CN110164558B - Tooth model parameterization method - Google Patents
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Abstract
The invention discloses a tooth model parameterization method, which comprises the following steps: calculating geometric center points of all teeth; fitting an upper jaw tooth plane and a lower jaw tooth plane, and calculating an upper jaw tooth arch curve and a lower jaw tooth arch curve; determining the cusp of the cuspids of the upper jaw and the lower jaw; determining a near-far midpoint, a near midpoint, and a far midpoint of the tooth; determining a tooth coordinate system according to the cusp, the near-far midpoint, the near-midpoint and the far-midpoint; calculating FA points, center points and incisal edge points of teeth and near-far middle cheek points of constant molar teeth; performing lip and cheek direction adjustment, lingual jaw direction adjustment, single tooth characteristic point adjustment and original tooth model long axis adjustment; the single-jaw teeth are arranged along the dental arch by taking the central line of the dental arch as a reference from the incisors according to the sequence of tooth positions; and calculating collision values of the single teeth on adjacent teeth with smaller tooth positions, and moving the near-middle edge point according to the collision values. The invention effectively improves the accuracy and rationality of the parameterized parameters of the tooth model.
Description
Technical Field
The present invention relates to a method of parameterizing a tooth model.
Background
Tooth model parameterization refers to the abstraction of a tooth model into a combination of a three-dimensional spatial coordinate system and several feature points for calculation and description of position and pose in space. The method comprises the steps of obtaining a digital three-dimensional model of teeth of a patient through 3D scanning of the biting mould of the patient, obtaining an independent digital model of each tooth through recognition and segmentation, and obtaining a three-dimensional space coordinate system and characteristic points of the tooth model by using a tooth model parameterization method.
The tooth model parameterization technology widely used at present mainly has two defects:
1) The integrity dependence on the teeth of the patient is high.
a) The existing tooth model parameterization technology obtains a three-dimensional space coordinate system of the tooth model by marking characteristic points and calculating the characteristic points according to the morphological characteristics of the tooth model, however, in actual cases, the teeth of a patient often have defects, abrasion and the like, so that the morphological characteristics of the tooth model of the patient cannot be accurately reflected.
b) In the previous step of digitally processing the tooth model, the operation of recognition and segmentation may cause the tooth model to be incomplete, or edema of gums when a patient bites the model, and may cause error and leakage of recognition and segmentation, thereby causing deviation of the obtained tooth model in parameterization.
2) Only the morphology of the teeth themselves is considered and the relationship between adjacent teeth is ignored.
a) The existing method carries out parameterization according to the morphological characteristics of the single teeth, but the concept of tooth arrangement is originally an evaluation of arrangement conditions of a plurality of teeth, so that only parameterization of the single teeth is considered, and reference effects of the parameters on tooth arrangement cannot be provided in the tooth arrangement process.
b) For the concept of oral aesthetics, a suitable adjustment range is given for each patient's different oral situation, in which each tooth has a certain elastic adjustable range, and the adjustable ranges between adjacent teeth are different, so that reasonable adjustment of each tooth can be better obtained only by comparing adjacent teeth.
The above problems reduce the accuracy and rationality with which tooth model parameterization provides parameters for subsequent tooth alignment operations.
Disclosure of Invention
The invention aims to provide a tooth model parameterization method, which effectively improves the accuracy and rationality of parameters of a tooth model after parameterization.
