇颊侧段和所述舌侧段上分别采样N1个形变控制点，以及在每一所述末端段上采样N2个形变点，得到一组形变控制点，其中，所述N1和N2是预定的自然数。
在一些实施方式中，所述采样是均匀采样。
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进行融合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制作牙颌实体模型的方法，其包括：利用所述的第二状态牙颌三维数字模型控制设备制作第二状态牙颌的实体模型。
在一些实施方式中，所述设备是立体光固化成型设备。
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龈三维数字模型的方法的示意性流程图；
图2，为本申请一个实施例中用于产生牙龈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下颌牙列的牙冠三维数字模型；
图3，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的底面的完整轮廓线；
图4，示意性地展示了一个例子中牙弓一侧最末端一颗牙齿的牙洞线的唇颊侧段、舌侧段、与邻牙的邻接段以及末端段；
图5，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的侧面网格；
图6，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的顶部网格；以及
图7，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的底部网格。
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龈三维数字模型的方法，基于牙冠三维数字模型沿牙龈高度方向的投影产生牙龈三维数字模型底面的轮廓线，分别在所述牙冠三维数字模型的牙洞线和所述牙龈三维数字模型底面的轮廓线上采样第一预定数量的点，获得所述第一预定数量的点对，基于每一所述点对产生外凸的曲线，并在每一所述曲线上采样第二预定数量的点，按顺序连接所述牙洞线、轮廓线以及曲线上的采样点，得到牙龈三维数字模型侧面网格。牙洞线是牙冠与牙龈交接处的边缘轮廓线。以下结合附图对本申请一个实施例中的产生牙龈三维数字模型的方法进行详细说明。
请参图1，为本申请一个实施例中的产生牙龈三维数字模型的方法100的示意性流程图。
在一个实施例中，所述产生牙龈三维数字模型的方法100由计算机执行。相应地，本申请又一方面提供了一种用于产生牙龈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，将执行所述产生牙龈三维数字模型的方法100。
在101中，获取牙冠三维数字模型。
在一个实施例中，所述牙冠三维数字模型包括患者完整牙列(即上颌牙列或下颌牙列)的牙冠的三维数字模型。
在一些实施方式中，可以通过口内扫描，或通过扫描牙齿印模或实体模型获得所述牙冠三维数字模型。在扫描获得完整牙列的牙冠的三维数字模型后，可以对其进行分割，使各牙冠相互独立，从而能够单独移动任意一颗牙冠。
请参图2，为本申请一个实施例中用于产生牙龈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下颌牙列的牙冠三维数字模型。
在103中，基于所述牙冠三维数字模型产生牙龈三维数字模型底部的轮廓线。
在一个实施例中，可以将垂直于咬合面的方向作为牙龈的高度方向。为了便于计算，可以如此建立世界坐标系，将咬合面作为X轴和Y轴所在平面，将所述牙冠三维数字模型的几何中心(即所有顶点的均值)作为所述世界坐标系的原点，使Y轴大致平行于牙弓对称轴。在本申请的启示下，可以理解，除了该例子外，还可以用任何其他合适的方式确定牙龈的高度方向以及建立世界坐标系。
在一个实施例中，可以基于所述牙冠三维数字模型，产生牙龈三维数字模型的底面的轮廓线。
在一个例子中，可以先产生牙龈三维数字模型的底面的内轮廓线。
