A gingival three-dimensional model shell extraction method and device based on a marching cube algorithm

Abstract

A gingival three-dimensional model shell extraction method and device based on the Marching Cube algorithm, the method comprising: (1) importing an initial gingival three-dimensional model and performing relevant pretreatment; (2) performing extrusion offset on non-point; (3) constructing a signed distance field by adopting a grid diffusion + hierarchical construction strategy; (4) deleting redundant repeated vertices and corresponding face sheets in the model; (5) traversing the vertices of the inner shell gingival model in the manifold, and removing topological errors; (6) stitching the bottom surface of the height compensation gingival model to obtain a closed outer shell gingival model; (7) combining the standard inner shell gingival model and the standard outer shell gingival model together to obtain an open shell gingival model; and (8) obtaining a complete and closed standard shell gingival model. The present application provides effective pretreatment and post-treatment processes before and after Marching Cube reconstruction, accurately repairs the construction defects of the Marching Cube result, and finally generates a standard shell gingival model without error when imported into CAD printing software, and the mesh quality is uniform and healthy.

Description

Technical Field

[0001] The present invention provides a method and device for shelling an initial 3D gingival model and subsequent model optimization. The method uses the classic Marching Cube mesh reconstruction algorithm to generate a preliminary inner shell gingival model. In order to address the common mesh quality issues, the method uses a hole-patching mesh reconstruction algorithm and the characteristics of the mesh half-edge data structure to ultimately obtain a complete, standard shelled gingival model with normal facets. Background Art

[0002] In recent years, rapid advances in dental medicine, such as the application of 3D scanning, CAD / CAM technology, the use of new materials, and the introduction of artificial intelligence and digital platforms, have greatly improved the precision and comfort of invisible braces. Furthermore, evidence-based medicine provides scientific evidence for their safety and effectiveness. These advancements have collectively driven the widespread use of invisible braces in orthodontics, making them a popular choice for an increasing number of people. The production of invisible braces requires 3D printing a virtual gingival model of the patient after simulated orthodontic treatment, which is then pressed into a mold. To conserve 3D printing materials, the virtual gingival model must be shelled while maintaining its strength. Shelling is a key operation in CAD software used for 3D printing. As the name suggests, shelling creates a solid object with uniform wall thickness. This function can be used to add thickness to an unsealed surface model to create a solid model, or to hollow out a closed model to create a shell with uniform thickness. This shell can expand or contract inwards.

[0003] The most common and classic shell extraction algorithm is based on Marching Cube mesh reconstruction. The Marching Cube algorithm is a classic algorithm for extracting isosurfaces from discrete 3D data fields. It is primarily used in medical visualization scenarios, such as 3D reconstruction of CT and MRI scans. The basic idea is to first construct a 3D voxel distance field based on the geometry to be reconstructed. The voxels in the distance field are then processed one by one, separating the cubes that intersect with the isosurface. Interpolation is then used to calculate the intersection points of the isosurface with the cube edges. Based on the relative position of each cube vertex and the isosurface, the intersection points of the isosurface with the cube edges are connected in a specific manner to generate an isosurface, which serves as an approximation of the isosurface within the cube. This is due to a fundamental assumption of Marching Cubes: the data field varies continuously along the edges of a hexahedron. Specifically, if two vertices on an edge are respectively greater than or less than the value of the isosurface, then there is one and only one point on that edge that intersects the isosurface. Intuitively, it is to use many small cubes to divide the space, and then use the plane inside the small cubes to approximate the current isosurface. Obviously, the more small cubes there are, the better the approximation effect.

[0004] Directly using the Marching Cube-based mesh reconstruction algorithm for shelling the initial 3D gingival model presents numerous problems. First, because the mesh is reconstructed by constructing planes within small cubes, the model is composed of discrete facets. Adjacent facets do not share vertices, but instead overlap. This not only complicates subsequent processing but also results in wasted vertices. Furthermore, facets often intersect, resulting in complex and non-manifold edges.

