CN103310483B - A kind of vascular bifurcation method of surface reconstruction based on hole region triangulation - Google Patents

Abstract

The present invention proposes a method for reconstructing a vessel bifurcation surface based on the triangulation of the hollow area, which includes the following steps: constructing the tubular surface of the vascular skeleton line; If the branch is equivalent to the inner side of the cylinder, delete the point, the edge connected to the point and the triangular surface; perform two-dimensional mapping on the bifurcation area, and project the bifurcation area into a two-dimensional plane topology; The area triangulation method fills the two-dimensional topological plane and reconstructs the surface of the vessel bifurcation area; the hollow area triangulation filling method is used to reconstruct the entire vessel tree. The invention revolves around the original topological direction of the blood vessel branch and the size of the pipeline to carry out branch "mutual eating", bifurcation two-dimensional mapping, triangulation and filling of triangular holes, so as to maintain the topological shape of the real blood vessel bifurcation, the reconstruction model is accurate, and the calculation amount is small , strong robustness, high reconstruction efficiency, and the reconstructed vessel model has complete vector and reconfigurability.

Description

A Vessel Bifurcation Surface Reconstruction Method Based on Cavity Region Triangulation

technical field

The invention relates to the technical fields of biomedical engineering and computer vision, in particular to a blood vessel bifurcation surface reconstruction method for reconstructing a surface model of an arbitrary bifurcation area of a blood vessel based on triangulation of a cavity area.

Background technique

The three-dimensional surface model of vascular structure is of great significance to clinical diagnosis, virtual surgery, radiotherapy and anatomy teaching. one of the main factors. The role of the three-dimensional model of blood vessels in clinical medicine is reflected in: (1) observing and determining the location of the lesion from the three-dimensional structure of the blood vessel, and making a rapid diagnosis; (2) conducting qualitative analysis on the shape of the pipeline such as length and size; 3) Provide intuitive reference basis for operation planning.

The reconstruction of vascular tree can be generally divided into simple surface reconstruction and vector model reconstruction. The simple surface reconstruction technology directly constructs the surface through the voxels of the blood vessel boundary, and mostly uses MarchingCube and MPU methods for reconstruction. Vector model reconstruction generally needs to first obtain vector information such as the skeleton structure and diameter information of the blood vessel, and reconstruct the blood vessel model based on these data. Conventional vector modeling methods include cylindrical fitting, conical fitting, B-spline, and direct construction based on cross-sectional contours.

The simple surface reconstruction method is simple and efficient, but because the whole model is only based on the triangulation of the object surface, the constructed model can only be used for the observation of blood vessels, and cannot reflect the classification, diameter, length, and curvature of the constructed object. Information. Vessel vector reconstruction method is relatively simple. Although the algorithm and establishment process of surface reconstruction are complex, it has incomparable advantages over other methods. First, the model established by this type of method is vector and reconfigurable; secondly, the model established by this method is The vascular model has a high-fidelity visualization effect, and this method can draw information such as vascular diameter and grading through different color and texture rendering methods, so that the reconstructed model is more realistic and has more information. Vascular vector reconstruction technology can be widely used in the diagnosis of hepatic vessels, cardiovascular and cerebrovascular, preoperative planning and simulation of organs, medical anatomy teaching and training.

However, vector modeling also has its own difficulties. One of the prominent problems is that it cannot efficiently and accurately reconstruct the closed transition surface of complex bifurcation regions. One is because the number of branches in the bifurcation area is different. Simple vascular bifurcations generally have 2 or 3 branches, but complex vascular bifurcations have more than 6 branches; It is difficult to construct a smooth transition surface between branches.

Contents of the invention

In order to overcome the defects in the above-mentioned prior art, the object of the present invention is to provide a method for reconstructing the surface of the vessel bifurcation based on the triangulation of the cavity area, which can not only efficiently reconstruct the shape and volume of the real vessel bifurcation Surface models with minimal errors can also improve reconstruction efficiency.

