CN108242056B - Three-dimensional tooth grid data segmentation method based on harmonic field algorithm - Google Patents
Three-dimensional tooth grid data segmentation method based on harmonic field algorithm Download PDFInfo
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Abstract
The invention relates to a segmentation method of three-dimensional tooth grid data based on a harmonic field algorithm, which comprises the steps of importing three-dimensional tooth grid data, sequentially picking up two points of each tooth to be segmented in the three-dimensional tooth grid data, and determining a foreground constraint point and a background constraint point of each tooth to be segmented; judging whether the vertex in the three-dimensional tooth grid data is in a concave surface, and further determining concave surface information of the vertex; calculating a Gaussian curvature value of a vertex in the three-dimensional tooth grid data; calculating a harmonic field scalar value based on a harmonic field algorithm; calculating an unknown coefficient matrix x; and obtaining a segmentation boundary contour of each tooth to be segmented through boundary contour threshold value segmentation processing, and performing smoothing processing on the segmentation boundary contour to finally complete the segmentation of the three-dimensional tooth grid data. The invention well solves the phenomenon of segmentation error caused by unobvious tooth boundaries, and has better segmentation effect on teeth with tooth missing, high crowding degree and the like, and high robustness.
Description
Technical Field
The invention relates to a segmentation method of three-dimensional tooth grid data based on a harmonic field algorithm, belonging to the technical field of three-dimensional grid segmentation.
Background
With the development of economic life, people have great pursuit for the beauty of teeth. However, 20% -30% of people in China have irregular teeth, and the orthodontic requirements of people are higher and higher. The traditional tooth correction scheme such as the strip steel tooth socket brings inconvenience to diet of patients and influences the beauty of the patients during treatment. In recent years, 3D printed invisible braces have been produced and have brought a great deal of way to patients. Accurate tooth segmentation is an extremely crucial step in medical dental clinical orthodontics. However, it is not a simple task to determine the tooth boundaries in tooth segmentation, because there is a great difference in the shape, crowdedness, arrangement, etc. between teeth of different patients in clinical trials, which brings great complexity to a scheme capable of dealing with all tooth segmentation.
The conventional Tooth segmentation algorithm is based on the average curvature information of the vertices, such as that used in the book segmentation on dental simulations sketching skin published by Kan Wu, LiChen, jinli, yanheng zhou, because the average curvature information of the vertices reflects the characteristics of the Tooth boundaries, then we obtain feature points by thresholding the curvatures of the vertices, and the feature points are subjected to morphological adjustment and region growing to obtain the Tooth and gum boundaries to realize Tooth segmentation, which is a very common mesh segmentation algorithm. However, for some scanned tooth models, the curvature at the boundary is not obvious, in other words, the tooth boundary is smooth, errors such as few segmentation or over-segmentation occur in the segmentation algorithm, the dependency of the segmentation result of the tooth on the curvature information of the tooth is large, and the procedure is not robust enough.
There are more mesh segmentation algorithms, but there are fewer algorithms available for performing tooth segmentation on three-dimensional mesh tooth data, and some segmentation algorithms have more interactions and are more costly for the user. In addition, some tooth segmentation algorithms are not suitable for various shapes, and for example, segmentation based on curvature information of mesh vertices causes few or many segmentation phenomena, and is not robust enough.
In order to solve the situation of insignificant curvature, a bridging tool is needed, and for a closed-loop feature point formed by noise points on one tooth, a deleting tool is needed, for example, patent 201610065608.1 proposes a method and an apparatus for segmenting tooth three-dimensional grid data, which are invented and created by the present invention, and the correctness of tooth segmentation can be ensured through these interactions. In addition, the interaction requires the user to have higher knowledge of dental medical anatomy common knowledge, computer skilled operation and the like, and the learning cost is higher.
Disclosure of Invention
The invention solves the problems: the method for segmenting the three-dimensional tooth grid data based on the harmonic field algorithm has the advantages that interaction is less and simple based on the harmonic field algorithm, the complexity of teeth is not depended on, the phenomenon of segmentation errors caused by unobvious tooth boundaries is well solved, in addition, the method can have better segmentation effect on teeth with the conditions of tooth missing, high crowding degree and the like, and the robustness is high.