The technical scheme for achieving the purpose is as follows:
a method of parameterizing a tooth model, comprising:
calculating the respective geometric center points of all teeth;
fitting an upper jaw tooth plane and a lower jaw tooth plane according to the calculated geometric center points of the teeth, and calculating an upper jaw dental arch curve and a lower jaw dental arch curve;
obtaining cusps of cuspids of the upper jaw and the lower jaw through Gaussian curvature calculation;
determining a near-far midpoint, a near-midpoint and a far-midpoint of the teeth by using the maxillary dental arch curve and the mandibular dental arch curve;
determining a tooth coordinate system according to the cusps of the cuspids of the upper jaw and the lower jaw, the near midpoint and the far midpoint of the teeth, and the near midpoint and the far midpoint;
calculating FA points, center points and incisal edge points of teeth and near-far middle cheek points of constant molar teeth;
straightening a dental arch curve of a single jaw into a straight line, and placing the straight line on an X axis of a world coordinate system; arranging single-jaw teeth on a straightened dental arch, arranging geometrical center points of the teeth on the dental arch, overlapping Y-axis of the teeth with the dental arch, and enabling Z-axis of the teeth to be consistent with Z-axis direction of a world coordinate system;
performing lip and cheek direction adjustment, lingual jaw direction adjustment, single tooth characteristic point adjustment and original tooth model long axis adjustment;
the single-jaw teeth are arranged along the dental arch by taking the central line of the dental arch as a reference from the incisors according to the sequence of tooth positions; when the teeth are arranged, the teeth firstly translate onto the dental arch according to the near-middle edge points and then rotate around the near-middle edge points, so that the far-middle edge points also fall on the dental arch;
and calculating collision values of the single teeth on adjacent teeth with smaller tooth positions, moving a near-middle edge point according to the collision values, and finishing tooth model parameterization when the collision values of all the teeth are 0, otherwise, arranging along the dental arch again.
Preferably, the projection points of the geometric center points of all teeth of the upper jaw and the plane of the upper jaw teeth are adopted, and the incisor points of the middle incisors, the cuspids and the near-middle cheek points of the molars of the single-jaw teeth are used as parameters according to a Beta function to calculate an upper jaw dental arch curve;
the projection points of the geometric center points of all teeth of the lower jaw on the mandibular teeth jaw plane are adopted, and according to a Beta function, the incisor edge points of the middle incisors, the cuspids and the near-middle cheek cuspids of the molar teeth of the single jaw teeth are used as parameters to calculate the mandibular dental arch curve.
Preferably, the maxillary dental arch curve is stretched along the maxillary dental plane Z-axis to form a curved surface, or the mandibular dental arch curve is stretched along the mandibular dental plane Z-axis to form a curved surface, the curved surface intersects with each tooth on two lines, the outermost point on each line is a near-far midpoint, the point near the incisor direction is a near-midpoint, and the other is a far-midpoint.
Preferably, determining the tooth coordinate system refers to: the Z axis is relative to incisors: the direction from the geometric center point of the tooth to the incisor point is: the direction from the geometric center point of the tooth to the cusp is, relative to the bicuspid tooth: the direction from the geometric center point of the tooth to the socket point is relative to the molar: the direction pointing from the geometric center point of the tooth to the socket point is the Y axis: the X-axis, Y-axis and Z-axis are the right hand coordinate system as the tooth coordinate system, pointing from the far midpoint of the tooth to the near midpoint.
Preferably, after the tooth coordinate system is determined, the tooth coordinate system is corrected, the near and far midpoints of the teeth are recalculated along the X-axis direction, and the Y-axis and Z-axis directions are adjusted.
Preferably, the intersection of the X-axis of the tooth coordinate system and the labial direction of the tooth model;
the center point refers to: intersection points of the Z axis of the tooth coordinate axis and the tooth model;
edge cutting point means: a point of maximum curvature in the labial direction on the intersection of the plane formed by the X axis and the Z axis of the tooth coordinate axis and the tooth model;
the near-far mid-cheek points of permanent molar refer to: two points of the four-point tooth near the labial side.
Preferably, the labial and buccal adjustment means: the teeth translate along the elongation depression direction, and the teeth rotate around the labial lingual axis passing through the FA point;
lingual jaw direction adjustment finger: the teeth translate along the labial tongue, and the teeth rotate around an elongation depression direction shaft passing through the geometric center point;
single tooth characteristic point adjustment means: adjusting a incisal edge point, a cusp, a steamed corn point, a near cheek cusp, a far cheek cusp, an FA point and a tooth coordinate system on the tooth;
the long axis adjustment of the original dental model is as follows: adjustment of both endpoints of the long axis of the crown on the tooth model.
Preferably, when the collision value is positive, the near-middle edge point moves along the dental arch in a direction away from the adjacent teeth, and the movement distance is equal to the collision value; when the collision value is negative, the mesial edge point moves along the dental arch to a direction approaching to the adjacent teeth, and the moving distance is equal to the absolute value of the collision value.