In order to achieve the above-mentioned purpose of the present invention, the present invention provides a method for reconstructing the surface of the vessel bifurcation based on the triangulation of the cavity area, comprising the following steps:

S1: Construct the tubular surface of the vascular skeleton line, the skeleton line is a multi-fork tree, the skeleton line is composed of continuous intermediate points, each skeleton line segment corresponds to a node of a tree, and the tubular surface is surrounded by triangular faces;

S2: In the bifurcation area of the tubular surface, if the contour point of any cross-section on a branch is inside the equivalent cylinder of other branches, delete the point, the edge connected to the point and the triangular surface, and at the same time Mark all other vertices adjacent to this point as empty boundary points;

S3: performing two-dimensional mapping on the bifurcation area, and equivalently projecting the bifurcation area into a two-dimensional planar topological map;

S4: Fill the two-dimensional topological plane with the method based on the subdivision of the cavity area, and reconstruct the surface of the vessel bifurcation area;

S5: Reconstruct the entire vascular tree by using the hole area triangulation filling method.

The invention reconstructs the tubular surface of the blood vessel based on the skeleton line of the blood vessel and the caliber, so that the reconstructed blood vessel model has complete vector and reconfigurability. It maintains the topological information consistent with the real blood vessels in the CT image, and can well reflect information such as the branch direction of the blood vessels and the size of the pipeline; at the same time, the vector feature adopted provides good information for more advanced interactive functions, such as dynamic deformation of blood vessels. geometric basis.

The method for reconstructing the surface of the vessel bifurcation based on the triangulation of the cavity area of the present invention fully utilizes the "mutually eating" relationship between branches when reconstructing the transitional surface of the bifurcating area, and forms the bifurcating area after "mutually eating" The holes in each subdivision triangle are equivalently subdivided into each subdivision triangle, and the transition surface of the whole bifurcation area can be reconstructed by filling the holes in each subdivision triangle; in addition, the transition splicing of the surface is only for the hole boundaries of each branch The non-regular quadrilateral filling is performed, the calculation amount is small, the robustness is strong, and the reconstruction efficiency is high. The reconstruction of the bifurcation area in the present invention closely revolves around the original topological direction of the vascular branch and the size of the pipeline to carry out branch "mutual eating", bifurcation two-dimensional mapping, triangulation and filling of triangular holes, keeping the reality as much as possible The topological shape of the vascular bifurcation, the reconstruction model is accurate.

In a preferred embodiment of the present invention, the method for constructing the tubular surface of the vascular skeleton line is:

S11: Reorganize the vascular skeleton line. For any current skeleton line segment, assuming that the code is SL(i), then the segments corresponding to each of its child nodes are arranged in descending order according to the average tube diameter, and the largest one shares the current segment code SL(i ), other segments are sequentially compiled as SL(i*10+k), where i is a positive integer, and k ranges from 2 to the total number of child nodes;

S12: Calculate the tangent vector of each intermediate point of the skeleton line, and determine the tangent vector of the second intermediate point by using the normalized connection vectors of three consecutive intermediate points, the formula is:

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, P _i-1 , P _i and P _i+1 represent three consecutive intermediate points, and N represents a normalization parameter;

S13: Construct the tubular surface of the vascular skeleton line, the specific method is: set the two adjacent cross-sectional contours as C _i and C _i+1 , and the middle points of the two cross-sectional contours are respectively and start with As the origin of coordinates, choose a point P on C _i to Pointing to P is the positive direction of the x-axis, with The tangent vector of is the positive direction of the y-axis, and The cross product of is the positive direction of the z-axis, project C _i+1 onto the plane where C _i is located, and calculate and find the point Q on C _i+1 such that and The included angle is the smallest, point P and point Q are the best pairing points on the contours C _i and C _i+1 , and the triangular surface is used to join the tubular surface from the best pairing point.

In another preferred embodiment of the present invention, two-dimensional mapping is performed on the bifurcation area, and the method of converting the projection of the bifurcation area into a two-dimensional plane topological map is as follows: for any bifurcation area, the pipe with the largest diameter The pipes of the branches are used as the carrier plate and cut and paved along the direction of the skeleton line. The other branches are projected onto the carrier plate in turn as each small panel, and the projection center point is selected and determined on the skeleton line of each projected branch as the small panel. equivalent center point of . Facilitates surface reconstruction of vessel bifurcation areas.

