A modeling method for three-dimensional point cloud cutting model based on orthogonal surfaces

Abstract

The present invention discloses a modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces, which realizes the authenticity of cutting simulation in virtual surgery. The method comprises: first, establishing orthogonal planes α, β, and γ centered on the scalpel tip according to the cutting direction and angle of the scalpel; then calculating the offset of each voxel point and the three orthogonal planes; then constructing a suitable incision shape function and cutting influence domain, judging whether the point needs to be displaced according to the three offsets of each voxel point, and if so, calculating its displacement, and performing displacement operations until all voxel points are traversed; finally, constructing a two-dimensional height field grid to render the cut surface. The modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces provided by the present invention obtains a relatively realistic incision shape by introducing a suitable incision shape function and a cutting influence domain; and obtains a relatively smooth incision rendering effect by introducing a two-dimensional height field grid to render the cut surface.

Description

Technical Field

[0001] The invention belongs to the technical field of virtual surgery in virtual reality, and in particular relates to a modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces, which belongs to a meshless method. Background Art

[0002] With the upgrading of computer technology, especially multimedia technology, virtual reality technology (VR) has become one of the fastest-growing fields in computer science. It is an interdisciplinary subject that integrates simulation technology, multimedia technology, sensor technology and other technologies. As an important application field of VR, virtual surgery provides a safe and effective method for surgical training and surgical planning. Before operating on a patient, surgeons can practice surgical operations on virtual human organs and tissues through surgical simulators to select the best surgical plan. The three-dimensional model reconstructed by the virtual surgical system allows doctors to understand the internal structure information of the diseased organs or tissues in advance, thereby helping doctors plan the surgical path and ensure that the operation is performed in the safest way. More importantly, adequate preoperative training can effectively reduce the surgical risks of patients and improve the success rate of surgery.

[0003] In virtual surgery, a good geometric cutting model plays a vital role in achieving realistic cutting surgery simulation. In the early days, the finite element method (FEM) was widely used in most surgical simulators to achieve cutting simulation. The tetrahedron removal method and the tetrahedron subdivision method are the early finite element methods used in cutting simulation. Simple cutting simulation can be achieved by deleting or splitting the triangular facets along the cutting path. These methods are easy to implement, but there are still shortcomings. On the one hand, it is very dependent on the mesh, and distorted or low-quality meshes can cause large errors and lead to instability.

[0004] In order to overcome the shortcomings of the finite element method, the meshless method (MM) was proposed. This method is a numerical method in the field of mechanical engineering. It has developed rapidly in recent years, and many meshless methods have emerged, such as the meshless Galerkin method (EFG), radial basis function method (RBF) and multi-scale reconstruction kernel particle method (MRKP). It reconstructs virtual soft tissue based on discrete point elements, and the relationship between each point element is not related to the grid. Point elements are random and not constrained by the grid, which makes them more suitable for discontinuous scenes. Compared with the mesh-based finite element method, the meshless method has strong adaptability, adopts a point cloud structure model, does not require a complex topological structure between points, and is suitable for large deformation and cutting.

[0005] Although the existing cutting simulation research has achieved good results, there is still room for improvement. The smoothness and authenticity of the incision have always been the key to simulating high-fidelity cutting surgery. Summary of the invention

[0006] In view of the shortcomings and difficulties in the prior art, the present invention aims to provide a modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces. The purpose of the present invention is to improve the authenticity of the cutting simulation effect.

[0007] The present invention is achieved through the following technical solutions:

[0008] A modeling method for a three-dimensional point cloud cutting model based on orthogonal surfaces comprises the following steps:

[0009] Step 1: Simplify the tip of the virtual surgical knife into a proxy ball. According to the cutting direction and angle of the scalpel, establish orthogonal planes α, β, and γ centered on the proxy ball;

[0010] Step 2: Calculate the offset between each voxel point and the three orthogonal planes respectively;

[0011] Step 3: According to the shape of the actual cut, construct a suitable cut shape function and cut influence domain. Then determine whether the voxel point is in the cut influence domain based on its distance to the three orthogonal planes. If so, mark it as a point that needs to be moved. If not, skip it until all voxel points are traversed;

[0012] Step 4: Calculate the displacement of each voxel point that needs to be moved and perform the displacement operation;

[0013] Step 5: Construct a two-dimensional height field mesh to render the cut surface.