The beneficial effects of the invention are as follows: the invention reduces the dependence on individual teeth, and reduces the deviation influence on tooth parameterization caused by the shape loss such as errors in tooth cutting or loss of the teeth. The invention refers to the relation between adjacent teeth when the teeth are parameterized, so that the parameterized result leads to higher accuracy and aesthetic property of tooth arrangement.
Drawings
Fig. 1 is a flow chart of a method of parameterizing a tooth model of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, the method for parameterizing a tooth model of the present invention comprises the following steps:
step S1, calculating the respective geometric center points of all teeth; i.e. the arithmetic mean of the Mesh points of the tooth model, i.e. the coordinates of all vertices are added up and divided by the number of vertices.
Step S2, fitting a maxillary dental plane by using geometric center points of all teeth of the maxillary; the projection points of the geometrical center points of all teeth of the upper jaw and the upper jaw tooth jaw plane are used for calculating an upper jaw dental arch curve by taking the incisor edge points of incisors, the cuspids and the near-middle cheek cuspids of molar teeth in single-jaw teeth as parameters according to a Beta function.
Fitting a mandibular dental plane with geometric center points of all teeth of the mandible; the projection points of the geometrical center points of all teeth of the lower jaw on the mandibular teeth jaw plane are used for calculating a mandibular dental arch curve by taking the incisal edge points of the middle incisors, the cuspids and the near-middle cheek cuspids of the molar teeth of the single jaw teeth as parameters according to a Beta function.
And S3, calculating Gaussian curvature of all model vertexes of the cuspids of the upper jaw and the lower jaw, and obtaining the point with the maximum curvature as the cusp of the corresponding cuspid.
And S4, stretching the maxillary dental arch curve along the Z axis of the maxillary dental plane to form a curved surface, or stretching the mandibular dental arch curve along the Z axis of the mandibular dental plane to form a curved surface, wherein the curved surface and each tooth are intersected on two lines, the outermost point on each line is a near-far midpoint, and the point close to the incisor direction is a near-midpoint, and the other point is a far-midpoint.
Step S5, calculating a tooth coordinate system: the Z axis is the direction from the geometric center point to the incisor edge point of the tooth for incisors, the geometric center point to the cusp direction for cuspids, the geometric center point to the socket point for bicuspids, the geometric center point to the socket point for molars, the Y axis is the far-middle point to near-middle point direction, and the X axis, the Y axis and the Z axis form a right-hand coordinate system.
And S6, correcting the tooth coordinate system, recalculating the near and far midpoints along the X-axis direction, and adjusting the Y-axis direction and the Z-axis direction.
And S7, calculating the FA point. I.e. the point where the X-axis of the tooth coordinate system intersects the tooth model in the labial direction;
step S8, calculating a center point. I.e. the intersection of the Z-axis of the tooth coordinate system and the tooth model.
Step S9, calculating a cutting edge point. I.e. the point of maximum curvature in the labial direction on the intersection of the plane of the tooth coordinate system, formed by the X-axis and the Z-axis, with the tooth model.
Step S10, calculating the near-far middle cheek points of the constant molar. I.e. teeth with four cusps, two cusps near the labial side.
Step S11, the dental arches of the individual jaws are straightened into a straight line and placed on the X-axis of the world coordinate system, i.e. the absolute coordinate system in space.
And S12, arranging the single-jaw teeth on the straightened dental arch, arranging the geometric center points of the teeth on the dental arch, wherein the geometric center points of the adjacent teeth are 20mm apart, the Y-axis of the teeth is coincident with the dental arch, and the Z-axis of the teeth is coincident with the Z-axis direction of the world coordinate system.
Step S13, adjusting:
the labial adjustment includes translation of the tooth in the elongated depressed direction and rotation of the tooth about the labial-lingual axis passing through the FA point.
Lingual adjustment, including translation of the tooth along the labial lingual direction and rotation of the tooth about an elongated depressed axis passing through the geometric center point.
Individual tooth feature point adjustments include adjustments to the incisal edge points, cusp points, pocket points, mesial cheek tip points, distal cheek tip points, FA points, and the tooth coordinate system on the tooth.
The original tooth model long axis adjustment comprises adjustment of two endpoints of the long axis of the dental crown on the tooth model.