In yet another preferred embodiment of the present invention, the method for filling the two-dimensional topological plane and reconstructing the surface of the vessel bifurcation area by using the method based on the triangulation of the cavity area is as follows:

S41: Establishing an equivalent topological plan of the bifurcation area;

S42: Establish an opposite relationship, the opposite relationship refers to the opposite relationship between the boundaries of the small panels and between the boundaries of the small panels and the boundary of the cavity of the carrier board, and the condition that the opposite relationship satisfies is:

In the process of equivalently enlarging the two small panels, in the direction of the line connecting the middle points of the small panels, the boundary where the boundary of any small panel intersects for the first time must be the boundary of another small panel;

S43: Find multiple points on the boundary of the cavity on the carrier board, where the multiple points refer to boundary points where there are two opposite boundaries;

S44: Establish a triangulation, using the opposite relationship established in step S42, connect the center points of each small panel and the multiple points on the carrier board to form a triangulation, if any three small panels or carrier boards form a pairwise opposite relationship , then connect their corresponding center points or multiple points into a triangle, and mark the intersection points of the sides of the triangle and the border of the panel;

S45: Filling triangular holes, using irregular quadrilaterals to fill holes.

The filling method of the present invention based on the subdivision of the cavity area only performs irregular quadrilateral filling on the surface of the vessel bifurcation area for the transition splicing of the surface of the vascular bifurcation area, which has a small amount of calculation, strong robustness, high reconstruction efficiency, and maintains as much as possible The topological shape of the real vascular bifurcation is obtained, and the reconstruction model is accurate.

In a preferred embodiment of the present invention, the following steps are also included between the steps S4 and S5:

Use the Loop subdivision method to subdivide the surface of the vessel bifurcation area. Smoother and more realistic.

Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Description of drawings

The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

Fig. 1 is a flow chart of the method for reconstructing the vessel bifurcation surface based on the triangulation of the cavity area in a preferred real-time mode of the present invention;

Fig. 2 is a schematic diagram of a blood vessel skeleton line before and after recombination in a preferred real-time mode of the present invention, wherein (a) is a schematic diagram of a marked skeleton line before reorganization; (b) is a schematic diagram of merging skeleton line segments into a single branch;

Fig. 3 is a schematic diagram of constructing a tubular surface between adjacent contours C _i and C _i+1 , in which (a) establishes a coordinate system and determines paired points P and Q; (b) starts from the paired point with a triangular surface Schematic illustration of spliced tubular surfaces;

Fig. 4 is a schematic diagram of two-dimensional mapping and triangulation of the bifurcation area in a preferred real-time mode of the present invention, wherein (a) is a 3-bifurcation area of a blood vessel to be reconstructed, and (b) is a "mutually eating" branch Schematic diagram of cavity formation, (c) is a two-dimensional mapping of the cavity area after "mutual eating", (d) is a schematic diagram of vessel bifurcation surface reconstruction based on cavity area segmentation;

Fig. 5 is a flow chart based on the triangulation of the cavity area in a preferred real-time mode of the present invention;

Fig. 6 is a schematic diagram of the subdivision process of the cavity region in a preferred real-time mode of the present invention, wherein (a) is a topological plan view to be subdivided, (b) is a schematic diagram of finding multiple points of the cavity boundary of the carrier board, and (c) is a structure Schematic illustration of the triangulation of the void region;

Fig. 7 is a schematic diagram of two point sequences being filled by irregular polygons in a preferred real-time mode of the present invention;

Fig. 8 is a schematic diagram of filling a triangular hole in Fig. 6(c) in a preferred real-time mode of the present invention, wherein, (a) is an unfilled triangular hole, and (b)-(d) is a step-by-step filling of the triangular hole schematic diagram;

