CN118212376A - Tooth three-dimensional model reconstruction method based on tooth parameterized model and tooth photo - Google Patents
Tooth three-dimensional model reconstruction method based on tooth parameterized model and tooth photo Download PDFInfo
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Abstract
The invention relates to a tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo, which comprises the following steps: constructing a tooth parameterized model; acquiring single or multiple teeth photos, and extracting tooth contour lines of specific teeth according to the photo angles; obtaining tooth missing information, and carrying out projection and contour matching based on a tooth parameterized model to obtain contour corresponding points; parameter optimization: optimizing a loss function based on tooth size, pose, shape probability distribution and contour corresponding points in the tooth parameterized model to obtain optimal parameter estimation; updating the tooth parameterized model according to the optimal parameter estimation, carrying out projection, contour matching and parameter optimization again, updating the parameter estimation until the iteration termination condition is met, outputting a final parameter estimation result, updating the tooth parameterized model according to the final parameter estimation result, and reconstructing the tooth three-dimensional model. Compared with the prior art, the method can reconstruct the tooth three-dimensional model based on the tooth photo shot by the uncalibrated camera.
Description
Technical Field
The invention relates to the technical field of digital medical treatment, in particular to a tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo.
Background
Orthodontic is a process of straightening teeth, improving the appearance of teeth and relieving deformity, and aims to restore the alignment of teeth to normal occlusion, and is mainly applicable to the situation that teeth are not aligned but jaw bones are normal. Since orthodontic has a long duration, typically ranging from six months to three years, periodic review of dental monitors is required to track the course of treatment, with review periods typically ranging from four to six weeks. Taking a set of intraoral teeth photographs is the most common method used by orthodontists for dental monitoring and orthodontic recording. A typical group of intraoral dental photographs generally includes photographs taken from five angles, respectively: front opening, left side Zhang Kouzhao, right side opening, maxillofacial and mandibular facial. The orthodontist regularly takes and records pictures of the teeth of the patient and monitors the progress of the current orthodontic treatment. The multi-angle intraoral teeth photograph, while providing geometric features of the teeth, lacks spatial information of intraoral tooth arrangement and interengagement compared to a three-dimensional model of the teeth. In orthodontic treatment, there are generally two modes of traditional plaster cast extraction and oral scan modeling using an oral scanner to obtain a three-dimensional model of a tooth. Traditional plaster mould taking is time-consuming and labor-consuming, requires long mouth opening time of a patient, and can lead the patient to feel stronger foreign body sensation; digital oral scanners are simple to operate, efficient and fast, but such scanners are often costly and difficult to miniaturize. In addition, the current two tooth three-dimensional modeling modes require the patient to participate in the face of the patient, and cannot meet the requirements of future remote orthodontic consultation.
Disclosure of Invention
The invention aims to provide a tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo, which can reconstruct a tooth three-dimensional model based on the tooth photo shot by an uncalibrated camera without the participation of a patient.
The aim of the invention can be achieved by the following technical scheme:
A tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo comprises the following steps:
Step 1) constructing a tooth parameterized model;
step 2) obtaining single or multiple teeth photos, and extracting tooth contour lines of specific teeth according to photo angles;
Step 3) obtaining tooth missing information, and carrying out projection and contour matching based on a tooth parameterized model, wherein the projection and contour matching is as follows: extracting specific tooth positions of tooth contour lines from the tooth missing information and different tooth photos, projecting the specific tooth positions into a three-dimensional tooth parameterized model to obtain tooth contours, and matching the tooth contours obtained by projection in the step 3) with the tooth contour lines obtained by photo extraction in the step 2) to obtain contour corresponding points;
Step 4) parameter optimization: optimizing a loss function based on tooth size, pose, shape probability distribution and contour corresponding points in the tooth parameterized model to obtain optimal parameter estimation;
And 5) updating the tooth parameterized model according to the optimal parameter estimation, carrying out projection and contour matching and parameter optimization again, updating the parameter estimation until the iteration termination condition is met, outputting a final parameter estimation result, updating the tooth parameterized model according to the final parameter estimation result, and reconstructing the tooth three-dimensional model.
Said step 1) comprises the steps of:
Step 1-1) obtaining three-dimensional mesh dental models of upper and lower jaws obtained by a plurality of groups of intraoral scanners from a database, and obtaining an upper and lower dentition three-dimensional model with tooth numbers through segmentation, numbering and complementation operations, wherein the three-dimensional mesh dental model consists of triangular patches, describes the surfaces of crowns and peripheral parts of gingival tissues of the upper and lower dentitions, respectively extracts triangular patch meshes belonging to different teeth, numbering refers to using a digital marking method to number the extracted meshes of different teeth according to the tooth positions, and complementation refers to repairing defects in the extracted tooth meshes to form closed meshes;
Step 1-2) carrying out dentition alignment registration on a plurality of groups of upper dentition three-dimensional models and lower dentition three-dimensional models with tooth numbers, and establishing a dentition local coordinate system, wherein the alignment registration refers to the steps of calculating the center of gravity of each tooth of each dentition, and aligning the group of dentition models through rigid transformation according to the corresponding relation of the tooth numbers;
Step 1-3) carrying out similar transformation alignment registration on tooth grid vertexes with the same tooth positions in a plurality of groups of upper and lower dentition three-dimensional models by using a consistency point drift algorithm, carrying out non-rigid registration by using a Gaussian process, searching a corresponding point matching relation of a minimized Euclidean distance by using a greedy algorithm, finally reserving N corresponding points for each tooth grid, counting tooth size and pose probability distribution of each tooth position, and modeling by using a plurality of normal distributions;
step 1-4) constructing a statistical shape model for teeth of the same tooth positions with the same number of points after registration by using a point distribution model, and describing probability distribution of each shape characteristic of each tooth position tooth by using normal distribution;
step 1-5) fusing the tooth size and pose probability distribution and the statistical shape model of each kind of teeth to obtain a tooth parameterized model which is used for describing the space pose distribution and shape characteristics of each tooth in the dentition.