首先，对所述牙冠三维数字模型中的每一单个牙冠计算离所述世界坐标系原点最近的顶点，并将其投影至XY平面，作为初始标志点。其中，对于两个末端牙齿的初始标志点，可以将其沿Y轴朝牙弓开口方向移动预定的距离δ1，以使后续拟合的曲线长度足够。在一个实施例中，δ1可以是2mm。可以理解，δ1的值可以根据具体需求和情况进行调整。
接着，基于所述初始标志点产生一条三阶贝塞尔曲线。在一个实施例中，可以如此产生该三阶贝塞尔曲线：将最末端的两个标志点作为该三阶贝塞尔曲线的两个控制点，基于所有标志点计算得到另外两个控制点，使得基于该四个控制点产生的贝塞尔曲线距离所有标志点的和最小。
然后，对于每一当前标志点，计算当前贝塞尔曲线上与其最近的点，若该点离坐标系原点更近，那么，将当前标志点更新为该点。
重复上述两个步骤k次，得到牙龈三维数字模型底面的内轮廓线。在一个实施例中，k可以是2。在又一实施例中，可以不设置k值，一直迭代，直至标志点不再更新。迭代的目的在于使所述内轮廓线尽量靠牙弓之内，使牙冠在XY平面上的投影尽量位于所述内轮廓线之外。将最终的三阶贝塞尔曲线作为牙龈三维数字模型的底面的内轮廓线。
接着，产生牙龈三维数字模型的底面的外轮廓线。
首先，对所述牙冠三维数字模型中的每一单个牙冠计算离所述世界坐标系原点最远的顶点，并将其投影至XY平面，作为初始标志点。
然后，基于所述初始标志点产生一条三阶贝塞尔曲线。在一个实施例中，可以如此产生该三阶贝塞尔曲线：将最末端的两个标志点作为该三阶贝塞尔曲线的两个控制点，基于所有标志点计算得到另外两个控制点，使得基于该四个控制点产生的贝塞尔曲线距离所有标志点的和最小。
接着，对于每一当前标志点，计算当前贝塞尔曲线上与其最近的点，若该点离坐标系原点更远，那么，将当前标志点更新为该点。
重复上述两个步骤k次之后，使靠牙弓末端的两个控制点分别沿X轴向两侧外移δ2，使另两个控制点沿Y轴朝与牙弓开口相反的方向移动δ3，再基于更新后的控制点产生新的三阶贝塞尔曲线，使曲线外扩。在一个实施例中，δ2和δ3可以是2mm。可以理解，δ2和δ3的值可以根据具体需求和情况进行调整。将最终的三阶贝塞尔曲线作为牙龈三维数字模型的底面的外轮廓线。
然后，可以产生所述内、外轮廓线的连接线，得到牙龈三维数字模型的底面的完整轮廓线。
在一个实施例中，可以采用以下方法产生所述内、外轮廓线的连接线。将所述内、外轮廓线同侧的端点的中点沿Y轴朝牙弓开口方向移动预定距离，例如，2mm。然后，以该点以及对应的两个端点作为控制点，产生二阶贝塞尔曲线，作为该侧所述内、外轮廓线的连接线。在本申请的启示下，可以理解，产生连接 线的方法并不限于上述具体实施例，只要产生的连接线外凸圆润即可。
请参图3，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的底面的完整轮廓线，内轮廓线对应的控制点a1、b1、c1及d1，外轮廓线对应的控制点a2、b2、c2及d2，左侧连接线的控制点a1、a2及e1，以及右侧连接线的控制点d1、d2及e2。
在本申请的启示下，可以理解，基于牙冠三维数字模型产生牙龈三维数字模型的底面的轮廓线的方法并不限于以上具体实施例。例如，可以将每一牙冠投影至XY平面，并将该投影离所述坐标系原点最近的点作为用于产生内轮廓线的初始标志点，将该投影离所述坐标系原点最远的点作为用于产生外轮廓线的初始标志点。
在105中，基于所述牙冠三维数字模型的牙洞线和所述牙龈三维数字模型的底面的轮廓线产生牙龈三维数字模型。
在一个实施例中，对于每一牙冠，可以基于其与邻牙的位置关系，在其牙洞线上分割出唇颊侧段和舌侧段，并基于这些牙冠的牙洞线的唇颊侧段和舌侧段与所述牙龈三维数字模型的底面的轮廓线，产生牙龈三维数字模型侧面的网格。
在一个实施例中，可以先定义一个距离阈值。对于两侧均有邻牙的牙冠，在其牙洞线上找到与邻牙距离小于所述距离阈值的点，基于此，将牙洞线分割为四段，分别为唇颊侧段、舌侧段以及分别靠两侧邻牙的两个邻接段。对于两个末端的牙冠，在其牙洞线上找到与邻牙距离小于所述距离阈值的点，以及预定数量(可以根据具体情况和需求定，例如，8-12个点)的与邻牙距离最大的点，基于此，将牙洞线分割为四段，分别为唇颊侧段、舌侧段、与邻牙的邻接段以及末端段。
请参图4，示意性地展示了一个例子中牙弓一侧最末端两颗牙齿的牙洞线的唇颊侧段、舌侧段、与邻牙的邻接段以及末端段。
