CN107230255B - Tooth restoration method based on universal template - Google Patents
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Abstract
The invention discloses a tooth restoration method based on a universal template. The initial dental model obtained by three-dimensional scanning is divided into various tooth models, and then the tooth models are processed: repairing the edge, deleting the everted dough sheet and smoothing the edge; registering the selected template tooth model with the tooth model to be restored according to the local coordinate system of the tooth model; and deforming the template tooth model according to the projection relation, splicing the deformed partial template tooth model to the tooth model to be restored, and performing smooth operation to finish restoration of the tooth model. The invention can efficiently and accurately restore the missing side of the tooth model obtained after three-dimensional scanning, and restore the base, so that the tooth becomes a closed and complete triangular mesh model, and the later correction is favorably realized.
Description
Technical Field
The invention relates to the field of digital oral cavities, in particular to a tooth restoration method based on a universal template.
Background
In recent years, digital oral techniques have been rapidly developed, and invisible orthodontics of teeth have been gradually popularized. In the process of orthodontics, a three-dimensional grid model of teeth needs to be established for virtual correction. However, data of the side edge and the base of the tooth model obtained after scanning and cutting are lost, and the tooth model needs to be repaired to form a complete and independent tooth model, so that virtual correction can be conveniently carried out.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a tooth restoration method based on a universal template.
As shown in fig. 14, the technical solution adopted by the present invention is to divide the initial dental model obtained by three-dimensional scanning into each tooth model, and then process the tooth models therein by the following steps:
A. repairing the edge, deleting the everted dough sheet and smoothing the edge;
B. taking the selected template tooth model as a universal template, and registering the selected template tooth model with the tooth model to be restored according to a local coordinate system of the tooth model;
C. and deforming the template tooth model according to the projection relation, splicing the deformed partial template tooth model to the tooth model to be restored, and performing smooth operation to finish restoration of the tooth model.
The step A is specifically as follows:
a-1) calculating the root mean square curvature of each vertex in the tooth model, and dividing all the vertices into two types of vertices with large curvature and small curvature according to a curvature threshold T;
a-2) traversing each tooth model for multiple times, and deleting boundary triangular patches with high curvature vertexes at the edges of the tooth model until all the boundary triangular patches at the edges of the tooth model have no vertexes with high curvature;
a-3) traversing each tooth model for multiple times, and deleting boundary triangular patches of which three vertexes of the edge of the tooth model are boundary points until at least one point of all the boundary triangular patches of the edge of the tooth model is not a boundary point;
and A-4) traversing all the tooth models, and performing Taubin smoothing operation on two layers of triangular patches (including a boundary triangular patch and a layer of triangular patch in the boundary triangular patch) of each tooth model positioned at the edge.
The typical number of traversals in said steps a-2) and a-3) is 4-5.
The step B specifically comprises the following steps:
b-1) carrying out axis fixing operation on the tooth model to be restored, and determining a local coordinate system of the tooth model to be restored;
b-2) finding a corresponding template tooth model from a template tooth model library according to the type of the tooth model to be restored;
and B-3) matching the tooth model to be restored and the template tooth model according to the local coordinate systems of the tooth model to be restored and the template tooth model.
The axis fixing operation in the step B-1) is to determine a local coordinate system of the tooth according to the morphological characteristics of the tooth. The final local coordinate system takes the central point of the tooth model as an origin, the Z axis points to the direction of the dental crown surface from the central point of the tooth model, the X axis is vertical to the direction of the dental arch line and points to the labial side from the lingual side, and the Y axis passes through two sides of the tooth.
In the step B-2), because 32 types of teeth are provided, the shapes of the teeth of the same type are relatively close, and the corresponding template tooth model is found from the template tooth model library according to the type of the tooth model to be restored.
In the step B-3), the local coordinate system of the template tooth model is subjected to coordinate transformation, so that the local coordinate system of the template tooth model is superposed with the local coordinate of the tooth model to be restored, and the same coordinate transformation matrix is acted on the template tooth model, so that the matching of the template tooth model and the tooth model to be restored is completed. In practice, a transformation matrix between the template tooth model and the local coordinate system of the tooth model to be restored is constructed, and the local coordinates of the template tooth model are transformed to the local coordinates of the tooth model to be restored by using the transformation matrix.
The step B can also adopt the technical scheme in the invention content in the specification of an algorithm for constructing a local coordinate system of the tooth by using a standard model library, wherein the application number is 201710348848.7, the application date is 2017.5.17.
The step C specifically comprises the following steps:
c-1) according to the projection condition of the vertex on the template tooth model projected onto the tooth model to be restored, dividing the template tooth model into a projection area and a non-projection area;
c-2) deforming the die tooth model according to the projection relation, directly projecting the deformation to the tooth model to be restored in the projection area, and carrying out accompanying projection deformation in the non-projection area;
c-3) splicing the non-projection area on the deformed template tooth model with the tooth model to be restored, and performing smoothing operation on the seam.