The method for establishing the dentition local coordinate system in the step 1-2) comprises the following steps: taking the average gravity center of each tooth of the dentition as a coordinate origin O, taking the midpoint A of the connecting line of the gravity centers of the left and right central incisors of the dentition, and taking vectorsIs taken as the Z-axis forward direction, the center B, C of gravity of the left and right second molar of the dentition is taken to/>The direction of the X-axis is obtained by vector cross multiplication of the Y-axis forward direction and the Z-axis forward direction.
Said steps 1-4) comprise the steps of:
Step 1-4-1) the number of tooth samples of the same tooth position is denoted as M, the ith N-th tooth surface point cloud is denoted as Γ i, and the average of the set of tooth surface point clouds is denoted as Namely, a dental average model, and marking a covariance matrix as/>Wherein,
Step 1-4-2) versus covariance matrixPrincipal component analysis, record/>For covariance matrix/>From the top to the bottom, p j is its corresponding right eigenvector, i.e.,
Tooth surface shape of a sample reconstructed using B parametersIt is indicated that the number of the elements is,
Wherein b j obeys normal distribution with a mean value of 0 and a standard deviation of 1;
Step 1-4-3) sequentially performing the above operations on a plurality of tooth samples of each tooth position, and obtaining a tooth statistical shape model of 28 tooth positions of the upper and lower dentitions and morphological feature distribution thereof without considering third molar.
Said steps 1-5) comprise the steps of:
Step 1-5-1) note:
P＝[p1,p2,…,pB]∈R3N×B
σ＝[σ1,σ2,…,σB]T∈RB
b＝[b1,b2,…,bB]T∈RB
then its tooth shape is characterized in the local coordinate system of the ith tooth by using the B parameters of the statistical shape model as:
Wherein, as indicated by the ratio of the two vectors to the corresponding element;
Step 1-5-2) note vec N,3 as the operator to arrange a 3N length column vector into an N x 3 matrix according to the order of row priority, note s (i) as the relative size of the ith tooth with respect to the tooth mean model, r (i) as the rotation vector with respect to the tooth mean model, t (i) as the translation vector with respect to the tooth mean model, the pose transformed tooth model is denoted as Y (i),
Wherein Rot (·) represents a rotation matrix generated from the rotation vector,Representing adding a row vector to each row of the matrix;
Step 1-5-3) translating vectors transforming the local coordinate system of the ith dentition tooth into the dentition coordinate system are noted as Then/>A dentition parameterized model representing the mesh vertex coordinate matrix of the tooth in a dentition coordinate system, with K teeth, is expressed as:
Constructing a dentition parameterized model based on the upper dentition and the lower dentition to obtain a tooth parameterized model:
wherein P ul represents the relative pose of the upper and lower dentitions, A dentition parameterized model representing the upper dentition,A dentition parameterized model representing the following dentition.
Said step 2) comprises the steps of:
Step 2-1) obtaining a single or multiple dental photographs;
step 2-2) constructing and training a convolution neural network model based on residual connection, a cavity space convolution pooling pyramid and U-net, and extracting tooth contours of specific teeth in a tooth photo;
And 2-3) carrying out morphological erosion operation on the extracted tooth contour line to refine the contour line.
The dental photographs are classified into five categories according to photographing angles, i.e., frontal opening, left side Zhang Kouzhao, right side opening, maxillofacial photographing and mandibular facial photographing.
The step 2-2) of extracting the tooth profile of the specific tooth position in the tooth photo specifically comprises the following steps: the contours of all teeth except the upper and lower second third molars in the front mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the right side and the upper and lower second third molars on the left side in the left side mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the left side and the upper and lower second third molars on the right side in the right side mouth opening photograph are extracted, and the contours of all teeth except the third molars in the maxillofacial photograph and the mandibular facial photograph are extracted.