在一个实施例中，可以如此计算一个牙冠的牙洞线上与邻牙距离小于所述距离阈值的点，针对当前牙冠的牙洞线上的每一个点，计算邻牙牙洞线上与之最近 的点，若两者之间的距离小于所述距离阈值，则将当前牙冠的牙洞线上的该点作为与邻牙距离小于所述距离阈值的点。
在一个实施例中，所述距离阈值可以根据具体情况和需求给定，例如，在0.5mm至牙冠近远中长度的1/3的范围内进行取值，例如，1mm。
接着，在所述牙龈三维数字模型的底面的轮廓线找到与所述各牙冠的牙洞线的唇颊侧段和舌侧段以及两个末端牙冠的牙洞线的末端段相对应的段。在一个实施例中，可以如此对所述轮廓线进行分段，对于一颗牙冠，分别计算其牙洞线上距离两侧邻牙牙冠的牙洞线最近的点，然后，在所述内轮廓线上分别找到与该两个点最近的点，以所述内轮廓线在该两个点之间的一段作为与所述牙冠的牙洞线的舌侧段相对应的一段；类似地，在所述外轮廓线上分别找到与所述两个与邻牙最近的点，以所述外轮廓线在该两个点之间的一段作为与所述牙冠的牙洞线的唇颊侧段相对应的一段。对于一颗末端的牙冠，可以将所述内、外轮廓线上与该末端牙冠的牙洞线的舌侧段和唇颊侧段相对应的段的靠末端的端点之间的一段作为与该末端牙冠的牙洞线的末端段相对应的段。
在本申请的启示下，可以理解，除了以上方法之外，可以采用任何其他适用的方法对所述底面轮廓线进行分段。例如，可以将所述各牙冠的牙洞线的唇颊侧段以及舌侧段投影至XY平面，以其端点的法线与所述底面轮廓线的内、外轮廓线的交点对其进行分段。
在所述底面轮廓线上找到与所述各牙冠的牙洞线的唇颊侧段、舌侧段以及末端段一一对应的段之后，可以分别在所述底面轮廓线和牙洞线上的各段上采样预定数量的点，其中，在两个相对应的段上采样相同数量的点。例如，可以在每一唇颊侧段和舌侧段上采样N1个点，在所述底面轮廓线上的对应段上也采样N1个点，在每一末端段上采样N2个点，在所述底面轮廓线上的对应段上也采样N2个点。在一个实施例中，所述采样可以是均匀采样。
所述牙洞线上的采样点与所述底面轮廓线上对应数量的采样点按顺序形成一一对应的点对，例如，对于一颗牙冠，其牙洞线的唇颊侧段上沿顺时针方向的 第3个采样点与所述底面轮廓线上与该唇颊侧段相对应的一段上沿顺时针方向的第3个采样点构成一个点对。
基于每一点对，产生一条外凸的曲线。在一个实施例中，可以将一个点对中的底部点(即位于所述底面轮廓线上的点)沿其法向量朝牙龈外侧移动预定距离得到一个控制点，再将该控制点沿Z轴朝该点对的顶部点(即位于所述牙洞线上的点)移动所述底部点和顶部点的Z坐标平均值，得到另一个控制点。所述预定距离可以根据具体情况和需求确定，例如，2mm。将所述顶部点、底部点以及两个计算得到的控制点作为4个控制点，产生一条三阶贝塞尔曲线。在本申请的启示下，可以理解，产生外凸曲线的方法并不限于以上例子，可以采用任何其他合适的方法，此处不再一一列举。然后，在每一所述外凸曲线上采样N3个点。
接着，将所述牙洞线、底面轮廓线以及所述外凸曲线上的采样点按顺序连接，形成牙龈三维数字模型的侧面网格。请参图5，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的侧面网格。
可以理解，可以根据对牙龈三维数字模型的网格精度要求来确定N1、N2及N3。
可选地，可以为牙龈三维数字模型建立顶部网格。在一个实施例中，对于每一牙冠，可以在其牙洞线两侧的邻接段/末端段上分别采样N2个点。接着，将其牙洞线唇颊侧段和舌侧段的N1个点一一对应相连，并在每一连线上采样N2个点。最后，将所述邻接段/末端段、唇颊侧段、舌侧段以及连线上的采样点按顺序连接，形成牙龈三维数字模型的顶部网格。
请参图6，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的顶部网格。
接下来，可以为牙龈三维数字模型建立底部网格。在一个实施例中，可以将所述底面轮廓线上的采样点分成数量相等的牙弓内侧和外侧两部分，然后，将这些采样点按顺序连接，形成牙龈三维数字模型的底部网格。
请参图7，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的底部网格。