The projection of the vertex on the template tooth model to the tooth model to be restored is specifically as follows: each vertex is projected to a triangular face of the tooth model to be restored along the respective normal direction.
Since the tooth model to be restored is a model with a deletion and the template tooth model is a model without a deletion, not all points can be projected on the surface of the tooth model to be restored. Therefore, in the step C-1), on the template tooth model, an area formed by the vertexes of the template tooth model which can be projected onto the tooth model to be restored is used as a projection area, an area formed by the vertexes of the template tooth model which cannot be projected onto the tooth model to be restored is used as a non-projection area, the non-projection area is regarded as a missing part on the tooth model to be restored, and the missing part is subsequently spliced onto the tooth model to be restored.
In the step C-2), because the non-deformation region obtained in the step C-1) can not be well attached to the boundary of the tooth model to be restored, certain deformation operation needs to be carried out on the non-deformation region. The method comprises the following specific steps:
traverse all vertices on the template tooth model:
firstly, moving all vertexes in a projection area to the surface of the tooth model to be restored through projection to obtain the corresponding projection point position and moving distance;
then, the vertex in the non-projection area is processed in the following way:
starting from a non-projection region vertex adjacent to a projection point of a vertex on the inner edge of a projection region, moving each vertex to a new vertex along a projection direction according to the average moving distance of all adjacent and projected points around the vertex, thereby completing the projection of the vertex, continuously iterating and processing layer by layer towards the vertex of the non-projection region farthest from the projection region, wherein each layer of vertex is a circle of vertex parallel to the edge of the projection region, and stopping iteration until the sum of the moving distances of all the vertices between two adjacent iteration processing is less than a moving threshold (specifically, 0.01 can be adopted), and not performing vertex projection.
The method for calculating the sum diff of the moving distances of all the vertexes between two iterations is as follows:
wherein d (i) represents the ith vertex viP denotes the set of vertices of the projection area, viIndicates the position of the ith vertex, vipRepresents the ith vertex viPosition of the projection point on the tooth model to be restored, vj kRepresenting the kth iteration viIs the jth adjacent vertex of, | | vi-vipI means Vi-vipAnd vipThe euclidean distance between them.
The non-projection area on the template tooth model obtained through the previous operation can be used for filling the missing part of the tooth model to be repaired, therefore, in the step C-3), the projection area of the template tooth model is deleted, the surface model obtained by performing projection processing on the non-projection area is used as a patch model, and at this time, a gap exists between the patch model and the tooth model to be repaired, as shown in fig. 15, and then the gap between the patch model and the tooth model to be repaired is filled in the following seam mode:
c-3-1) firstly obtaining an ordered boundary point set patchSet of the patch model and an ordered boundary point set originSet of the tooth model to be restored, wherein the boundary points in the ordered boundary point set are marked by ordered serial numbers, namely, the points are numbered in the same direction.
C-3-2) traversing the boundary points in the ordered boundary point set originSet of the tooth model to be restored, wherein for the ith boundary point ob (i) and the (i +1) th boundary point ob (i +1), the boundary point ob (i) and the boundary point ob (i +1) are adjacent:
finding out a boundary point pb (1) nearest to the boundary point ob (i) in the ordered boundary point set patchSet of the patch model, then finding out a boundary point pb (2) nearest to the boundary point ob (i +1) in the ordered boundary point set patchSet of the patch model, adding a triangular patch formed by taking ob (i), ob (i +1) and pb (1) as vertexes,
c-3-3) then judging whether pb (1) and pb (2) are the same boundary point and processing:
if pb (1) and pb (2) are not the same boundary point, traversing the boundary point pb (j) between pb (1) and pb (2), pb (1) is less than or equal to pb (j) and less than pb (2), and adding a triangular patch formed by ob (i +1), pb (j) and pb (j +1) as vertexes for each boundary point pb (j);
if pb (1) and pb (2) are the same boundary point, no new surface is added;
c-3-4) repeating the steps C-3-2) and C-3-3), constructing a joint by connecting triangular patches between the ordered boundary point set patchSet of the patch model and the ordered boundary point set originSet of the tooth model to be repaired, and smoothing the jointed triangular patches by adopting Laplace smoothing in order to enable the quality of the grids at the joint to be more natural.
The invention has the beneficial effects that:
the invention can accurately restore the missing side edge and the base of the tooth model obtained after three-dimensional scanning, so that the tooth becomes a closed and complete triangular mesh model close to reality, and the later correction is favorably realized.