[0005] The standard shell gingival model generation algorithm of the present invention performs appropriate extrusion preprocessing based on the special structure of the initial gingival three-dimensional model and the final invisible braces production requirements; and adjusts the construction process of the signed distance field, and proposes a grid diffusion + hierarchical signed distance field construction idea. In addition, the present invention proposes a series of optimization processes after the reconstruction of MarchingCube: based on the results of the preliminary inner shell gingival model, duplicate vertices are removed, vertices and facets with topological errors are deleted, holes are repaired, and finally the bottom surface is cut and stitched. The optimized standard shell gingival model can be better recognized by 3D printing software, which improves the quality of mesh reconstruction. If the standard shell gingival model is used for further processing, the usability is also higher and more stable. Summary of the Invention

[0006] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provides a method and device for extracting a gingival three-dimensional model based on MarchingCube.

[0007] The goal of the present invention is to provide a shelling method specifically for the initial gingival three-dimensional model based on the classic Marching Cube mesh reconstruction algorithm, as well as a method for optimizing and repairing the preliminary inner shell gingival model after shelling, so as to solve the problems of the shelling gingival model and obtain a healthy and robust model.

[0008] The present invention uses the classic Marching Cube mesh reconstruction algorithm to generate a preliminary inner shell gingival model. In order to solve the common mesh quality problem, the hole repair mesh reconstruction algorithm and the characteristics of the mesh half-edge data structure are used to finally obtain a complete and normal-faceted standard shell gingival model.

[0009] The input for mesh optimization is the initial 3D gum model; the output is a complete, mesh-healthy standard shelled gum model. The process involves position correction, downward extrusion, distance field and inner shell construction, half-edge reconstruction, inner shell repair, Boolean operations, bottom face trimming, and bottom edge stitching.

[0010] A first aspect of the present invention provides a method for extracting a gingival three-dimensional model based on Marching Cube, the specific steps of which are as follows:

[0011] Step 1: Import the initial gingival 3D model and set it as M o The bottom surface of the model is not closed, and all the bottom edge points are in the same plane. Find the half edge that is only used by one face to get all the bottom edge points, and set the set of all bottom edge points as PS b According to PS b The bottom plane normal can be calculated, and the transformation matrix can be further calculated to transform the initial gingival 3D model to a position where the bottom surface is parallel to the XoY plane (the XoY plane is the plane orthogonal to the X-axis and Y-axis of the world coordinate system), and then translated to a position where the geometric center coincides with the origin of the world coordinate system. Finally, the reset gingival model M is obtained. r .

[0012] Step 2: Based on M r The bottom edge of the PS is extruded 2.0mm in the negative direction of the Z axis. b Make a copy and get PS bc . Put PS bc The point is translated 2.0mm in the negative direction of Z axis, and then compared with PS b Stitch the surface piece point by point and add it to M r In the middle, the highly compensated gingival model M is obtained h .

[0013] Step 3: Next, construct the signed distance field, or SDF. The SDF is constructed using a grid diffusion + hierarchical strategy. First, a grid diffusion with a lower resolution is constructed. h The bounding box voxelization constructs a blank field, in which each voxel can be set to a value. Through the breadth-first search (BFS) algorithm, from M h The surface expands inward and outward layer by layer to fill the value of the corresponding voxel. Since the diffusion is discrete, parallel computing is used here, which is relatively efficient.

[0014] Assume the required thickness of the shell is T mm, find all voxels with a value of -T, and put them into the voxel set VS ori Next, put VS ori The voxels in are further subdivided by a hierarchical strategy to calculate the local subdivision signed distance field LDSDF. The value of each subvoxel is obtained by interpolating the values ​​of nearby voxels. Find all the subvoxels with the closest value to -T and use the classic MarchingCube to generate the isosurface to obtain the preliminary inner shell gingival model, which is set as

[0015] Step 4: Traverse All the faces, record the three vertex positions of each face. Then delete the redundant duplicate vertices in the model, leave only one vertex at each position, and delete all the faces at the same time, at this time the model becomes a point cloud model. Then according to the three vertex positions of each face recorded before and The remaining vertex without duplication in the middle, restructure the topology, With a light number of vertices, and the same number of faces as before. At this time, the model is no longer a bunch of scattered faces, but a mesh model with half edge data structure, which is called the manifold inner gingival model, set as Subsequently, the characteristics of the half edge data structure can be used to Further processing.