The technical scheme of the invention is as follows: a segmentation method of three-dimensional tooth grid data based on a harmonic field algorithm comprises the following steps:
the method comprises the steps of firstly, importing three-dimensional tooth grid data, sequentially picking up two points for each tooth to be segmented in the three-dimensional tooth grid data, and determining a foreground constraint point and a background constraint point of each tooth to be segmented; judging whether the vertex in the three-dimensional tooth grid data is in a concave surface, and further determining concave surface information of the vertex; calculating a Gaussian curvature value of a vertex in the three-dimensional tooth grid data;
secondly, calculating a harmonic field scalar value based on a harmonic field algorithm according to the foreground constraint point, the background constraint point, the concave information of the vertex and the Gaussian curvature value of the vertex in the first step; constructing a Laplace matrix L, a penalty factor matrix P and a coefficient matrix b of the three-dimensional tooth grid data by using a harmonic field scalar value based on a harmonic field algorithm;
thirdly, calculating an unknown coefficient matrix x according to the Laplace matrix L, the penalty factor matrix P and the coefficient matrix b in the second step; the unknown coefficient matrix x represents a boundary contour threshold of each tooth to be segmented in the three-dimensional tooth grid data, a segmented boundary contour of each tooth to be segmented is obtained through boundary contour threshold segmentation processing, the segmented boundary contour is subjected to smoothing processing, and finally segmentation of the three-dimensional tooth grid data is completed.
In the first step of the step, the method for determining the foreground constraint point and the background constraint point of each tooth to be segmented in the three-dimensional tooth grid data is as follows:
two points marked as A, B are sequentially picked up along the direction of an arch of teeth at the dental cusp of each tooth to be segmented, the radius of each tooth to be segmented is calculated according to A, B points, and a foreground constraint point and a background constraint point of each tooth to be segmented are obtained by using a vertex search of a k-neighborhood algorithm according to the radius of each tooth.
In the first step, the method for determining the concave information of the three-dimensional tooth grid data vertex is as follows:
and determining the concave information of the vertex by using a vertex concave calculation formula, wherein the concave calculation formula reflects whether the vertex in the three-dimensional tooth grid data is in a concave surface or not by calculating the difference between the position of the vertex in the three-dimensional tooth grid data and the average position of the vertex in the three-dimensional tooth grid data searched by a k-neighborhood algorithm, and further determining the concave information of the vertex.
In the second step, a Laplace matrix L, a penalty factor matrix P and a coefficient matrix b of the three-dimensional tooth grid data are constructed by the harmonic field scalar values based on the harmonic field algorithm, and the specific method comprises the following steps: and using the Gaussian curvature value of the vertex in the three-dimensional tooth grid data as the weighted value of the Laplace matrix L, and correcting the weighted value of the Laplace matrix L according to the concave information of the vertex and simultaneously correcting the penalty factor matrix P and the coefficient matrix b.
In the third step, a segmentation boundary contour of each tooth to be segmented is obtained through threshold value division processing and is subjected to smoothing processing, and the method is specifically realized as follows:
(1) carrying out color mapping display on the unknown coefficient matrix x according to the solved unknown coefficient matrix x, and carrying out statistics on the result value of the color according to the difference of the foreground constraint point and the background constraint point of each tooth to be segmented to obtain the segmentation boundary contour of each tooth to be segmented;
(2) and smoothing the obtained segmentation boundary contour of each tooth through a cubic B-spline, and finally completing the segmentation of the three-dimensional tooth grid data.
Compared with the prior art, the invention has the advantages that:
(1) the existing grid segmentation algorithms are more, but the algorithms which can be used for tooth segmentation on three-dimensional grid tooth data are less, and the interaction operation in the existing segmentation algorithms is more, so that the cost is higher for a user. In addition, some tooth segmentation algorithms are not suitable for various shapes, and for example, segmentation based on curvature information of mesh vertices causes few or many segmentation phenomena, and is not robust enough. Therefore, the harmonic field segmentation algorithm is used, so that a plurality of problems in tooth segmentation are solved to a great extent, the tooth segmentation with complex shape and high crowding degree can be processed, the interactivity is less, the interaction is simple, the practicability is high, the segmented tooth boundary is more in line with the medical anatomy of teeth, the tooth model segmentation with different complexities can be adapted, the guarantee is provided for the subsequent tooth deformity correction, and meanwhile, the algorithm can reduce the operation difficulty of a user and has important practical significance and application value.