将所述侧面网格、顶部网格以及底部网格进行拼接即可获得封闭的牙龈三维数字模型。
设图2所示的牙冠三维数字模型为第一状态牙冠三维数字模型，即这些牙冠处于第一牙齿布局。相应的，所产生的与之对应的牙龈三维数字模型为第一状态牙龈三维数字模型。
在利用壳状牙齿矫治器进行牙齿正畸治疗的场景中，患者逐次佩戴一系列逐次的壳状牙齿矫治器，以将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。
制作这一系列逐次的壳状牙齿矫治器，首先要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，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。接着，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。
另外，在实施治疗之前，牙科专业人员可能会向患者展示牙齿正畸治疗的效果，其中一个方式是以动画的方式展示牙颌从初始状态到第一中间状态、第二中间状态……最后中间状态直至目标状态的变化，那么，就需要相应地为牙齿的初始布局到第一中间布局、第二中间布局……最后中间布局直至目标布局的牙冠三维数字模型分别产生对应的牙龈三维数字模型，以获得这些牙颌三维数字模型。
由以上可知，存在为不同状态牙冠三维数字模型产生对应状态牙龈三维数字模型的需求。
在107中，基于所述第一状态牙龈三维数字模型和第二状态牙冠三维数字模型，产生第二状态牙龈三维数字模型。
在一个实施例中，对于一系列逐次状态的牙龈三维数字模型，可以基于第一状态牙龈数字模型直接产生自第二状态牙龈数字模型至最后状态牙龈三维数字模型的每一个。在该实施例中，在一系列逐次的状态中，所述第一状态是初始状态，所述第二状态可以是所述一系列逐次的状态中除所述第一状态之外的任一状态。
在又一实施例中，还可以基于前一状态牙龈三维数字模型产生当前状态牙龈三维数字模型。在该实施例中，在一系列逐次的状态中，所述第一状态是所述第二状态的前一状态。
本申请是基于第二状态牙冠三维数字模型的牙洞线，对所述第一状态牙龈三维数字模型的侧面网格进行形变处理，以得到第二状态牙龈三维数字模型的侧面网格。
由以上可知，所述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对应各牙齿的牙洞线的唇颊侧段、舌侧段以及对应末端牙齿的牙洞线的末端段上已通过采样得到预定数量的采样点。若将所述第一状态牙龈三维数字模型上的采样点以及所述第二状态牙冠三维数字模型上的相同采样点作为控制点，对所述第一状态牙龈三维数字模型进行形变处理，在一些情况下，尤其是当牙齿绕长轴扭转较多时，容易发生网格扭结或穿模。这种形变处理的方式是基于牙龈边缘与牙齿相对位置不变的假设，然而，本申请的发明人发现，虽然牙龈随牙齿的移动而发生变形，但在牙齿移动过程中，牙龈的边缘与牙齿的相对位置可能发生变化，例如，当牙齿扭转时。
因此，本申请的发明人设计了一种新的形变方法，通过在所述第二状态牙冠三维数字模型的牙洞线上重新采样控制点，将重新采样获得的控制点作为所述第一状态牙龈三维数字模型上的对应控制点的新位置，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，这样获得的第二状态牙龈三维数字模型更接近真实情况。
在一个实施例中，可以沿用105中在所述第一状态牙冠三维数字模型的牙洞 线以及所述底面轮廓线上采样获得的采样点作为所述第一状态牙龈三维数字模型的控制点，那么，可以采用相同的方法在所述第二状态牙冠三维数字模型的牙洞线上采样得到相应的控制点。
在又一实施例中，也可以相同的方法，分别在所述第一状态牙龈三维数字模型的牙洞线上以及所述第二状态牙冠三维数字模型的牙洞线上重新采样得到相应的控制点。
可以理解，与所述第一状态牙冠三维数字模型相比，所述第二状态牙冠三维数字模型的至少一颗牙冠的位置发生了变化，两者对应该牙冠的控制点在该牙冠的牙洞线上的位置可能不同。
简单地说，所述形变处理是将所述第二状态牙冠三维数字模型的牙洞线上的控制点作为所述第一状态牙龈三维数字模型的牙洞线上的对应控制点的新位置，保持所述第一状态牙龈三维数字模型的底面轮廓线上的控制点不动，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。