Fig. 9 is a schematic diagram after filling all the triangular gaps in Fig. 6 (c) in a preferred real-time mode of the present invention;

Fig. 10 is a schematic diagram of filling holes in the four subdivision regions obtained in Fig. 4(d) in a preferred real-time mode of the present invention, wherein (a)-(d) are respectively filling the first to the fourth holes ;

Fig. 11 is a schematic diagram after surface subdivision of the bifurcation area filled in Fig. 10;

Figure 12 is the reconstruction of the entire vascular tree using the triangulation filling method of the hollow area, where (a) is an original vascular voxel model, and (b) is a non- Vector surface model and its partial enlarged view, (c) is the model and its local surface enlarged view obtained by utilizing the Marchingcubes method with limited smoothness; (d) is the vector surface model obtained based on the present invention and its partial surface enlarged effect drawing .

detailed description

Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

The present invention provides a method for reconstructing the surface of a blood vessel bifurcation based on the triangulation of the cavity region, as shown in Figure 1, comprising the following steps:

S1: Construct the tubular surface of the vascular skeleton line, the skeleton line is a multi-fork tree, the skeleton line is composed of continuous intermediate points, each skeleton line segment corresponds to a node of a tree, and the tubular surface is surrounded by triangular faces;

S2: In the bifurcation area of the tubular surface, if the contour point of any cross-section on a branch is inside the equivalent cylinder of other branches, delete the point, the edge connected to the point and the triangular surface, and at the same time Mark all other vertices adjacent to this point as empty boundary points;

S3: performing two-dimensional mapping on the bifurcation area, and equivalently projecting the bifurcation area into a two-dimensional planar topological map;

S4: Fill the two-dimensional topological plane with the method based on the subdivision of the cavity area, and reconstruct the surface of the vessel bifurcation area;

S5: Reconstruct the entire vascular tree by using the hole area triangulation filling method.

In a preferred embodiment of the present invention, the specific steps of the vessel bifurcation surface reconstruction method based on the triangulation of the cavity area are:

The first step: constructing the tubular surface of the vascular skeleton line, in this embodiment, the method for constructing the tubular surface of the vascular skeleton line is:

S11: Reorganize the vascular skeleton line. In this embodiment, the initial vascular skeleton line needs to be extracted from the segmented vascular voxel model. As shown in FIG. The condition of the multi-fork tree is a common multi-fork tree condition in the art. In the skeleton line of blood vessels, each skeleton line segment corresponds to a node of a tree, and the skeleton line is composed of continuous intermediate points, each intermediate Each point has a profile radius passing through that point. Reorganize the skeleton line in this way: for any current skeleton line segment, assuming that the code is SL(i), i is a positive integer, then the segments corresponding to each of its child nodes are arranged in descending order of the average pipe diameter, and the largest one shares the current The segment code is SL(i), and other segments are sequentially coded as SL(i*10+k), and k ranges from 2 to the total number of child nodes. Figure 2(b) shows a marked sub-skeleton line, in which the section coded as SL(1) is composed of BS(1), BS(11) and BS with the largest diameter in Figure 2(a) (111); SL (13) is composed of BS (13) and BS (131) in Figure 2 (a); SL (12), SL (132) and SL (112) are BS (12) , BS(132) and BS(112) themselves remain unchanged.

S12: Calculate the tangent vector of each intermediate point of the skeleton line, and determine the tangent vector of the second intermediate point by using the normalized connection vectors of three consecutive intermediate points, the formula is:

${\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Among them, P _i-1 , P _i and P _i+1 represent three consecutive intermediate points, and N represents a normalization parameter;

In this embodiment, the normalization parameters take values according to specific circumstances. The values of the three normalization parameters N in the above formula can be the same or different, and N can be represented by different symbols. For example, N1 is used in the above formula , N2, and N3 represent three normalization parameters respectively.