(2) The invention based on the harmonic field segmentation algorithm has the advantages of less interactivity and simple interaction, and reduces the interactive labor intensity of users. Furthermore, the user does not need to have too much knowledge skills in medicine, computers, etc. At present, some domestic tooth segmentation software performs segmentation based on curvature information of grid vertexes, on one hand, the interactive labor intensity is high, and on the other hand, the segmentation result is greatly influenced by the tooth model noise points after being scanned by gypsum and the like. However, the segmentation algorithm based on the harmonic field is more robust, can process more complex tooth models with missing teeth, high crowdedness and the like, is basically not influenced by noise points of the tooth models, and a user only needs to pick up two points on each tooth to be segmented according to the previous rule. Therefore, the method has important practical significance and application value and high market application potential.
Drawings
FIG. 1 is a flow chart of an implementation of the method of the present invention;
FIG. 2 is a schematic diagram of foreground constraint points FS and background constraint points BS of each tooth to be segmented in three-dimensional tooth mesh data;
FIG. 3 is a graph of three-dimensional dental mesh data vertex concavity information determination;
FIG. 4 is a Laplace matrix L plot of three-dimensional dental mesh data;
FIG. 5 is a graph showing the effect of the segmentation according to the present invention, wherein (a), (c), (e) are three-dimensional tooth mesh data and original model data, and (b), (d), and (f) are segmented according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
As shown in fig. 1, the process of the present invention mainly includes determining each tooth foreground constraint point FS, background constraint point BS and concave information of three-dimensional tooth grid data vertex to be segmented in three-dimensional tooth grid data; constructing a Laplacian matrix L, a penalty factor matrix P, a coefficient matrix b and an unknown coefficient matrix x of the three-dimensional tooth grid data by using a harmonic field scalar value based on a harmonic field algorithm; and solving to obtain an unknown coefficient matrix x, performing threshold value division processing to obtain a segmented boundary contour of each tooth to be segmented, and smoothing the boundary contour by using a cubic B spline.
1. Determining each tooth foreground constraint point FS and background constraint point BS to be segmented in the three-dimensional tooth grid data:
as shown in fig. 2, a foreground constraint point FS and a background constraint point BS of each tooth to be segmented are constructed:
(11) the user picks two points in sequence for each tooth to be segmented, and the program is automatically labeled A, B, with the point A, B being located as close as possible to the interproximal spaces between adjacent teeth.
(12) A Path label from the point A to the point B is obtained by using a distance shortest Path search algorithm and is marked as Path (A, B), a mesh vertex C corresponding to a central point in the Path (A, B) is taken as a sphere center, and a sphere equation is constructed by taking half of the Euclidean distance between A, B two points as a radius r. And (5) carrying out k-neighbor algorithm grid search by taking the point C as a starting point to obtain a set S, wherein the k value is the number of grid vertexes in Path (A, B).
(13) And traversing the mesh vertexes in the set S, substituting the vertexes in the traversing process into a sphere equation, judging whether the vertexes are positioned in the sphere, marking the point as the constraint point of the tooth in the sphere, otherwise, discarding the point, and repeating the operation on other teeth to be segmented until the constraint points of all the teeth to be segmented are determined. And in the segmentation process, the teeth are segmented one by one according to the interaction result, the constraint point of the current tooth is used as a foreground constraint point and is marked as FS, the constraint points of the other teeth are used as background constraint points and are marked as BS, and the next tooth is segmented similarly until the segmentation is finished.
2. The method for determining the concave information of the three-dimensional tooth grid data vertex comprises the following steps:
as shown in fig. 3, the determination of the concavity information for the vertices of the three-dimensional dental mesh data: in the harmonic field-based segmentation algorithm, the segmentation result is sensitive to the concave surface of the grid, so that whether the point is on the concave surface or not is judged in the weight calculation process of the Laplace matrix L, and the weight is modified to achieve a good segmentation effect. The grid vertex is in the concave surface judgment calculation formula:
(Vavg，i-Vi)·Ni>λ
wherein ViIndicates the position of the point, NiRepresents ViNormal to, VavgiiRepresents the vertex ViK is the average position of (k ═ 1), n represents the number of k-adjacent vertices,. represents the dot product of the two vectors, and E represents the edge in the mesh. In the experimental process, according to the empirical value of λ, taking the value of λ to be 0.001 will obtain the correct concave judgment result.