[0014] Preferably, the formula for calculating the offset between each voxel point and the three orthogonal planes in step 2 is:

[0015]

[0016]

[0017]

[0018] In the formula, K α , K β , K γ are the offsets of the voxel point (x, y, z) and the orthogonal planes α, β, and γ respectively; (x tp ,y tp ,z tp ) is the position coordinate of the proxy ball, and a, b, and c are the normal vectors of the orthogonal planes α, β, and γ respectively. x ,a y ,a z ),(b x ,b y ,b z ),(c x ,cy ,c z ) are the three components of vectors a, b, c. ||a||,||b||,||c|| are the moduli of vectors a, b, c.

[0019] Preferably, the cut shape function in step 3 is:

[0020]

[0021] Where k1, k2 are constant parameters that control the shape of the cut. σ is the depth coefficient, which is defined as:

[0022] σ=1+μ1(μ2-z tp )

[0023] Where μ1 and μ2 are parameters that determine the relationship between the depth coefficient and the range of the influence domain.

[0024] Preferably, the range of the cutting impact domain in step 3 is:

[0025]

[0026] Preferably, the displacement calculation formula of each voxel point that needs to be moved in step 4 is:

[0027]

[0028]

[0029] Where η1, η2, and η3 are parameters that control the displacement length.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The modeling method of the three-dimensional point cloud cutting model based on orthogonal surfaces provided by the present invention obtains a relatively realistic incision shape by introducing a suitable incision shape function and a cutting influence domain; and obtains a relatively smooth and realistic incision rendering effect by introducing a two-dimensional height field grid to render the cut surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of establishing orthogonal planes according to the present invention.

[0033] Figure 2 It is a schematic diagram of calculating the normal vector of a two-dimensional height field mesh node according to the present invention.

[0034] Figure 3 This is a diagram showing the surface effect of cutting soft tissue according to the present invention. DETAILED DESCRIPTION

[0035] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0036] The present invention provides a modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces, which can obtain a smooth and realistic incision shape and rendering effect, and improve the authenticity of cutting simulation in virtual surgery. The implementation method specifically includes:

[0037] First, the tip of the virtual surgical knife is simplified into a proxy ball. According to the cutting direction and angle of the scalpel, orthogonal planes α, β, and γ are established with the proxy ball as the center, as shown in Figure 1 shown.

[0038] Afterwards, the offsets of each voxel point from the three orthogonal planes are calculated respectively.

[0039] The formula for the offset of a voxel point from three orthogonal planes is:

[0040]

[0041]

[0042]

[0043] In the formula, K α , K β , K γ are the offsets of the voxel point (x, y, z) and the orthogonal planes α, β, and γ respectively; (x tp ,y tp ,z tp ) is the position coordinate of the proxy ball, and a, b, and c are the normal vectors of the orthogonal planes α, β, and γ respectively. x ,a y ,a z ),(b x ,b y ,b z ),(c x ,c y ,c z ) are the three components of vectors a, b, c. ||a||,||b||,||c|| are the moduli of vectors a, b, c.

[0044] After that, according to the shape of the real cut, the appropriate cut shape function and cut influence domain are constructed. Then, according to their distances to the three orthogonal planes, it is determined whether the voxel point is in the cut influence domain. If so, it is marked as a point that needs to be moved. If not, it is skipped until all voxel points are traversed.

[0045] The cut shape function is:

[0046]

[0047] Where k1 and k2 are constant parameters that control the shape of the cut. The direction of vector c is the positive direction of the X axis, and the direction of vector a is the positive direction of the Y axis. σ is the depth coefficient, which is defined as:

[0048] σ=1+μ1(μ2-z tp )

[0049] Where μ1 and μ2 are parameters that determine the relationship between the depth coefficient and the range of the influence domain.

[0050] Among them, the range of the cutting influence domain is:

[0051]

[0052] In this embodiment, k1 and k2 are taken as 100 / 9 and 25 / 36, and μ1 and μ2 are taken as 1 and 1 / 4.

[0053] After that, the displacement of each voxel point that needs to be moved is calculated and the displacement operation is performed.

[0054] The calculation formula for the displacement of each voxel point that needs to be moved is:

[0055]

[0056]

[0057] Where η1, η2, and η3 are the parameters that control the displacement.

[0058] In this embodiment, η1, η2, and η3 are taken as 0.06, 0.1, and 0.1 respectively.