Drawings
FIG. 1 is a plot of root mean square curvature of a tooth, the darker the grayscale, the greater the curvature;
FIG. 2 is a root-mean-square curvature diagram of a single tooth, wherein the deeper the gray scale, the larger the curvature is represented;
FIG. 3 is a diagram of a tooth model with everted patches removed and a smoothing operation completed;
FIG. 4 is a comparison of a single tooth model before and after performing the operation of step 1);
FIG. 5 is a diagram of a tooth model with sides and bottom to be restored;
FIG. 6 is a schematic illustration of local coordinates after a tooth centering operation;
FIG. 7 is a graph illustrating the registration of the dental model to be restored and the template dental model;
FIG. 8 is a diagram illustrating the effect of deformation of the projection area of the template tooth model onto the tooth model to be restored;
FIG. 9 is a graph of the effect of a deformed non-projected region of a template tooth model;
FIG. 10 is a diagram of a patch model extracted from the non-deformed region of the template tooth model;
FIG. 11 is a diagram of the results of the seaming operation performed on the patch model and the tooth model to be restored;
FIG. 12 is a graph of the results of smoothing a seam after splicing;
FIG. 13 is a schematic view of a process for creating a joint between a patch model and a dental model to be restored;
FIG. 14 is a flow chart of a template tooth model deformation algorithm;
FIG. 15 is a flow chart of the seaming algorithm.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The embodiment and the specific implementation process of the invention are as follows:
the edges of the teeth just cut out can have a plurality of everted surface sheets and burrs, and the edges need to be repaired in order to ensure the accuracy of the tooth model. As shown in fig. 1, the tooth model can be colored according to the curvature, the dark area is an area with a larger curvature, the light area is an area with a smaller curvature, and in this embodiment, the curvature threshold is 6. Fig. 2 is a schematic view of curvature distribution of a single tooth model. Firstly, traversing all tooth models, deleting boundary triangular patches with vertexes marked as larger curvatures at the edges of the tooth models, and in the embodiment, performing iteration on the operation of each tooth model for 8 times; then, removing burrs, traversing all tooth models, and deleting boundary triangular patches of which three vertexes of the edge of the tooth model are boundary points, wherein in the embodiment, the operation is performed for each tooth model for 5 times of iteration. And then traversing all the tooth models, marking two layers of triangular patches of the boundary of each tooth model, and performing Taubin smoothing operation on the marked part. The tooth model after the border restoration is shown in fig. 3, and the tooth model before and after the border restoration is shown in fig. 4.
When the tooth model is cut, the cut tooth model has a loss in the side surface portion and the bottom surface portion because some adjacent teeth are close and the gum is blocked. These missing tooth models need to be restored in order to obtain a complete single tooth model. The tooth model to be restored is shown in fig. 5.
Next, a fixed axis operation is performed, as shown in fig. 6, according to the local coordinate axis and the type of the tooth to be restored, a corresponding template tooth model can be searched from the universal template tooth model library, and a registration operation is performed with the template tooth model, as shown in fig. 7. After the registration, a projection operation is performed on the template tooth model, the template tooth model is divided into a projection area and a non-projection area, and the projection area is directly deformed onto the tooth model to be restored, as shown in fig. 8, the dark area represents the projection area, and the light area represents the non-projection area. The non-deformed region of the die tooth model is also subjected to a deformation operation, as shown in fig. 9. And after deformation, the non-projection area is independently extracted to obtain a patch model for repairing the missing part of the tooth model to be repaired, as shown in fig. 10, at the moment, a tiny gap exists between the patch model and the tooth model to be repaired, and splicing operation is realized by utilizing a seam algorithm.
The splicing operation is illustrated by taking the points in fig. 13 as an example, and the flow is shown in fig. 15:
(1) for the ith boundary point ob (1) and the (i +1) th boundary point ob (i +1) in the ordered set of boundary points originSet of the tooth model to be restored:
finding out a boundary point pb (1) nearest to the boundary point ob (i) in the ordered boundary point set patchSet of the patch model, then finding out a boundary point pb (2) nearest to the boundary point ob (i +1) in the ordered boundary point set patchSet of the patch model, adding a triangular patch formed by taking ob (i), ob (i +1) and pb (1) as vertexes,
then judging whether pb (1) and pb (2) are the same boundary point and processing: if pb (1) and pb (2) are not the same boundary point, traversing the boundary point pb (j) between pb (1) and pb (2), pb (1) is less than or equal to pb (j) and less than pb (2), and adding a triangular patch formed by ob (i +1), pb (j) and pb (j +1) as vertexes for each boundary point pb (j);
if pb (1) and pb (2) are the same boundary point, no new facets are added.
By analogy, a joint is formed by the triangular patches connected between the ordered boundary point set patchSet of the patch model and the ordered boundary point set originSet of the tooth model to be restored, and the joint is shown in fig. 11.