[0016] Step 5, delete All the error vertices. The specific method is: first traverse all the vertices, check the connection of the vertices with the help of the connection characteristics of the half edge data structure, find out the vertices with structural errors, and delete them to get the optimized inner gingival model, set as The error vertices of may be vertices with unreasonable topological connection, or two points of non-popular edges that are reused more than twice. After removing the error vertices, holes may appear. Next, find out all the holes of Call the hole repair algorithm to fill the holes.

[0017] The principle of the hole repair algorithm is first to calculate the average value l of the boundary edge length according to the boundary point information of the hole; Then calculate the angle size of the two adjacent edges of each boundary point; Find out the three boundary points with the smallest angle between the two edges, calculate the distance s between the left and right two boundary points of the three points, judge whether s<2×l is true, if true, add a triangle, if not, add two triangles. Then find the new boundary point, judge whether the hole still exists, if it still exists, continue the above process, otherwise end. Some models are relatively complex, and the hole filling algorithm can only add a part of the faces at a time, and cannot completely close, so you need to loop to find out if there are holes, and if there are, repair them, until there are no holes, get the standard inner gingival model, set as

[0018] Step 6, according to PS bc Suture and close the bottom surface of M h , get the closed outer gingival model, set as The reason for closing M h to get is that the parameters of the Boolean operation must be a closed model, otherwise an error will occur. Make a Boolean addition operation between all the tooth models of this jaw surface and , get the Boolean outer gingival model Then the suture bottom surface is removed to obtain an unsealed standard shell gingival model

[0019] Step 7, the and model is combined to obtain an open shell gingival model, which is set as Since the MarchingCube algorithm is not accurate in edge problem processing, the inner shell part still has some random cutting problems. At this time, the bottom vertex is cut off a part to obtain a cut shell gingival model, which is set as After the cutting vertex is completed, the new bottom surface edge point is displaced in the Z-axis direction, is transformed to the same plane, and the new bottom surface is made parallel to the XoY plane, to prepare for subsequent suturing.

[0020] Step 8, the inner shell part and the two circle bottom surface edge points of the outer shell part are respectively connected according to the edge topology connection sorting, and the starting points of the two are ensured to correspond and the sorting directions are consistent. Then the two circle bottom surface edge points are sutured point by point to obtain a face sheet which is added to to finally obtain a closed perfect shell model, which is called a standard shell gingival model is the final output result of the method.

[0021] The second aspect of the application provides a gingival three-dimensional model shell extraction device based on Marching Cube, comprising a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the gingival three-dimensional model shell extraction method based on Marching Cube.

[0022] The technical concept of the application is that special preprocessing strategies and a new signed distance field construction method are tailored for the specific structure of the initial gingival three-dimensional model and the final actual demand of generating a contact lens, and a series of innovative post-processing optimization methods are performed on the MarchingCube reconstruction results, such as deleting incorrect topology and iterative repair process. Finally, the bottom is sutured with the shell to obtain a standard shell gingival model.

[0023] The advantages of the present invention are: achieving fast and high-performance signed distance field construction of the initial gingival three-dimensional model, and providing effective pre-processing and post-processing processes before and after MarchingCube reconstruction; accurately repairing the construction defects of the Marching Cube results, and the final generated standard shell gingival model is error-free after being imported into CAD printing software, with uniform and healthy mesh quality, which also lays the foundation for further processing of the standard shell gingival model and adding base plates and pins and other production processes, making it more usable and stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is the overall logical framework for generating the standard shell-drawing gingival model of the present invention.

[0025] Figures 2(a) and 2(b) are the gingival model after position correction of the present invention, with the bottom surface aligned with the XoY plane and the XYZ axis of the world coordinate system; Figure 2(a) is a left-side top view, and Figure 2(b) is a left-side bottom view.