Said step 3) comprises the steps of:
Step 3-1), manually marking whether teeth are missing in the upper and lower dentitions to be reconstructed, and coding the teeth missing information by using Boolean vectors, wherein vector elements corresponding to the teeth missing are assigned as false, and the rest are true;
Step 3-2) using Boolean vector to encode specific teeth with extracted contours in different photos, if the contours of the teeth are extracted, the corresponding vector elements are assigned as true, otherwise, the corresponding vector elements are assigned as false;
Step 3-3) sequentially carrying out intersection operation on the Boolean vectors for extracting specific tooth contours by codes of different photos and the Boolean vectors for describing tooth missing labeling information, if a certain element of the obtained vector is true, indicating that the tooth needs to be projected in the tooth parameterized model, and respectively determining that the tooth parameterized model corresponds to the tooth required to be projected by different photos;
Step 3-4) initializing camera parameters and parameters in a tooth parameterized model according to shooting angles of different photos;
Step 3-5) respectively projecting teeth required to be projected by the tooth parameterized model according to different categories of the pictures divided according to shooting angles, representing the contour extracted from the pictures in step 2) as a set { c i } of points on a contour line in a pixel coordinate system, and similarly representing the visible contour line projected in the step as Then for some extracted contour point c i, the corresponding point on the projected contour line is/>The calculation is carried out by the following formula,
Where n i is the normal vector at the line of the contour of point c i,Point/>Normal vector at the contour line where (a) is located, < -, represents the vector inner product, σ is a preconfigured constant;
Step 3-6) removing the mismatching in the corresponding point relation, reserving the corresponding points of the residual outline, and specifically operating the corresponding point pairs According to the corresponding point matching loss value/>Sorting from small to large, reserving the corresponding point relation of the pre-configured proportion before sorting, wherein,
Said step 4) comprises the steps of:
Step 4-1) initializing parameters X to be estimated, including camera pose, camera internal parameters, parameters in a tooth parameterization model and relative pose of upper and lower dentitions of different photos, wherein the camera pose, the camera internal parameters and the relative pose of the upper and lower dentitions are tested by adopting a plurality of groups of experience values according to the shooting angles of the photos, a group of parameters with minimum sum of corresponding point matching loss values is reserved for initialization, and the parameters of the tooth parameterization model are initialized by probability distribution mean values of the tooth pose and shape characteristics;
Step 4-2) the penalty function to be optimized is noted as Where X is the parameter to be estimated, V is the number of teeth photographs, B v is the tooth contour extracted from the V-th photograph, and L (X, B v) is the single photograph loss function:
L(X,Bv)＝wpLp+wnLn+Lprior
Wherein w p and w n are weight constants, L p is a projection error, describes the relative position deviation of the corresponding points, L n is a normal error, describes the relative deviation of the profile normals of the corresponding points, L prior is a penalty term based on the tooth pose and shape probability distribution in the tooth parameterized model,
Wherein n is the number of corresponding points of the contour lines in the photo, m is the number of teeth projected by the tooth parameter model in the photo, s is the size vector of all the teeth projected in the photo, p i is the pose vector of the ith tooth, b i is the shape feature vector of the ith tooth, and D size,Dpose and D shape are the Markov distances of the size, pose and shape features of the teeth projected by each photo in the probability distribution respectively, and are used for describing the deviation degree of the current parameter estimation and the mean value of the probability distribution;
step 4-3) according to The optimal parameter estimate X * is output.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, the tooth mesh model with pose information is obtained through cutting, numbering and complementing operation of a plurality of groups of three-dimensional mesh dental models, corresponding points are extracted through similar transformation registration of dentition and teeth and non-rigid registration in a Gaussian process, registration parameters are reserved for modeling tooth size and pose distribution, a statistical shape model is constructed according to corresponding point relation to describe tooth shape characteristics, a parameterized three-dimensional tooth model is realized and established, the parameterized three-dimensional tooth model has deformability, tooth space distribution, pose and shape characteristics of different users can be fitted by an optimized method, and accuracy of model reconstruction is high.
(2) The invention uses the convolution neural network model based on residual connection, the cavity space convolution pooling pyramid and the U-net to realize the extraction of the tooth contours of specific tooth positions in the flaring photos with different angles, and has high contour extraction precision and high operation speed.
(3) According to the invention, based on the tooth size, pose and shape probability distribution in the tooth parameterized model, the outline corresponding point relation is calculated iteratively, and the loss function is optimized by using a sequence least square algorithm, so that the optimal parameter estimation is obtained, wherein the parameters to be estimated comprise camera pose matrixes corresponding to different photos, camera internal parameters, tooth relative position relations, the size, pose and shape vectors of each tooth, the three-dimensional parameterized model of the tooth is deformed to reconstruct the three-dimensional model corresponding to the tooth photo shot by the uncalibrated camera, so that an orthodontist can conveniently plan an orthodontic treatment scheme and monitor the orthodontic progress, the orthodontic review efficiency is improved, and the time of both doctors and patients is saved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
The embodiment provides a tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo, as shown in fig. 1, comprising the following steps:
step 1) constructing a tooth parameterized model.
Step 1-1) obtaining three-dimensional mesh dental models of upper and lower jaws obtained by a plurality of groups of intraoral scanners from a database, and obtaining an upper and lower dentition three-dimensional model with tooth numbers through segmentation, numbering and complementation operations, wherein the three-dimensional mesh dental model consists of triangular patches, describes the surfaces of crowns and peripheral parts of gingival tissues of the upper and lower dentitions, extracts triangular patch meshes belonging to different teeth respectively, numbering refers to using a digital marking method to number the extracted meshes of different teeth according to the tooth positions, and complementation refers to repairing defects in the extracted tooth meshes to form closed meshes.
Specifically, the scanned three-dimensional mesh dental model of the upper and lower jaws comprises two files of an upper jaw mesh model and a lower jaw mesh model, and the two files are stored in the file format of OBJ or STL. Tooth segmentation can be realized by manual segmentation or other computer-aided tooth segmentation algorithms, and aims to segment tooth grids belonging to different tooth positions and grids belonging to gingiva. In the process of numbering, the triangular patches belonging to the gingiva are represented by the number 0, the triangular patches belonging to different dental sites are numbered by using the FDI dental site representation method, which is also called a digital mark method, and other numbering methods can be used for numbering. After numbering, since the triangular patches of teeth with the same tooth positions have the same numbers, they can be extracted respectively to represent the crown surfaces (excluding the tooth roots) of the teeth with different tooth positions, and the obtained triangular patch grid can be fully closed by using computer software such as MeshLab and the like to become a watertight grid.