After the tooth model is adjusted, the tooth coordinate system remains unchanged.
And S14, generating a dental arch curve of the single jaw by using a polynomial equation according to the incisor edge point, the cuspid point and the near-middle cheek point of the molar, namely substituting the incisor edge point, the cuspid point and the near-middle cheek point of the molar into the polynomial equation to calculate the curve equation by taking the incisor edge point, the cuspid point and the near-middle cheek point of the molar as parameters. The single teeth are arranged along the dental arch based on the dental arch midline from the incisors according to the sequence of the tooth positions. When the teeth are arranged along the dental arch, the teeth firstly translate onto the dental arch according to the near-middle edge point and then rotate around the near-middle edge point, so that the far-middle edge point also falls on the dental arch. The above-mentioned mesial edge point and distal edge point are the points of intersection of the straightened dental arch with each tooth model in step S12.
In step S15, a collision value is calculated for each tooth with smaller tooth position number, and when the collision value is positive, the near-middle edge point moves along the dental arch in the direction away from the adjacent tooth, and the movement distance is equal to the collision value. When the collision value is negative, the mesial edge point moves along the dental arch to a direction approaching to the adjacent teeth, and the moving distance is equal to the absolute value of the collision value. Tooth model parameterization is completed when the collision values of all teeth are 0. Otherwise, step S14 is executed again.
The above embodiments are provided for illustrating the present invention and not for limiting the present invention, and various changes and modifications may be made by one skilled in the relevant art without departing from the spirit and scope of the present invention, and thus all equivalent technical solutions should be defined by the claims.
Claims (6)
1. A method of parameterizing a tooth model, comprising:
calculating the respective geometric center points of all teeth;
fitting an upper jaw tooth plane and a lower jaw tooth plane according to the calculated geometric center points of the teeth, and calculating an upper jaw dental arch curve and a lower jaw dental arch curve;
obtaining cusps of cuspids of the upper jaw and the lower jaw through Gaussian curvature calculation;
determining a near-far midpoint, a near-midpoint and a far-midpoint of the teeth by using the maxillary dental arch curve and the mandibular dental arch curve;
determining a tooth coordinate system according to the cusps of the cuspids of the upper jaw and the lower jaw, the near midpoint and the far midpoint of the teeth, and the near midpoint and the far midpoint;
calculating FA points, center points and incisal edge points of teeth and near-far middle cheek points of constant molar teeth;
straightening a dental arch curve of a single jaw into a straight line, and placing the straight line on an X axis of a world coordinate system; arranging single-jaw teeth on a straightened dental arch, arranging geometrical center points of the teeth on the dental arch, overlapping Y-axis of the teeth with the dental arch, and enabling Z-axis of the teeth to be consistent with Z-axis direction of a world coordinate system;
performing lip and cheek direction adjustment, lingual jaw direction adjustment, single tooth characteristic point adjustment and original tooth model long axis adjustment;
the single-jaw teeth are arranged along the dental arch by taking the central line of the dental arch as a reference from the incisors according to the sequence of tooth positions; when the teeth are arranged, the teeth firstly translate onto the dental arch according to the near-middle edge points and then rotate around the near-middle edge points, so that the far-middle edge points also fall on the dental arch;
calculating collision values of the single teeth on adjacent teeth with smaller tooth positions, moving near-middle edge points according to the collision values, finishing tooth model parameterization when the collision values of all the teeth are 0, otherwise, arranging along the dental arch again;
the upper jaw arch curve is stretched along the Z axis of the upper jaw tooth plane to form a curved surface, or the lower jaw arch curve is stretched along the Z axis of the lower jaw tooth plane to form a curved surface, the curved surface and each tooth are intersected on two lines, the outermost point on each line is a near-far midpoint, the point close to the incisor direction is a near-midpoint, and the other point is a far-midpoint;
determining the tooth coordinate system refers to: the Z axis is relative to incisors: the direction from the geometric center point of the tooth to the incisor point is: the direction from the geometric center point of the tooth to the cusp is, relative to the bicuspid tooth: the direction from the geometric center point of the tooth to the socket point is relative to the molar: the direction pointing from the geometric center point of the tooth to the socket point is the Y axis: the X-axis, Y-axis and Z-axis are the right hand coordinate system as the tooth coordinate system, pointing from the far midpoint of the tooth to the near midpoint.