3. As shown in fig. 4, a laplacian matrix L, a penalty factor matrix P, a coefficient matrix b, an unknown coefficient matrix x of the three-dimensional tooth mesh data are constructed:
(31) the segmentation of the teeth in the present invention mainly uses the computation of the harmonic field and the boundaries of the teeth to be segmented more closely conform to the medical anatomy of the teeth. In addition, the harmonic field value in the harmonic field algorithm is a scalar value, the calculation result is sensitive to the concave information of the grid vertex, and the boundary of the tooth is generally at the concave position, so the boundary of the tooth can be well extracted by using the harmonic field.
(32) The harmonic field scalar value can be calculated by solving the poisson equation △ x as 0 and satisfying the dicke boundary condition, where x is an unknown coefficient matrix, △ is a Laplacian operator, and a matrix formed by the Laplacian operator is a symmetric positive definite matrix, and Cholesky decomposition is performed on the matrix to form the equation as follows:
(L+P)x＝Pb,
wherein L is a Laplace matrix, P is a penalty factor matrix, b is a coefficient matrix, and x is an unknown coefficient matrix.
Where i, j are the three-dimensional tooth mesh data vertex indices, L, respectivelyijRepresenting Laplacian matrix L, FS and BS of vertex indexes i and j corresponding to three-dimensional tooth grid data are respectively a foreground constraint point and a background constraint point, α is a penalty factor coefficient, and P is a penalty factor coefficientijPenalty factor representing the index i, j of the corresponding vertex of the three-dimensional tooth grid data, bijA coefficient matrix b representing the vertex indices i, j corresponding to the three-dimensional dental grid data, E representing the edges of the three-dimensional dental grid data, wijL in Laplace matrix L for indexing i, j corresponding to vertexes of three-dimensional tooth grid dataijWeight of (1), wijThe calculation mode of the weight is different from most Laplacian cotangent weight calculation formulas, and the following conclusion is obtained by comprehensively considering the medical anatomical shape of the three-dimensional grid tooth and the like: the weights calculated will make the harmonic field sufficiently smooth and sensitive to concave shapes. The former constraint makes the segmented tooth boundary smoother, and the latter constraint makes the segmented tooth boundary segmented in the correct direction.
(33)wijThe specific calculation method is as follows:
wherein, | eijI represents one side e of the three-dimensional tooth grid dataijLength of (G)iAnd GjRespectively, three-dimensional tooth mesh data vertex ViAnd VjThe curvature of Gauss, gamma is a small floating point number, and the value of gamma is 10-4In order to avoid zero division errors in the scores, a large variation such as multiplication by β is given to the vertex weights at some concave surfaces to make the vertex weights obviously different from other points, and a reasonable β value is set, wherein the value of β is 10-2Thus, the correct segmentation effect can be achieved.
4. Linear system of equations (L + P) x Pb, smoothing of the boundary contour:
(41) and (4) solving a linear equation system (L + P) x ═ Pb according to the equation (32), and performing color histogram statistical analysis on the solved unknown coefficient matrix x.
(42) And obtaining the boundary contour of the tooth to be segmented through threshold processing according to the color histogram statistics and the foreground constraint point FS and the background constraint point BS of each tooth to be segmented, and performing three-time B-spline smoothing processing on the rough tooth boundary contour obtained preliminarily to achieve tooth segmentation precision required by clinical medical orthodontics and finally complete the segmentation of the three-dimensional tooth grid data.
(43) As shown in fig. 5, (a), (c), (e) are three-dimensional tooth model data raw data to be segmented, and (b), (d), and (f) are segmentation effects calculated by the present invention. Wherein (a) the more common three-dimensional tooth model data in fig. 5 can achieve a correct segmentation effect well through the algorithm of the present invention, and red dots in the graph represent control points obtained through cubic B-spline smoothing; in (c) of fig. 5, the three-dimensional tooth model data density is high, and the crowdedness is high, but the segmentation of the present invention still can achieve the correct segmentation effect, which illustrates the robustness of the present invention to the segmentation of the three-dimensional tooth model data with high crowdedness; one tooth is lost in the three-dimensional tooth model data in (e) in fig. 5, and a correct segmentation effect can still be achieved through segmentation based on a harmonic field algorithm, which shows that the three-dimensional tooth model data of the missing tooth still has strong robustness; in conclusion, through the division of the plurality of groups of three-dimensional tooth model data, the tooth segmentation method has good tooth segmentation effect on the teeth with the situations of tooth missing, high crowdedness and the like, has high robustness, and can be suitable for the division of the more complex three-dimensional tooth model data.