[0026] Figure 3 It is the height-compensated gum model effect obtained by extruding the bottom edge downward.

[0027] Figures 4(a) and 4(b) are side views of example distance field construction; the lightly shaded portion of Figure 4(a) is a rough initial result voxel set in the initial distance field, and the darkly shaded portion of Figure 4(b) is a more detailed final result voxel set after the initial result voxels are subdivided.

[0028] Figures 5(a) and 5(b) are preliminary inner shell gingival models after MarchingCube mesh reconstruction; Figure 5(a) is a bottom-down perspective, and Figure 5(b) is a right-side-down perspective.

[0029] Figures 6(a) and 6(b) are diagrams showing the error topology; Figure 6(a) shows an error topology of the inner shell gingival model to be optimized, and Figure 6(b) shows the state with holes after deleting the error topology.

[0030] Figures 7(a) and 7(b) are schematic diagrams of adding vertices and facets in the hole repair algorithm; Figure 7(a) shows the case of adding one triangle, and Figure 7(b) shows the case of adding two triangles.

[0031] Figure 8(a) and Figure 8(b) are comparisons before and after hole repair; Figure 8(a) shows the state before hole repair, and Figure 8(b) shows the state after hole repair.

[0032] Figure 9(a) and Figure 9(b) are comparisons of teeth before and after Boolean addition operation; Figure 9(a) is the effect diagram before Boolean addition operation, and Figure 9(b) is the effect diagram after Boolean addition operation.

[0033] Figure 10 It is a demonstration of the random cut problem on the bottom edge.

[0034] Figure 11 It is a cutting diagram.

[0035] Figure 12(a) and Figure 12(b) are comparisons of the effects before and after the bottom edge is sewn; Figure 12(a) shows the effect before the bottom edge is sewn, and Figure 12(b) shows the effect after the bottom edge is sewn.

[0036] Figures 13(a) and 13(b) are the final renderings of the standard shelled gingival model; Figure 13(a) is a mesh topology and facet display from the left side top view, and Figure 13(b) is a facet display from the bottom side top view. DETAILED DESCRIPTION

[0037] Next, the present invention will be described in further detail with reference to the accompanying drawings.

[0038] Example 1

[0039] This embodiment relates to a method for shelling a three-dimensional gum model based on Marching Cube.

[0040] The general idea behind generating a standard shell-drawing gingival model is as follows: after inputting the initial gingival 3D model, the position is first corrected to the XoY plane, and the bottom edge is extruded downward to obtain a height-compensated gingival model. A signed distance field is then constructed based on it, and a preliminary inner shell gingival model is reconstructed using the MarchingCube method. Next, the preliminary inner shell gingival model is processed, and while preserving the vertex topology of the facets, duplicate vertices in the same position are deleted and the topology is reconnected to obtain a half-edge data structure. The erroneous vertices are searched for, and they and a neighboring vertex are deleted. The holes are then repaired using a hole-repairing algorithm to obtain a standard inner shell gingival model. At the same time, after the bottom surface of the height-compensated gingival model is closed, a Boolean addition operation is performed with all the teeth to split the bottom surface to obtain a standard outer shell gingival model. After merging them, a portion of the bottom is cut off, and then the bottom edges are stitched together to obtain the final standard shell-drawing gingival model.

[0041] Figure 1 This is the overall logical architecture for generating standard shell and gum models. The following is a detailed introduction.

[0042] A method for extracting a gingival three-dimensional model shell based on Marching Cube includes the following steps:

[0043] Step 1: First, import the initial gingival 3D model and set it as M o, the bottom surface of the model is not closed, and all the bottom edge points are in the same plane. Find the half edge that is only used by one face to get all the bottom edge points, and set the set of all bottom edge points as PS b According to PS b The bottom plane normal can be calculated, and the transformation matrix can be further calculated to transform the initial gingival 3D model to a position where the bottom surface is parallel to the XoY plane (the XoY plane is the plane orthogonal to the X-axis and Y-axis of the world coordinate system), and then translated to a position where the geometric center coincides with the origin of the world coordinate system. Finally, the reset gingival model M is obtained. r , as shown in the two perspectives of Figure 2(a) and Figure 2(b).