Step 1-2) performing dentition alignment registration on a plurality of groups of upper dentition three-dimensional models and lower dentition three-dimensional models with tooth numbers, and establishing a dentition local coordinate system, wherein the alignment registration refers to the calculation of the center of gravity of each tooth of each dentition, and the alignment of the dentition models through rigid transformation according to the corresponding relation of the tooth numbers.
The method for establishing the dentition local coordinate system comprises the following steps: taking the average gravity center of each tooth of the dentition as a coordinate origin O, taking the midpoint A of the connecting line of the gravity centers of the left and right central incisors of the dentition, and taking vectorsIs taken as the Z-axis forward direction, the center B, C of gravity of the left and right second molar of the dentition is taken to/>The direction of the X-axis is obtained by vector cross multiplication of the Y-axis forward direction and the Z-axis forward direction.
Specifically, for all the upper dentition three-dimensional models, the average coordinates of the mesh vertices of the respective dentition teeth, that is, the center of gravity of the respective teeth, of each upper dentition three-dimensional model are calculated. Taking an upper dentition three-dimensional model without tooth missing (without considering a third molar), taking the gravity centers of all the dentition teeth of the upper dentition three-dimensional model as a reference point set, carrying out rigid transformation alignment registration on the reference point set by using 14 points in total according to the dentition corresponding relation, and carrying out rigid transformation alignment registration on all the gravity centers of the teeth of other upper dentition three-dimensional models. Calculating the average barycenter coordinates of the barycenter of each tooth sample of each tooth position after registration to obtain 14 average barycenter coordinates, calculating the average coordinates of the 14 coordinates again, recording as the coordinate origin O of a tooth row local coordinate system, taking the average barycenter coordinate connecting line midpoint A of the left and right central incisors in the upper tooth row, taking the average barycenter sitting marks of the left and right second molar teeth of the upper tooth row as B, C, and thenThe above procedure was repeated for all the following three-dimensional models of dentition.
Step 1-3) carrying out similar transformation alignment registration on tooth grid vertexes with the same tooth positions in a plurality of groups of upper and lower dentition three-dimensional models by using a consistency point drift algorithm, carrying out non-rigid registration by using a Gaussian process, searching a corresponding point matching relation of a minimized Euclidean distance by using a greedy algorithm, finally reserving N corresponding points for each tooth grid, counting the tooth size and pose probability distribution of each tooth position, and modeling by using a plurality of normal distributions.
Step 1-3-1) downsampling tooth mesh vertexes of all samples to 2N points by using a furthest point sampling algorithm, taking the tooth mesh vertexes of all samples as point clouds to be registered, downsampling tooth sample number 0 to N points by using the furthest point sampling algorithm, moving the gravity center of the tooth sample to a coordinate origin, taking the gravity center as an initial reference point cloud, and establishing a tooth local coordinate system, wherein the coordinate axis direction is the same as that of a tooth column coordinate system. Specifically, n=1500 is taken during the implementation.
Step 1-3-2) sequentially performing similar transformation registration on all tooth samples and a reference point cloud in a tooth local coordinate system by using a consistency point drift algorithm. Specifically, each similarity transformation registration includes a size, a rotation vector, a translation vector, and a total of 7 parameters.
Step 1-3-3) deforming the reference point cloud by using a Gaussian process, enabling the deformed reference point cloud to be attached to the registered source point cloud by minimizing the chamfering distance, and searching for a corresponding point matching relation of the minimized Euclidean distance by using a greedy algorithm. Specifically, the chamfer distance between point sets S 1 and S 2 is denoted as,
Step 1-3-4) generating a new N-point mean point cloud as a new reference point cloud based on the corresponding point relation among all samples, wherein the mean value of all size scaling factors obtained in the constrained registration process is 1, the mean value of Euler angles corresponding to all rotation matrixes is [0, 0], and the mean value of all translation vectors is [0, 0].
Step 1-3-5), if the relative Euclidean distance error between the new reference point cloud and the reference point cloud of the previous iteration is smaller than a threshold value, ending the iteration, otherwise, returning to step 1-3-2), and continuing the iteration.
Step 1-3-6) preserving registration parameters of the last similarity transformation, namely rotation vectors, translation vectors and scaling factors of the similarity transformation, modeling statistical distributions of sizes and tooth postures of teeth of each tooth position respectively by using multi-element normal distribution, wherein the sizes refer to scaling factors of the teeth of the sample relative to a mean value sample, and the postures refer to relative rotation vectors and translation vectors of the teeth sample relative to the mean value, so as to obtain probability distributions of the sizes and the postures of the teeth of each tooth position. Specifically, the pose probability distribution of each tooth position is a six-degree-of-freedom multi-element normal distribution, and comprises three-degree-of-freedom rotation parameters and three-degree-of-freedom translation parameters.
Step 1-4) constructing a statistical shape model for the teeth of the same tooth position with the same number of points after registration by using the point distribution model, and describing probability distribution of each shape characteristic of each tooth position by using normal distribution.