[0059] Afterwards, a 2D height field mesh is constructed to render the cut surfaces.

[0060] The steps for constructing a two-dimensional height field grid are as follows:

[0061] (1) Establish a uniform two-dimensional height field grid for the soft tissue cutting area and set an initial height threshold for all grids.

[0062] (2) Traverse all voxel points and calculate the grid position of each voxel point based on the position coordinates of the point.

[0063] (3) If the height of the voxel point exceeds the threshold of the grid where the point is located, the threshold is updated with the height of the voxel point; otherwise, it is not updated.

[0064] (4) Smoothing the height of each grid (generally taking the average of the surrounding 5×5 adjacent grids) to reduce the height difference between adjacent grids and improve the smoothness of the cut surface.

[0065] (5) Calculate the normal vector of each mesh node (such as Figure 2 ) and normalized to facilitate rendering under the lighting model.

[0066] Among them, the normal vector at the grid node (i, j) is:

[0067]

[0068] In the formula, the vector P A , P B , P C , P D The calculation process is as follows:

[0069] P A =A×B

[0070] P B =B×C

[0071] P C =C×D

[0072] P D =D×A

[0073] In the formula, vectors A, B, C, and D represent four vectors pointing to the grid node (i, j), and their calculation process is as follows:

[0074]

[0075] In the formula, Pos(i,j) represents the position coordinates of the grid node (i,j).

[0076] In this embodiment, the RGB value of the blood color is selected as (0.8, 0, 0) to render the cut surface.

[0077] By adopting the modeling method of the three-dimensional point cloud cutting model based on orthogonal surfaces provided by the present invention, a relatively realistic incision shape is obtained by introducing a suitable incision shape function and cutting influence domain; by introducing a two-dimensional height field grid to render the cutting surface, a relatively smooth and realistic incision rendering effect is obtained. Figure 3 It can be seen that, by using the method provided by the present invention, smooth cut marks with different incision shapes are achieved, which conforms to the real soft tissue cutting effect.

[0078] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to the specific details and the illustrations described herein.

Claims

1. A modeling method for a three-dimensional point cloud cutting model based on orthogonal surfaces, characterized in that: The modeling method comprises the following steps: Step 1: Simplify the tip of the virtual surgical knife into a proxy ball; establish an orthogonal plane centered on the proxy ball according to the cutting direction and angle of the scalpel α , β , γ ; Step 2: Calculate the offset between each voxel point and the three orthogonal planes respectively; Step 3: According to the shape of the actual incision, construct a suitable incision shape function and cutting influence domain; then determine whether the voxel point is in the cutting influence domain according to its distance to the three orthogonal planes. If so, mark it as a point that needs to be moved; if not, skip it until all voxel points are traversed; Step 4: Calculate the displacement of each voxel point that needs to be moved and perform the displacement operation; Step 5: Construct a two-dimensional height field grid to render the cut surface; In step 3, the cut shape function is: ， In the formula, k 1 , k 2 is a constant parameter that controls the shape of the cutout. K α , K γ They are voxel points ( x , y , z ) and the orthogonal plane α , γ The offset of σ is the depth coefficient, which is defined as: ， In the formula, µ 1 , µ 2 is a parameter that determines the relationship between the depth coefficient and the range of the influence domain, ( x tp , y tp , z tp ) is the position coordinate of the proxy ball; In step 3, the scope of the cut influence domain is: ， K β is a voxel point ( x , y , z ) and the orthogonal plane β The offset of 2. The modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces according to claim 1, characterized in that: In step 2, the offset between each voxel point and the three orthogonal planes is calculated as: ， ， ， In the formula, K α , K β , K γ They are voxel points ( x , y , z ) and the orthogonal plane α , β , γ The offset of x tp , y tp , z tp ) is the position coordinate of the proxy ball, a , b , c Orthogonal planes α , β , γ The normal vector of ( a x , a y , a z ), ( b x , b y , b z ), ( c x , c y , c z ) are vectors respectively a , b , c The three components of || a ||, || b ||, || c || are vectors a , b , c The mold length.

3. The modeling method of a three-dimensional point cloud cutting model based on orthogonal surfaces according to claim 2 is characterized in that: The calculation formula for the displacement of each voxel point that needs to be moved in step 4 is: ， ， In the formula η 1 , η 2 , η 3 is the parameter that controls the displacement.

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