在一个实施例中，在对所述第一状态牙龈三维数字模型模板进行形变处理时，可以基于所述第二状态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第一状态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，可以通过布尔运算将同一状态的牙冠三维数字模型和牙龈三维数字模型进行融合，以得到对应状态的牙颌三维数字模型。
在一些应用场景下，可以利用牙颌三维数字模型控制设备(立体光固化成型设备)制作牙颌实体模型。
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 (11)

  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；
    在所述第一状态牙龈三维数字模型的牙洞线上以第一方法采样得到第一组形变控制点；
    获取第二状态牙冠三维数字模型；
    在所述第二状态牙冠三维数字模型的牙洞线上以所述第一方法采样得到第二组形变控制点；以及
    基于所述第一组和第二组形变控制点，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，所述第一组和第二组形变控制点数量相等。
  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组形变控制点作为所述第一组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，它还包括：在所述第一状态牙龈三维数字模型的底面轮廓线上采样得到第三组形变控制点，在所述形变处理中，所述第三组形变控制点保持不动。
  4. 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以下形变方法之一：TPS形变方法、拉普拉斯形变方法以及刚体形变方法。
  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，所述第一状态是初始状态。
  6. 如权利要求5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：
    获取第三状态牙冠三维数字模型；
    在所述第三状态牙冠三维数字模型的牙洞线上以所述第一方法采样得 到第四组形变控制点；以及
    基于所述第一组和第四组形变控制点，对所述第一状态牙龈三维数字模型进行形变处理，得到第三状态牙龈三维数字模型，其中，所述第四组和第二组形变控制点数量相等，所述第一状态至第三状态是逐次的状态。
  7. 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，所述第一方法包括：
    在对应各牙冠的牙洞线上分割出唇颊侧段和舌侧段，对于两个末端牙冠，将其牙洞线在所述唇颊侧段和舌侧段之间靠末端的一段作为末端段；以及
    在每一所述唇颊侧段和所述舌侧段上分别采样N1个形变控制点，以及在每一所述末端段上采样N2个形变点，得到一组形变控制点，其中，所述N1和N2是预定的自然数。
  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，所述采样是均匀采样。
  9. 一种产生牙颌三维数字模型的方法，其包括：将如权利要求1所述的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进行融合得到第二状态牙颌三维数字模型。
  10. 一种制作牙颌实体模型的方法，其包括：利用如权利9所述的第二状态牙颌三维数字模型控制设备制作第二状态牙颌的实体模型。
  11. 如权利要求10所述的制作牙颌实体模型的方法，其特征在于，所述设备是立体光固化成型设备。
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