Step 1-4-1) the number of tooth samples of the same tooth position is denoted as M, the ith N-th tooth surface point cloud is denoted as Γ i, and the average of the set of tooth surface point clouds is denoted asNamely, a dental average model, and marking a covariance matrix as/>Wherein,
Step 1-4-2) versus covariance matrixPrincipal component analysis, record/>For covariance matrix/>From the top to the bottom, p j is its corresponding right eigenvector, i.e.,
Tooth surface shape of a sample reconstructed using B parametersIt is indicated that the number of the elements is,
Wherein b j obeys a normal distribution with a mean value of 0 and a standard deviation of 1. Specifically, b=20 was taken during the implementation so that the model obtained by using the first B principal components for principal component analysis had a dissolubility of 95%.
Step 1-4-3) sequentially performing the above operations on a plurality of tooth samples of each tooth position, and obtaining a tooth statistical shape model of 28 tooth positions of the upper and lower dentitions and morphological feature distribution thereof without considering third molar.
Step 1-5) fusing the tooth size and pose probability distribution and the statistical shape model of each kind of teeth to obtain a tooth parameterized model which is used for describing the space pose distribution and shape characteristics of each tooth in the dentition.
Step 1-5-1) note:
P＝[p1,p2,…,pB]∈R3N×B
σ＝[σ1,σ2,…,σB]T∈RB
b＝[b1,b2,…,bB]T∈RB
then its tooth shape is characterized in the local coordinate system of the ith tooth by N parameters of the statistical shape model as:
Wherein, as indicated by the ratio of the two vectors to the corresponding element;
Step 1-5-2) note vec N,3 as the operator to arrange a 3B length column vector into an N x 3 matrix according to the order of row preference, s (i) as the relative size of the ith tooth relative to the tooth mean model, r (i) as the rotation vector relative to the tooth mean model, t (i) as the translation vector relative to the tooth mean model, the pose transformed tooth model is denoted as Y (i),
Wherein Rot (·) represents a rotation matrix generated from the rotation vector,Representing adding a row vector to each row of the matrix;
Step 1-5-3) translating vectors transforming the local coordinate system of the ith dentition tooth into the dentition coordinate system are noted as (Coordinate axis direction is the same, no rotation transformation) then/>A dentition parameterized model representing the mesh vertex coordinate matrix of the tooth in a dentition coordinate system, with K teeth, is expressed as:
Constructing a dentition parameterized model based on the upper dentition and the lower dentition to obtain a tooth parameterized model:
wherein p ul represents the relative pose of the upper and lower dentitions, A dentition parameterized model representing the upper dentition,A dentition parameterized model representing the following dentition. In particular, p ul has six degrees of freedom, including three rotational parameters and three translational parameters.
Step 2) obtaining a single or multiple teeth photo, and extracting tooth contour lines of specific teeth according to photo angles.
Step 2-1) obtain a single or multiple dental photographs, in this embodiment, the dental photographs are classified into five categories according to the photographing angle, i.e., front opening, left side Zhang Kouzhao, right side opening, maxillofacial photographing, and mandibular photographing.
Step 2-2) constructing and training a convolution neural network model based on residual connection, a cavity space convolution pooling pyramid and U-net, and extracting tooth contours of specific teeth in a tooth photo, wherein the method specifically comprises the following steps: the contours of all teeth except the upper and lower second third molars in the front mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the right side and the upper and lower second third molars on the left side in the left side mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the left side and the upper and lower second third molars on the right side in the right side mouth opening photograph are extracted, and the contours of all teeth except the third molars in the maxillofacial photograph and the mandibular facial photograph are extracted.
Specifically, the convolutional neural network model uses a standard-sized U-net, i.e., a residual-connected encoder-decoder structure, in which the encoder consists of five convolutional modules, downsampling is performed using a max-pooling layer, each convolutional module includes two convolutional layers, and the number of convolution kernels of one of the five convolutions of the downsampled convolutional modules is 64, 128, 256, 512, 1024 in order, and the decoder consists of five convolutional modules, each convolutional module includes two convolutions, upsampling is performed using a bilinear upsampling layer. A hole space convolution pooling pyramid is disposed between the last encoder convolution module and the first upsampling convolution module. Residual connections are deployed among each convolution module.
And 2-3) carrying out morphological erosion operation on the extracted tooth contour line to refine the contour line. Specifically, the width of the finally extracted thinned contour line is three pixel points.
Step 3) obtaining tooth missing information, and carrying out projection and contour matching based on a tooth parameterized model, wherein the projection and contour matching is as follows: and 3) extracting specific tooth positions of tooth contour lines from the tooth missing information and different tooth photos, projecting the specific tooth positions into a three-dimensional tooth parameterized model to obtain tooth contours, and matching the tooth contours obtained by projection in the step 3) with the tooth contour lines obtained by extraction in the step 2) according to the photos to obtain contour corresponding points.
Step 3-1) manually marking whether teeth are missing in the upper and lower dentitions to be reconstructed, and using Boolean vectors to encode the teeth missing information, wherein vector elements corresponding to the teeth missing are assigned as false, and the rest are true.
Step 3-2) using Boolean vector to encode specific teeth with extracted contours in different photos, if the contours of the teeth are extracted, the corresponding vector elements are assigned as true, otherwise, false.
Step 3-3) sequentially carrying out intersection operation on the Boolean vectors for extracting the specific tooth contours by the codes of different photos and the Boolean vectors for describing the tooth missing labeling information, if a certain element of the obtained vector is true, indicating that the tooth needs to be projected in the tooth parameterized model, and respectively determining that the tooth parameterized model corresponds to the tooth required to be projected by different photos.