S13: Construct the tubular surface of the vascular skeleton line, the specific method is: set the intermediate points of the two adjacent cross-sectional contours C _i and C _i+1 respectively as and As shown in Figure 3(a), first use As the origin of coordinates, choose a point P on C _i to Pointing to P is the positive direction of the x-axis, with The tangent vector of is the positive direction of the y-axis, then and The cross product of is the positive direction of the z-axis, project C _i+1 onto the plane where C _i is located, and find the point Q on C _i+1 by calculation so that and The included angle is the smallest. At this time, P and Q are the best pairing points on the contours C _i and C _i+1 . Figure 3(b) shows that the triangular surface is used to join the tubular surface from the best pairing point.

Step 2: In the bifurcated area of the tubular surface, if any contour point on a branch is inside the equivalent cylinder of other branches, delete the point and the edge and triangular surface connected to the point, and mark other points at the same time All the vertices adjacent to this point are empty boundary points, that is, the branches of the bifurcation area "eat each other". In order to reduce unnecessary overhead and avoid errors, the bifurcation area is intercepted before rebuilding the bifurcation area, as shown in Figure 4 In the 3-branch region shown in (a), in this embodiment, since the branched tubular surface is formed by surrounding the adjacent equivalent circular contours with triangular faces, it is possible to approximate the adjacent contour surfaces and the The tubular surface of is equivalent to a cylindrical surface with equal base and bottom radii. Therefore, if any contour point on a branch is inside the equivalent cylinder of other branches, delete the point and the edges and triangles connected to the point, and mark all other vertices adjacent to the point as holes boundary point. Figure 4(b) is the effect of the bifurcation area shown in Figure 4(a) after "mutual eating", in which SL(1) is the object to be dug, SL(12) and SL(13) are shown as end truncation, Hollow boundaries are formed on each branch, and these boundaries are point sequence rings connected end to end.

Step 3: Carry out two-dimensional mapping on the bifurcation area, and equivalently project the bifurcation area into a two-dimensional planar topological map. In this embodiment, two-dimensional mapping is performed on the bifurcation area, and the method of equivalently projecting the bifurcation area into a two-dimensional planar topological map is as follows: for any bifurcation area, the pipe with the largest pipe diameter is used as the carrier The board is cut and paved along the skeleton line direction, and other branches are projected onto the carrier board in turn as each small panel, and the projection center point is selected and determined on the skeleton line of each projected branch as the equivalent center point of the small panel. The specific method is that, for any bifurcation area, the pipe of the excavated branch (the branch with the largest pipe diameter) is used as the carrier plate to cut and pave along the direction of the skeleton line, and other branches are projected onto this carrier plate in turn, and the projected branch is along the skeleton line. A suitable point on the line is taken as the projection center point. In this embodiment, the center of the small panel may be taken as the projection center point. Figure 4(c) is the result of two-dimensional mapping in Figure 4(b), where SL(1) is used as the carrier, and SL(12) and SL(13) are sequentially projected onto the carrier as small panels. The corresponding centers of projection are P ₁ and P ₂ , respectively. The blank area between each projection branch and between the carrier and the projection branch corresponds to the void formed by "mutual eating" in Figure 4(b). It can be seen that after the mapping from 3D to 2D, the surface reconstruction of the 3D bifurcation area is equivalent to filling the corresponding 2D topological plane with triangulation.

Step 4: Use the triangulation method based on the cavity area to fill the two-dimensional topological plane and reconstruct the surface of the vessel bifurcation area. The subdivision filling method is used for the surface reconstruction of the vascular bifurcation area. What needs special treatment is that the carrier plate cavity boundary and other branch boundaries in the bifurcation are composed of ordered discrete vertices and corresponding half edges. In this embodiment, as shown in Figure 5, the two-dimensional topological plane is filled based on the triangulation method of the void area, the purpose of which is to divide the voids between each small panel and between the small panel and the carrier board into reasonable fill-in Area, different from the polygon scan fill in graphics, each filled area here needs to have a pair of reasonable boundaries. Specifically, based on the triangulation method of the hollow area to fill the two-dimensional topological plane, the method of reconstructing the surface of the blood vessel bifurcation area is as follows:

S41: Establish a fork equivalent topological plan. In this embodiment, in order to intuitively describe the versatility of the algorithm, it is assumed that there is a topological plan as shown in FIG. , wherein there is an annular carrier plate SL(1) with a cavity, and there are several small panels SL(i) with a center point P _i in the cavity, where i is from 12 to 14; there is a cavity between the small panels, There are also voids between the small panel and the carrier; in addition, the boundary of the void on the carrier and the boundary of the small panel are point sequence rings composed of continuous boundary points.