Then, laplace smoothing operation is performed on the seam region to obtain a finally repaired model, as shown in fig. 12.
Therefore, the missing side edge and the missing base of the tooth model obtained after the three-dimensional scanning are accurately repaired, and the tooth becomes a closed and complete triangular mesh model close to reality.
Claims (4)
1. A tooth restoration method based on a universal template is characterized in that: the method comprises the following steps of (1) dividing an initial dental model obtained by three-dimensional scanning into various tooth models, and then processing the tooth models by adopting the following steps:
A. repairing the edge, deleting the everted dough sheet and smoothing the edge;
B. registering the selected template tooth model with the tooth model to be restored according to the local coordinate system of the tooth model;
C. deforming the template tooth model according to the projection relation, splicing the deformed partial template tooth model to the tooth model to be restored, and performing smooth operation to finish restoration of the tooth model;
the step C specifically comprises the following steps:
c-1) according to the projection condition of the vertex on the template tooth model projected onto the tooth model to be restored, dividing the template tooth model into a projection area and a non-projection area;
c-2) deforming the die tooth model according to the projection relation, directly projecting the deformation to the tooth model to be restored in the projection area, and carrying out accompanying projection deformation in the non-projection area;
c-3) splicing the non-projection area on the deformed template tooth model with the tooth model to be restored, and performing smoothing operation on the seam;
the step C-2) is specifically as follows:
traverse all vertices on the template tooth model:
firstly, moving all vertexes in a projection area to the surface of the tooth model to be restored through projection to obtain the corresponding projection point position and moving distance;
then, the vertex in the non-projection area is processed in the following way: starting from the vertex of a non-projection area adjacent to the projection point of the vertex of the inner edge of the projection area, moving each vertex to a new vertex along the projection direction according to the average moving distance of all adjacent and projected points around the vertex, continuously iterating layer by layer towards the vertex of the non-projection area farthest from the projection area, stopping iteration until the sum of the moving distances of all the vertexes between two adjacent iterations is smaller than a moving threshold value, and not performing vertex projection any more;
in the step C-3), the projection area of the template tooth model is firstly deleted, the surface model subjected to projection processing in the non-projection area is used as a patch model, and then the gap between the patch model and the tooth model to be repaired is filled in by adopting the following seam mode:
c-3-1) firstly obtaining an ordered boundary point set patchSet of the patch model and an ordered boundary point set originSet of the tooth model to be restored;
c-3-2) traversing the boundary points in the ordered set of boundary points originSet of the tooth model to be restored, and for the ith boundary point ob (i) and the (i +1) th boundary point ob (i + 1):
finding out a boundary point pb (1) closest to a boundary point ob (i) in the ordered boundary point set patchSet of the patch model, then finding out a boundary point pb (2) closest to the boundary point ob (i +1) in the ordered boundary point set patchSet of the patch model, and adding a triangular patch formed by taking ob (i), ob (i +1) and pb (1) as vertexes;
c-3-3) then judging whether pb (1) and pb (2) are the same boundary point and processing:
if pb (1) and pb (2) are not the same boundary point, traversing the boundary point pb (j) between pb (1) and pb (2), pb (1) is less than or equal to pb (j) and less than pb (2), and adding a triangular patch formed by ob (i +1), pb (j) and pb (j +1) as vertexes for each boundary point pb (j);
if pb (1) and pb (2) are the same boundary point, no new surface is added;
c-3-4) repeating the steps C-3-2) and C-3-3), constructing a joint by connecting triangular patches between the ordered boundary point set patchSet of the patch model and the ordered boundary point set originSet of the tooth model to be restored, and then smoothing the jointed triangular patches by adopting Laplace smoothing.
2. A universal template-based dental restoration method according to claim 1, wherein: the step B specifically comprises the following steps:
b-1) carrying out axis fixing operation on the tooth model to be restored, and determining a local coordinate system of the tooth model to be restored;
b-2) finding a corresponding template tooth model from a template tooth model library according to the type of the tooth model to be restored;
and B-3) matching the tooth model to be restored and the template tooth model according to the local coordinate systems of the tooth model to be restored and the template tooth model.
3. A universal template-based dental restoration method according to claim 1, wherein: the projection of the vertex on the template tooth model to the tooth model to be restored is specifically as follows: each vertex is projected to a triangular face of the tooth model to be restored along the respective normal direction.
4. A universal template-based dental restoration method according to claim 1, wherein: in the step C-1), on the template tooth model, a region formed by the vertexes of the template tooth model which can be projected onto the tooth model to be restored is taken as a projection region, and a region formed by the vertexes of the template tooth model which cannot be projected onto the tooth model to be restored is taken as a non-projection region.
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