Step 3-4) initializing camera parameters and parameters in the tooth parameterized model according to the shooting angles of different photos, wherein the camera parameters comprise camera pose and camera internal parameters such as focal length and principal point.
Step 3-5) respectively projecting teeth required to be projected by the tooth parameterized model according to different categories of the pictures divided according to shooting angles, representing the contour extracted from the pictures in step 2) as a set { c i } of points on a contour line in a pixel coordinate system, and similarly representing the visible contour line projected in the step asThen for some extracted contour point c i, the corresponding point on the projected contour line is/>The calculation is carried out by the following formula,
Where n i is the normal vector at the line of the contour of point c i,Point/>Normal vector at the contour line where (c) is located, < -, represents the vector inner product, σ is a preconfigured constant.
Step 3-6) removing the mismatching in the corresponding point relation, reserving the corresponding points of the residual outline, and specifically operating the corresponding point pairsAccording to the corresponding point matching loss value/>Sorting from small to large, reserving 99% of corresponding point relations before sorting, wherein,
Step 4) parameter optimization: and optimizing a loss function based on the tooth size, the pose, the shape probability distribution and the contour corresponding points in the tooth parameterized model to obtain optimal parameter estimation.
Step 4-1) initializing parameters X to be estimated, including camera pose, camera internal parameters, parameters in a tooth parameterized model and relative pose of upper and lower dentitions of different photos, wherein the camera pose, the camera internal parameters and the relative pose of the upper and lower dentitions are tested by adopting a plurality of groups of empirical values according to shooting angles of the photos, a group of parameters with minimum sum of corresponding point matching loss values is reserved for initialization, and the parameters of the tooth parameterized model are initialized by probability distribution mean values of the tooth pose and shape characteristics.
Specifically, after the tooth parameterized model is projected by using the empirical camera parameters, the obtained visible contour line is regarded as a two-dimensional point set, the two-dimensional similarity transformation registration is used for registering the obtained visible contour line and the extracted tooth contour line, and the sum of loss values of the matching points is calculated according to the corresponding relation between the projection contour points and the extraction contour points after transformation and is used for selecting the most suitable empirical camera parameters. After determining the used empirical camera parameters, the current empirical camera parameters are updated by using a direct linear transformation algorithm according to the projection contour point correspondence before and after transformation, for camera parameter initialization.
Step 4-2) the penalty function to be optimized is noted asWhere X is the parameter to be estimated, V is the number of teeth photographs, B v is the tooth contour extracted from the V-th photograph, and L (X, B v) is the single photograph loss function:
L(X,Bv)＝wpLp+wnLn+Lprior
Wherein w p and w n are weight constants, L p is a projection error, describes the relative position deviation of the corresponding points, L n is a normal error, describes the relative deviation of the profile normals of the corresponding points, L prior is a penalty term based on the tooth pose and shape probability distribution in the tooth parameterized model, and specifically,
Wherein n is the number of corresponding points of the contour lines in the photo, m is the number of teeth projected by the tooth parameter model in the photo, s is the size vector of all the teeth projected in the photo, p i is the pose vector of the ith tooth, b i is the shape feature vector of the ith tooth, and D size,Dpose and D shape are the Marsh distances of the size, pose and shape features of the teeth projected by each photo in the probability distribution respectively, and are used for describing the deviation degree of the current parameter estimation and the mean value of the probability distribution.
Step 4-3) according toThe optimal parameter estimate X * is output. Specifically, in the optimization process, the gradient of the loss function is calculated, and the optimization is performed by using a sequence least square algorithm.
And 5) updating the tooth parameterized model according to the optimal parameter estimation, carrying out projection and contour matching and parameter optimization again, updating the parameter estimation until the iteration termination condition is met, outputting a final parameter estimation result, updating the tooth parameterized model according to the final parameter estimation result, and reconstructing the tooth three-dimensional model.
Step 5-1), after matching corresponding points of the projection contour line and the photo extraction contour line each time, performing global optimization according to corresponding point relations in single photo or multiple photos, and updating all parameter estimates simultaneously, wherein the parameter estimates comprise camera pose, camera internal parameters, parameters in a tooth parameterized model and relative pose of upper and lower dentitions of different photos;
Step 5-2) adjusting camera parameters according to the updated parameter estimation, deforming the tooth parameterized model to obtain a new tooth parameterized model, projecting again and matching corresponding points of the contour lines;
And 5-3) re-performing parameter estimation based on the new tooth parameterized model and the corresponding points of the outline, and outputting a final parameter estimation result until a termination condition is met, wherein the termination condition means that the maximum iteration number or the loss function value is smaller than a threshold value, the tooth pose and the shape characteristic in the final parameter estimation and the relative pose of the upper dentition and the lower dentition are used for deforming the tooth parameterized model, and the upper dentition and the lower dentition parameterized model are converted into a three-dimensional tooth triangular patch grid model through a Poisson process, so that the three-dimensional tooth model reconstruction is completed.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by a person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (10)
1. A tooth three-dimensional model reconstruction method based on a tooth parameterized model and a tooth photo, which is characterized by comprising the following steps:
Step 1) constructing a tooth parameterized model;
step 2) obtaining single or multiple teeth photos, and extracting tooth contour lines of specific teeth according to photo angles;
Step 3) obtaining tooth missing information, and carrying out projection and contour matching based on a tooth parameterized model, wherein the projection and contour matching is as follows: extracting specific tooth positions of tooth contour lines from the tooth missing information and different tooth photos, projecting the specific tooth positions into a three-dimensional tooth parameterized model to obtain tooth contours, and matching the tooth contours obtained by projection in the step 3) with the tooth contour lines obtained by photo extraction in the step 2) to obtain contour corresponding points;
Step 4) parameter optimization: optimizing a loss function based on tooth size, pose, shape probability distribution and contour corresponding points in the tooth parameterized model to obtain optimal parameter estimation;
And 5) updating the tooth parameterized model according to the optimal parameter estimation, carrying out projection and contour matching and parameter optimization again, updating the parameter estimation until the iteration termination condition is met, outputting a final parameter estimation result, updating the tooth parameterized model according to the final parameter estimation result, and reconstructing the tooth three-dimensional model.
2. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 1, wherein said step 1) comprises the steps of:
Step 1-1) obtaining three-dimensional mesh dental models of upper and lower jaws obtained by a plurality of groups of intraoral scanners from a database, and obtaining an upper and lower dentition three-dimensional model with tooth numbers through segmentation, numbering and complementation operations, wherein the three-dimensional mesh dental model consists of triangular patches, describes the surfaces of crowns and peripheral parts of gingival tissues of the upper and lower dentitions, respectively extracts triangular patch meshes belonging to different teeth, numbering refers to using a digital marking method to number the extracted meshes of different teeth according to the tooth positions, and complementation refers to repairing defects in the extracted tooth meshes to form closed meshes;
Step 1-2) carrying out dentition alignment registration on a plurality of groups of upper dentition three-dimensional models and lower dentition three-dimensional models with tooth numbers, and establishing a dentition local coordinate system, wherein the alignment registration refers to the steps of calculating the center of gravity of each tooth of each dentition, and aligning the group of dentition models through rigid transformation according to the corresponding relation of the tooth numbers;
Step 1-3) carrying out similar transformation alignment registration on tooth grid vertexes with the same tooth positions in a plurality of groups of upper and lower dentition three-dimensional models by using a consistency point drift algorithm, carrying out non-rigid registration by using a Gaussian process, searching a corresponding point matching relation of a minimized Euclidean distance by using a greedy algorithm, finally reserving N corresponding points for each tooth grid, counting tooth size and pose probability distribution of each tooth position, and modeling by using a plurality of normal distributions;
step 1-4) constructing a statistical shape model for teeth of the same tooth positions with the same number of points after registration by using a point distribution model, and describing probability distribution of each shape characteristic of each tooth position tooth by using normal distribution;
step 1-5) fusing the tooth size and pose probability distribution and the statistical shape model of each kind of teeth to obtain a tooth parameterized model which is used for describing the space pose distribution and shape characteristics of each tooth in the dentition.
3. The method for reconstructing a tooth three-dimensional model based on a tooth parameterized model and a tooth photograph according to claim 2, wherein the method for establishing a dentition local coordinate system in step 1-2) is as follows: taking the average gravity center of each tooth of the dentition as a coordinate origin O, taking the midpoint A of the connecting line of the gravity centers of the left and right central incisors of the dentition, and taking vectorsIs taken as the Z-axis forward direction, the center B, C of gravity of the left and right second molar of the dentition is taken to/>The direction of the X-axis is obtained by vector cross multiplication of the Y-axis forward direction and the Z-axis forward direction.
4. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 3, wherein said steps 1-4) comprise the steps of:
Step 1-4-1) the number of tooth samples of the same tooth position is denoted as M, the ith N-th tooth surface point cloud is denoted as Γ i, and the average of the set of tooth surface point clouds is denoted as Namely, a dental average model, and marking a covariance matrix as/>Wherein,
Step 1-4-2) versus covariance matrixPrincipal component analysis, record/>For covariance matrix/>From the top to the bottom, p j is its corresponding right eigenvector, i.e.,
Tooth surface shape of a sample reconstructed using B parametersIt is indicated that the number of the elements is,
Wherein b j obeys normal distribution with a mean value of 0 and a standard deviation of 1;
Step 1-4-3) sequentially performing the above operations on a plurality of tooth samples of each tooth position, and obtaining a tooth statistical shape model of 28 tooth positions of the upper and lower dentitions and morphological feature distribution thereof without considering third molar.
5. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 4, wherein said steps 1-5) comprise the steps of:
Step 1-5-1) note:
P＝[p1,p2,…,pB]∈R3N×B
σ＝[σ1,σ2,…,σB]T∈RB
b＝[b1,b2,…,bB]T∈RB
then its tooth shape is characterized in the local coordinate system of the ith tooth by using the B parameters of the statistical shape model as:
Wherein, as indicated by the ratio of the two vectors to the corresponding element;
Step 1-5-2) note vec N,3 as the operator to arrange a 3N length column vector into an N x 3 matrix according to the order of row priority, note s (i) as the relative size of the ith tooth with respect to the tooth mean model, r (i) as the rotation vector with respect to the tooth mean model, t (i) as the translation vector with respect to the tooth mean model, the pose transformed tooth model is denoted as Y (i),
Wherein Rot (·) represents a rotation matrix generated from the rotation vector,Representing adding a row vector to each row of the matrix;
Step 1-5-3) translating vectors transforming the local coordinate system of the ith dentition tooth into the dentition coordinate system are noted as ThenA dentition parameterized model representing the mesh vertex coordinate matrix of the tooth in a dentition coordinate system, with K teeth, is expressed as:
Constructing a dentition parameterized model based on the upper dentition and the lower dentition to obtain a tooth parameterized model:
wherein p ul represents the relative pose of the upper and lower dentitions, Dentition parameterized model representing upper dentition,/>A dentition parameterized model representing the following dentition.
6. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 1, wherein said step 2) comprises the steps of:
Step 2-1) obtaining a single or multiple dental photographs;
step 2-2) constructing and training a convolution neural network model based on residual connection, a cavity space convolution pooling pyramid and U-net, and extracting tooth contours of specific teeth in a tooth photo;
And 2-3) carrying out morphological erosion operation on the extracted tooth contour line to refine the contour line.
7. The method for reconstructing a three-dimensional model of teeth based on a parameterized model of teeth and a photograph of teeth according to claim 6, wherein said photograph of teeth is classified into five categories according to photographing angle, frontal opening, left side Zhang Kouzhao, right side opening, maxillofacial photographing and mandibular photographing.
8. The method for reconstructing a three-dimensional model of teeth based on a parameterized model of teeth and a photograph of teeth according to claim 7, wherein the step 2-2) of extracting the tooth profile of a specific tooth position in the photograph of teeth comprises: the contours of all teeth except the upper and lower second third molars in the front mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the right side and the upper and lower second third molars on the left side in the left side mouth opening photograph are extracted, the contours of all teeth except the upper and lower middle incisors on the left side and the upper and lower second third molars on the right side in the right side mouth opening photograph are extracted, and the contours of all teeth except the third molars in the maxillofacial photograph and the mandibular facial photograph are extracted.
9. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 1, wherein said step 3) comprises the steps of:
Step 3-1), manually marking whether teeth are missing in the upper and lower dentitions to be reconstructed, and coding the teeth missing information by using Boolean vectors, wherein vector elements corresponding to the teeth missing are assigned as false, and the rest are true;
Step 3-2) using Boolean vector to encode specific teeth with extracted contours in different photos, if the contours of the teeth are extracted, the corresponding vector elements are assigned as true, otherwise, the corresponding vector elements are assigned as false;
Step 3-3) sequentially carrying out intersection operation on the Boolean vectors for extracting specific tooth contours by codes of different photos and the Boolean vectors for describing tooth missing labeling information, if a certain element of the obtained vector is true, indicating that the tooth needs to be projected in the tooth parameterized model, and respectively determining that the tooth parameterized model corresponds to the tooth required to be projected by different photos;
Step 3-4) initializing camera parameters and parameters in a tooth parameterized model according to shooting angles of different photos;
Step 3-5) respectively projecting teeth required to be projected by the tooth parameterized model according to different categories of the pictures divided according to shooting angles, representing the contour extracted from the pictures in step 2) as a set { c i } of points on a contour line in a pixel coordinate system, and similarly representing the visible contour line projected in the step as Then for some extracted contour point c i, the corresponding point on the projected contour line is/> The calculation is carried out by the following formula,
Where n i is the normal vector at the line of the contour of point c i,Point/>Normal vector at the contour line where (a) is located, < -, represents the vector inner product, σ is a preconfigured constant;
Step 3-6) removing the mismatching in the corresponding point relation, reserving the corresponding points of the residual outline, and specifically operating the corresponding point pairs According to the corresponding point matching loss value/>Sorting from small to large, reserving the corresponding point relation of the pre-configured proportion before sorting, wherein,
10. A method for reconstructing a three-dimensional model of a tooth based on a parameterized model of a tooth and a photograph of a tooth according to claim 1, wherein said step 4) comprises the steps of:
Step 4-1) initializing parameters X to be estimated, including camera pose, camera internal parameters, parameters in a tooth parameterization model and relative pose of upper and lower dentitions of different photos, wherein the camera pose, the camera internal parameters and the relative pose of the upper and lower dentitions are tested by adopting a plurality of groups of experience values according to the shooting angles of the photos, a group of parameters with minimum sum of corresponding point matching loss values is reserved for initialization, and the parameters of the tooth parameterization model are initialized by probability distribution mean values of the tooth pose and shape characteristics;
Step 4-2) the penalty function to be optimized is noted as Where X is the parameter to be estimated, V is the number of teeth photographs, B v is the tooth contour extracted from the V-th photograph, and L (X, B v) is the single photograph loss function:
L(X,Bv)＝wpLp+wnLn+Lprior
Wherein w p and w n are weight constants, L p is a projection error, describes the relative position deviation of the corresponding points, L n is a normal error, describes the relative deviation of the profile normals of the corresponding points, L prior is a penalty term based on the tooth pose and shape probability distribution in the tooth parameterized model,
Wherein n is the number of corresponding points of the contour lines in the photo, m is the number of teeth projected by the tooth parameter model in the photo, s is the size vector of all the teeth projected in the photo, p i is the pose vector of the ith tooth, b i is the shape feature vector of the ith tooth, and D size,Dpose and D shape are the Markov distances of the size, pose and shape features of the teeth projected by each photo in the probability distribution respectively, and are used for describing the deviation degree of the current parameter estimation and the mean value of the probability distribution;
step 4-3) according to The optimal parameter estimate X * is output.
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