S42: Establish an opposite relationship, the opposite relationship refers to the opposite relationship between the boundaries of the small panels and between the boundaries of the small panels and the boundary of the carrier cavity, and the condition that the opposite relationship satisfies is: when the two small panels are combined During the effective zoom-in process, in the direction of the line connecting the middle points of the small panels, the boundary where the boundaries of any small panel intersect for the first time must be the boundary of another small panel. As shown in Figure 6(a), there is an opposite relationship between SL(12) and SL(13) and SL(14); there is no opposite relationship between SL(12) and SL(15), because after equivalent amplification, they are in The first intersection in the direction of the line connecting the intermediate points P ₁ and P ₄ must be SL(13) or SL(14). In addition, since the boundary is a point sequence ring composed of continuous boundary points, each boundary point also has an opposite boundary. A boundary point generally has only one opposite boundary, and there are at most two opposite boundaries.

S43: Find multiple points on the boundary of the cavity on the carrier board, where the multiple points refer to boundary points where there are two opposite boundaries. According to this, the multiple points on the boundary of the cavity on the carrier board can be searched out. The specific method is to randomly select a point on the hole boundary point sequence ring as the starting point, and then continue to search along the point to judge the number of opposite boundaries of the current search point. If there are two opposite boundaries at the point, it will be marked as multiple points. As shown in Fig. 6(b), MP ₁ , MP ₂ , MP ₃ and MP ₄ are four multi-points searched on the boundary of the SL(1) hole.

Like the two-dimensional topological plane, the opposite relationship of blood vessel bifurcation is the "mutual eating" relationship between branches. The reason why a hole boundary point becomes a boundary point is that its adjacent deleted vertices are "eaten" by other branches, and these branches that "eat" the deleted point are called the intolerant branches of the boundary point. Generally, a boundary point has only one inadmissible branch, but in the case of multi-fork intersection, some boundary points have two intolerant branches, and such a boundary point is called a multi-point. Based on this, all the multiple points are found from the point sequence ring of the void boundary of the carrier board. As shown in Figure 4(d), two multi-points, MP ₁ and MP ₂ , can be found from the hole boundary of SL(1), because there are two intolerant branches at these two boundary points.

S44: Establish triangulation, use the opposite relationship established in step S42 to connect the center point P _i of each small panel SL(i) and the multiple points MP _j on the carrier to form a triangulation. If any three small panels or carrier boards form a pairwise relationship, connect their corresponding center points or multiple points to form a triangle, then this triangle is a subdivision triangle, and mark the intersection points of the sides of the triangle and the border of the panel , represented by the symbol IP. Holes in the entire topological plane are subdivided into each subdivision triangle.

As shown in Figure 6(c), because there are pairs of opposite relationships among SL(12), SL(13) and SL(14), connect their center points to form a subdivision triangle ΔP ₁ P ₂ P ₃ , where IP ₁ and IP ₂ are intersecting points, and other intersecting points are shown as hollow dots in the figure; for multi-points and small panels, such as MP ₁ , the small panel where the two opposite boundaries exist is SL(12) and SL(13), so MP ₁ and P ₁ and P ₂ constitute a subdivision triangle ΔMP ₁ P ₂ P ₁ ; in addition, the fan-shaped triangle taking the point sequence segment of the carrier cavity boundary as a side has ΔMP ₂ MP ₁ P ₁ , ΔMP ₁ MP ₄ P ₂ , ΔMP ₄ MP ₃ P ₄ and ΔMP ₃ MP ₂ P ₃ , so a total of 10 subdivision triangles can be constructed.