[0044] Step 2: Based on M r The bottom edge of the PS is extruded 2.0mm in the negative direction of the Z axis. b Make a copy and get PS bc . Put PS bc The point is translated 2.0mm in the negative direction of Z axis, and then compared with PS b Stitch the surface piece point by point and add it to M r In the middle, the highly compensated gingival model M is obtained h .like Figure 3 shown.

[0045] Step 3: The construction of the signed distance field (SDF) adopts the strategy of grid diffusion + hierarchical construction. First, the grid diffusion construction with lower resolution is carried out. h The bounding box voxelization constructs a blank field, in which each voxel can be set to a value. Through the breadth-first search (BFS) algorithm, from M h The surface expands inward and outward layer by layer to fill the value of the corresponding voxel. Since the diffusion is discrete, parallel computing is used here, which is relatively efficient.

[0046] Assume the required thickness of the shell is T mm, find all voxels with a value of -T, and put them into the voxel set VS ori As shown in the shadow voxels in the cross-section of Figure 4(a), ori The voxels in are further subdivided by a hierarchical strategy to calculate the local subdivision signed distance field LDSDF. The value of each subvoxel is obtained by interpolating the values ​​of nearby voxels, as shown in the cross-section of Figure 4(b). Find all the subvoxels with the closest value to -T and use the classic MarchingCube to generate the isosurface to obtain the preliminary inner shell gingival model, which is set as The effect is shown in Figure 5(a) and Figure 5(b) from two perspectives. The surface entity models in the two figures are

[0047] Step 4: Traverse All the facets, record the three vertex positions of each facet. Then delete the redundant duplicate vertices in the model, leaving only one vertex at each position, and delete all the facets at the same time. At this time, the model becomes a point cloud model. Table 1 shows the number of vertices and facets before and after deleting the redundant vertices, and after rebuilding the topology. It can be seen that the number of vertices in the second column of Table 1 is much less than that in the first column, and the number of facets is 0. Then, based on the three vertex positions and The remaining non-duplicate vertices in the reconstruct the topology structure, The number of vertices and faces is shown in the third column of Table 1. The model is no longer a bunch of scattered faces, but a mesh model with a half-edge data structure, which is called a manifold inner shell gingival model, and is set to Later, we can use the characteristics of the half-edge data structure to for further processing.

[0048] Table 1

[0049]

[0050] Step 5: Traverse All vertices are checked for connectivity using the connectivity characteristics of the half-edge data structure, vertices with structural errors are found, and they are deleted to obtain the inner shell gingival model to be optimized, which is set as The wrong vertices may be vertices with unreasonable topological connections, or they may be two points on non-popular edges that are reused more than twice. Figure 6(a) shows a case of an wrong vertex. The wrong vertices are removed, so holes will appear, as shown in Figure 6(b). Next, traverse to find For all holes, call the hole repair algorithm to fill the holes.

[0051] The principle of the hole repair algorithm is to first calculate the average value l of the boundary edge length based on the hole boundary point information; then calculate the angle between the two adjacent edges of each boundary point; find the three boundary points that form the minimum angle between the two edges, calculate the distance s between the two left and right boundary points of the three points, and determine whether s<2×l is true. If so, add a triangle as shown in Figure 7(a); if not, add two triangles as shown in Figure 7(b). Then find the new boundary point to determine whether the hole still exists. If it still exists, continue the above process, otherwise end. The effects before and after repair are shown in Figure 8(a) and Figure 8(b) respectively. Because some models are relatively complex, the hole repair algorithm can only add a part of the face at a time and cannot be completely closed, so it is necessary to cyclically search for holes. If so, repair them until there are no holes and obtain a standard inner shell gingival model, set as

[0052] Step 6: Get the standard inner shell gum model Finally, a standard shell gingival model needs to be constructed. bc The point in the middle is M h The bottom edge point, according to PS bc Put M h The bottom surface is sutured and closed to obtain the closed shell gingival model The reason for closing M h Conclusion This is because the parameters of the Boolean addition operation must be closed models, otherwise an error will occur. Do Boolean addition operation to get the Boolean shell gingival model Then dismantle The sutured bottom surface is obtained to obtain an unsealed standard shell gingival model As shown in Figure 9(b).