The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.
Claims (5)
1. A segmentation method of three-dimensional tooth grid data based on a harmonic field algorithm is characterized by comprising the following steps:
the method comprises the steps of firstly, importing three-dimensional tooth grid data, sequentially picking up two points for each tooth to be segmented in the three-dimensional tooth grid data, and determining a foreground constraint point and a background constraint point of each tooth to be segmented; judging whether the vertex in the three-dimensional tooth grid data is in a concave surface, and further determining concave surface information of the vertex; calculating a Gaussian curvature value of a vertex in the three-dimensional tooth grid data;
secondly, calculating a harmonic field scalar value based on a harmonic field algorithm according to the foreground constraint point, the background constraint point, the concave information of the vertex and the Gaussian curvature value of the vertex in the first step; constructing a Laplace matrix L, a penalty factor matrix P and a coefficient matrix b of the three-dimensional tooth grid data by using a harmonic field scalar value based on a harmonic field algorithm; the coefficient matrix b is constructed according to the foreground constraint points and the background constraint points in the first step, and represents the constraint of the three-dimensional tooth grid data segmentation boundary;
thirdly, calculating an unknown coefficient matrix x according to the Laplace matrix L, the penalty factor matrix P and the coefficient matrix b in the second step; the unknown coefficient matrix x represents a boundary contour threshold of each tooth to be segmented in the three-dimensional tooth grid data, a segmented boundary contour of each tooth to be segmented is obtained through boundary contour threshold segmentation processing, the segmented boundary contour is subjected to smoothing processing, and finally segmentation of the three-dimensional tooth grid data is completed.
2. The segmentation method of three-dimensional tooth grid data based on harmonic field algorithm according to claim 1, characterized in that: in the first step, the method for determining the foreground constraint point and the background constraint point of each tooth to be segmented in the three-dimensional tooth grid data is as follows:
two points marked as A, B are sequentially picked up along the direction of an arch of teeth at the dental cusp of each tooth to be segmented, the radius of each tooth to be segmented is calculated according to A, B points, and a foreground constraint point and a background constraint point of each tooth to be segmented are obtained by using a vertex search of a k-neighborhood algorithm according to the radius of each tooth.
3. The segmentation method of three-dimensional tooth grid data based on harmonic field algorithm according to claim 1, characterized in that: in the first step, the method for determining the concave information of the three-dimensional tooth grid data vertex is as follows:
and determining the concave information of the vertex by using a vertex concave calculation formula, wherein the concave calculation formula reflects whether the vertex in the three-dimensional tooth grid data is in a concave surface or not by calculating the difference between the position of the vertex in the three-dimensional tooth grid data and the average position of the vertex in the three-dimensional tooth grid data searched by a k-neighborhood algorithm, and further determining the concave information of the vertex.
4. The segmentation method of three-dimensional tooth grid data based on harmonic field algorithm according to claim 1, characterized in that: in the second step, a Laplace matrix L, a penalty factor matrix P and a coefficient matrix b of the three-dimensional tooth grid data are constructed by the harmonic field scalar values based on the harmonic field algorithm, and the specific method comprises the following steps: and using the Gaussian curvature value of the vertex in the three-dimensional tooth grid data as the weighted value of the Laplace matrix L, and correcting the weighted value of the Laplace matrix L according to the concave information of the vertex and simultaneously correcting the penalty factor matrix P and the coefficient matrix b.
5. The segmentation method of three-dimensional tooth grid data based on harmonic field algorithm according to claim 1, characterized in that: in the third step, a segmentation boundary contour of each tooth to be segmented is obtained through threshold value division processing and is subjected to smoothing processing, and the method is specifically realized as follows:
(1) carrying out color mapping display on the unknown coefficient matrix x according to the solved unknown coefficient matrix x, and carrying out statistics on the result value of the color according to the difference of the foreground constraint point and the background constraint point of each tooth to be segmented to obtain the segmentation boundary contour of each tooth to be segmented;
(2) and smoothing the obtained segmentation boundary contour of each tooth through a cubic B-spline, and finally completing the segmentation of the three-dimensional tooth grid data.
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