Corresponding to the three-dimensional blood vessel bifurcation, the projection points or multiple points of the three branches that have a "mutually eating" relationship between them are connected to form a triangular area, and the entire bifurcation area can be equivalently divided into several triangular areas. The holes in the bifurcation area will also be subdivided into each class subdivision triangle accordingly. Mark the intersection point of each triangle with the cavity boundary of the branch, that is, mark the intersection point of the plane defined by the bifurcation point and the selected projected point in the three-dimensional bifurcation and the cavity boundary. As shown in Figure 4(d), in addition to the two multi-points of MP ₁ and MP ₂ , there are three intersection points on the cavity boundaries of SL(12) and SL(13). They are connected, that is, the whole bifurcation area is divided into four parts, and each part is in a corresponding triangular cavity.

S45: Fill the triangle hole. Since the intersection point divides the boundary point sequence ring of each branch into end-to-end point sequence segments, the hole in each triangle can be filled with an irregular polygon through the opposite point sequence segment. As shown in Figure 7, an irregular quadrilateral is gradually constructed for two point sequence segments V _i-> V _i+5 and V _j-> V _j+3 from both ends to the middle. Since the points of the two point sequence segments are not equal, the middle The positions directly fill two triangles, namely ΔV _i+2 V _j+2 V _i+3 and ΔV _i+3 V _j+2 V _i+4 .

Based on this, for the holes in each triangle, starting from the paired points at both ends, the irregular quadrilaterals are alternately used to fill them. As shown in Figure 8, the closed area is the hollow area of the subdivision triangle ΔP ₂ P ₄ P ₃ in Figure 6(c), and the corresponding filling process is: IP ₃ and IP ₄ as paired intersection points, IP ₅ and IP ₆ As another paired intersection point, in this embodiment, starting from these four paired intersection points, the irregular quadrilateral is used for filling, as shown in Figure 8(b) is the point sequence between IP ₄ and IP ₅ during the filling process A common selection point BP ₁ appears on the segment, and the selection points of the other two point sequence segments are BP ₂ and BP ₃ respectively; as shown in Figure 8(c), these three selection points are directly formed into _a triangle; The point sequence segment between BP ₂ and the point sequence segment between IP ₂ and BP ₃ are filled with irregular quadrilaterals, and the entire filled triangular hole is obtained as shown in Figure 8(d).

Fill all the triangular holes so that the entire topological plane area can be reasonably filled. Fig. 9 is the result of Fig. 6(c) after completely filling the void.

In this embodiment, irregular quadrilaterals are used to fill holes. Fig. 10 is a process of gradually filling each subdivided cavity in the 3-branch area that has been subdivided in Fig. 4(d), wherein Fig. 10(a)-Fig. 10(d) are respectively filling the first void, The second hole, the third hole and the fourth hole.

In a preferred embodiment of the present invention, after the fourth step, the following steps can also be performed:

Surface subdivision, in general, if the equivalent cross-sectional contour density of each branch in the bifurcation area is greater, the reconstructed bifurcation area will be more realistic, but the calculation cost will be greater. Therefore, the density of the equivalent cross-section ring is not suitable is too large, and there is a possibility that the preliminary surface reconstructed in this way is not smooth enough. In addition, the model of the present invention is constructed based on triangular faces, wherein the irregular quadrilateral can be split into two shared-side triangles. In this embodiment, The surface of the vessel bifurcation area can also be subdivided using the Loop subdivision method. Fig. 11 shows the surface subdivision results of the reconstructed 3-furcation region shown in Fig. 10(d). It can be seen that the surface of the obtained bifurcation can be smoothly transitioned very well, which is very close to the real blood vessel.