2. The method of tooth model parametrization according to claim 1, wherein the geometrical center points of all teeth of the upper jaw are used as projection points of the upper jaw tooth jaw plane, and the incisor edge points of the middle incisors, the cusps of the cuspids and the near-middle cheek cusps of the molars of the single jaw teeth are used as parameters according to the Beta function to calculate the upper jaw dental arch curve;
the projection points of the geometric center points of all teeth of the lower jaw on the mandibular teeth jaw plane are adopted, and according to a Beta function, the incisor edge points of the middle incisors, the cuspids and the near-middle cheek cuspids of the molar teeth of the single jaw teeth are used as parameters to calculate the mandibular dental arch curve.
3. The method of tooth model parameterization of claim 1, wherein after determining the tooth coordinate system, correcting the tooth coordinate system, recalculating the near and far midpoints of the tooth along the X-axis direction, and adjusting the Y-axis and Z-axis directions.
4. The method of tooth model parameterization of claim 1, wherein FA points refer to: intersection points of the X axis of the tooth coordinate system and the tooth model in the labial direction;
the center point refers to: intersection points of the Z axis of the tooth coordinate axis and the tooth model;
edge cutting point means: a point of maximum curvature in the labial direction on the intersection of the plane formed by the X axis and the Z axis of the tooth coordinate axis and the tooth model;
the near-far mid-cheek points of permanent molar refer to: two points of the four-point tooth near the labial side.
5. The method of parameterizing a dental model of claim 1,
lip and cheek adjustment means: the teeth translate along the elongation depression direction, and the teeth rotate around the labial lingual axis passing through the FA point;
lingual jaw direction adjustment finger: the teeth translate along the labial tongue, and the teeth rotate around an elongation depression direction shaft passing through the geometric center point;
single tooth characteristic point adjustment means: adjusting a incisal edge point, a cusp, a steamed corn point, a near cheek cusp, a far cheek cusp, an FA point and a tooth coordinate system on the tooth;
the long axis adjustment of the original dental model is as follows: adjustment of both endpoints of the long axis of the crown on the tooth model.
6. The method of tooth model parameterization of claim 1, wherein when the collision value is positive, the mesial edge point moves along the arch away from the adjacent tooth by a distance equal to the collision value; when the collision value is negative, the mesial edge point moves along the dental arch to a direction approaching to the adjacent teeth, and the moving distance is equal to the absolute value of the collision value.
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| CN112185509B (en) * | 2020-08-13 | 2024-03-29 | 上海埃蒙迪材料科技股份有限公司 | Parameterized tooth arrangement method |
| CN112288886B (en) * | 2020-09-15 | 2022-02-15 | 陈学鹏 | Tooth position arrangement method of accurate digital tooth model |
| US11116606B1 (en) | 2021-01-06 | 2021-09-14 | Arkimos Ltd. | Systems and methods for determining a jaw curve |
| CN112884711B (en) * | 2021-01-21 | 2023-06-13 | 上海埃蒙迪材料科技股份有限公司 | Dental crown identification method and device and electronic equipment |
| CN112932696B (en) * | 2021-01-21 | 2023-04-07 | 上海埃蒙迪材料科技股份有限公司 | Tooth feature point calculation method and device and electronic equipment |
| CN113449426B (en) * | 2021-07-01 | 2023-10-24 | 正雅齿科科技(上海)有限公司 | Digital tooth arrangement method, system, apparatus and medium |
| CN114431989B (en) * | 2022-01-07 | 2023-05-16 | 可丽尔医疗科技（常州）有限公司 | Method for establishing coordinate system based on target dental arch curve, automatic tooth arrangement method and tooth movement evaluation method |
| CN115588006B (en) * | 2022-11-11 | 2023-11-21 | 四川大学 | Extraction method of standardized dental arch form |
| CN117934885B (en) * | 2024-03-21 | 2024-06-18 | 沈阳市口腔医院 | Coordinate automatic matching method and system based on CBCT data and three-dimensional facial scan data |
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| CN102073776B (en) * | 2011-01-20 | 2012-12-19 | 西北大学 | Zonal statistic model based facial reconstruction method |
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