[0053] Step 7: and The models are merged together to obtain the open shell gingival model, which is set as Since the MarchingCube algorithm is not accurate in dealing with edge problems, There are still some random cutout issues on the inner shell, such as Figure 10 As shown. Cut off a part of the bottom vertex to get the cut-out shell gum model, set as Figure 11 The cut section is shown. After the vertex is cut, The new bottom edge points are displaced in the Z-axis direction, transformed to the same plane, and the new bottom surface is made parallel to the XoY plane to prepare for subsequent stitching.

[0054] Step 8: The two circles of bottom edge points of the inner shell and the outer shell are sorted according to the edge topology connection, and the sorting starting points of the two circles are guaranteed to correspond and the sorting directions are consistent. Then the two circles of bottom edge points are stitched point by point, and the resulting patch is added to Finally, a closed perfect shell model is obtained, which is called the standard shell gum model. As shown in Figure 12(b). This is the final output result of the proposed method, as shown in the two perspectives of Figure 13(a) and Figure 13(b).

[0055] Example 2

[0056] This embodiment provides a Marching Cube-based gingival three-dimensional model extraction device, including a memory and one or more processors. The memory stores executable code. When the one or more processors execute the executable code, they are used to implement a Marching Cube-based gingival three-dimensional model extraction method of Example 1.

[0057] Example 3

[0058] This embodiment relates to a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the method for extracting a gingival three-dimensional model shell based on Marching Cube described in Example 1 is implemented.

[0059] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for extracting a gingival three-dimensional model based on Marching Cube, characterized in that: The following steps are involved: 1) Position correction: After inputting the initial gingival 3D model, the position is first corrected to the XoY plane to obtain the gingival model after repositioning; 2) Extrude downwards. After the gingival model is reset, the bottom edge is extruded downwards to obtain a highly compensated gingival model. 3) Construct the distance field and inner shell, construct the signed distance field SDF according to the height-compensated gingival model, and reconstruct the preliminary inner shell gingival model using the MarchingCube method; the signed distance field is constructed using the grid diffusion + hierarchical strategy: first, the grid diffusion with a lower resolution is constructed, and then the The bounding box voxelization constructs a blank field, in which each voxel is set to a value, and the BFS breadth-first search algorithm is used to search from The surface expands inward and outward layer by layer to fill the value of the corresponding voxel. Since the diffusion is discrete, parallel calculation is used; Assume that the required thickness of the shell is T mm, find all voxels with a value of -T and form a voxel set ; Next, The voxels in the voxel are further subdivided by a hierarchical strategy to calculate the local subdivision signed distance field LDSDF. The value of each subvoxel is obtained by interpolating the values ​​of nearby voxels. Find all the subvoxels closest to the -T value and use the classic MarchingCube to generate the isosurface to obtain the preliminary inner shell gingival model, which is set as ; 4) Reconstruct the half-edge structure, while keeping the vertex topology of the patch unchanged, delete the repeated vertices at the same position of the preliminary inner shell gingival model and reconnect the topology to obtain the manifold inner shell gingival model; the rule of reconnecting the topology is: traverse All the patches, record the three vertex positions of each patch; then delete the redundant duplicate vertices in the model, leaving only one vertex at each position, and delete all the patches at the same time. At this time, the model becomes a point cloud model; then according to the three vertex positions of each patch recorded before and The remaining non-duplicate vertices in the patch are used to rebuild the patch topology. With a light vertex count and the same number of faces as before; the model at this time is a mesh model with a half-edge data structure, called a manifold inner shell gum model ; Using the characteristics of the half-edge data structure for further processing; 5) Inner shell repair: find and delete the incorrect vertices of the manifold inner shell gingival model, and then use the hole repair algorithm to repair its holes to obtain a standard inner shell gingival model; 6) Boolean operation: close the bottom surface of the height-compensated gingival model, perform Boolean addition operation on all teeth, and split the bottom surface to obtain the standard shell gingival model; 7) Bottom cutting: combine the standard outer shell gingiva model and the standard inner shell gingiva model and cut off a part of the bottom to obtain the cut shell gingiva model; 8) Bottom edge suturing: suturing the bottom edge of the cut shell-drawing gingival model to obtain the final standard shell-drawing gingival model.

2. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: Step (1) Import the initial gingival 3D model The bottom surface of is not closed, and all the bottom edge points are in the same plane; find the half edge that is only used by one face to get all the bottom edge points, and set the set of all bottom edge points as ;according to Calculate the bottom plane normal, and further calculate the transformation matrix to transform the initial gingival 3D model to a position where the bottom surface is parallel to the XoY plane. The XoY plane is the plane orthogonal to the X-axis and Y-axis of the world coordinate system, and translate it to the position where the geometric center coincides with the origin of the world coordinate system; finally, the reset gingival model is obtained. .

3. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: The downward extrusion in step (2) includes: The bottom edge of the Z axis is extruded 2.0mm in the negative direction; specifically: first Make a copy and get ;Bundle The point is translated 2.0mm in the negative direction of Z axis, and then compared with Stitch the surface piece point by point and add it to In the middle, a highly compensated gingival model is obtained .

4. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: Delete the manifold inner shell gingival model described in step (5) All the wrong vertices of , specifically including: first traverse all its vertices, check the connection of the vertices with the help of the connection characteristics of the half-edge data structure, find the vertices with structural errors, and delete them to obtain the inner shell gingival model to be optimized, set as ; The wrong vertices are vertices with unreasonable topological connections, or two points on non-popular edges that are reused more than twice; The wrong vertices are removed, so holes will appear; next, traverse to find For all holes, call the hole repair algorithm to fill the holes; The hole repair algorithm is as follows: first, based on the hole boundary point information, calculate the average length l of the boundary edge; then calculate the angle between the two adjacent edges of each boundary point; find the three boundary points where the two edges have the smallest angle, calculate the distance s between the two left and right boundary points of the three points, and determine whether s < 2×l. If so, add a triangle; if not, add two triangles; then find a new boundary point to determine whether the hole still exists. If so, continue the above process, otherwise end; some models are relatively complex, and the hole filling algorithm can only add a part of the face at a time and cannot be completely closed, so it is necessary to loop to find out whether there is a hole. If so, repair it until there is no hole and obtain a standard inner shell gingival model. .

5. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: Step (6) according to Bundle The bottom surface is sutured and closed to obtain the closed shell gingival model ; Combine all the tooth models of this maxillary face with Do Boolean addition operation to get the Boolean shell gingival model , then dismantle The sutured bottom surface is obtained to obtain an unsealed standard shell gingival model .

6. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: The step (7) of merging the standard outer shell gum model and the standard inner shell gum model means: merging the standard inner shell gum model and Merge them together to get the open shell gingival model, set as ;Bundle Cut off a part of the bottom vertex to get the cut-out shell gum model, set as ; After the vertex is trimmed, The new bottom edge points are displaced in the Z-axis direction, transformed to the same plane, and the new bottom surface is made parallel to the XoY plane to prepare for subsequent stitching.

7. The method for extracting a gingival three-dimensional model based on Marching Cube according to claim 1, characterized in that: Step (8) of sewing the bottom edge of the cut and shelled gingival model includes: The two circles of bottom edge points of the inner shell and the outer shell are sorted according to the edge topology connection, and the sorting starting points of the two circles are guaranteed to correspond and the sorting directions are consistent; then the two circles of bottom edge points are stitched point by point, and the obtained facets are added to Finally, a closed perfect shell model is obtained, which is called the standard shell gum model. , This is the final output of the method in this paper.

8. A gingival three-dimensional model extraction device based on Marching Cube, characterized in that: The method comprises a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement a method for extracting a gingival three-dimensional model based on Marching Cube according to any one of claims 1 to 7.

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