Step 5: Reconstruct the entire vascular tree using the triangulation filling method of the hollow area. Figure 12(a) is an original blood vessel voxel model, which is the result of direct volume rendering; Figure 12(b) uses the conventional method of directly constructing surfaces based on voxel boundaries (Marchingcubes) to the volume of Figure 12(b) The local surface magnification effect of surface reconstruction carried out by the pixel model; Fig. 12 (c) is the local surface magnification effect of the model obtained by using the limited smooth Marchingcubes method; Fig. 12 (d) is the vector surface model obtained based on the method of the present invention The local surface magnification effect of . The local enlarged images in Figure 12(b), Figure 12(c) and Figure 12(d) are local enlargements of the corresponding positions on the surface of blood vessels respectively. From the comparison in the figure, it can be seen that even if the traditional non-vector surface modeling method is After smoothing, there will also be noise-like or deformed surfaces, but the surface model of the vascular tree constructed by the present invention is smooth and accurate.

The invention reconstructs the tubular surface of the blood vessel based on the skeleton line of the blood vessel and the caliber, so that the reconstructed blood vessel model has complete vector and reconfigurability. It maintains the topological information consistent with the real blood vessels in the CT image, and can well reflect information such as the branch direction of the blood vessels and the size of the pipeline; at the same time, the vector feature adopted provides good information for more advanced interactive functions, such as dynamic deformation of blood vessels. geometric basis.

When reconstructing the transition surface of the bifurcation area, the "mutual eating" relationship between the branches is fully utilized, and the holes formed after the "mutual eating" of the bifurcation area are equivalently divided into each subdivision triangle. The holes in each subdivision triangle are filled to reconstruct the transitional surface of the bifurcated area; in addition, the transitional splicing of the surface is only the irregular quadrilateral filling of the hole boundaries of each branch. The calculation amount is small, the robustness is strong, and the reconstruction efficiency is high.

For the reconstruction of the bifurcation area, the branches "eating each other", bifurcation two-dimensional mapping, triangulation and filling of triangular holes are carried out closely around the original topology of the vascular branches and the size of the pipeline, so as to maintain the real vascular branch as much as possible. The topological shape of the fork, the reconstruction model is accurate.

In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the invention is defined by the claims and their equivalents.

Claims (2)

1. A blood vessel bifurcation surface reconstruction method based on cavity area triangulation, is characterized in that, comprises the steps: S1: Construct the tubular surface of the vascular skeleton line. The skeleton line is a multi-fork tree. The skeleton line is composed of continuous intermediate points. Each skeleton line segment corresponds to a node of a tree. The tubular surface is surrounded by triangular faces. The method for constructing the tubular surface of the vascular skeleton line is as follows: S11: Reorganize the vascular skeleton line. For any current skeleton line segment, assuming that the code is SL(i), then the segments corresponding to each of its child nodes are arranged in descending order according to the average tube diameter, and the largest one shares the current segment code SL(i ), other segments are sequentially compiled as SL(i*10+k), where i is a positive integer, and k ranges from 2 to the total number of child nodes; S12: Calculate the tangent vector of each intermediate point of the skeleton line, and determine the tangent vector of the second intermediate point by using the normalized connection vectors of three consecutive intermediate points, the formula is: Among them, P _i-1 , P _i and P _i+1 represent three consecutive intermediate points, and N represents a normalization parameter; S13: Construct the tubular surface of the vascular skeleton line, the specific method is: set the two adjacent cross-sectional contours as C _i and C _i+1 , and the middle points of the two cross-sectional contours are respectively and start with As the origin of coordinates, choose a point P on C _i to Pointing to P is the positive direction of the x-axis, with The tangent vector of is the positive direction of the y-axis, and The cross product of is the positive direction of the z-axis, project C _i+1 onto the plane where C _i is located, and calculate and find the point Q on C _i+1 such that and The included angle is the smallest, point P and point Q are the best pairing points on the contours C _i and C _i+1 , starting from the best pairing point to stitch the tubular surface with triangular faces; S2: In the bifurcation area of the tubular surface, if the contour point of any cross-section on a branch is inside the equivalent cylinder of other branches, delete the point, the edge connected to the point and the triangular surface, and at the same time Mark all other vertices adjacent to this point as empty boundary points; S3: Carry out two-dimensional mapping on the bifurcation area, and convert the bifurcation area into a two-dimensional planar topological map by equivalent projection. The method is: for any bifurcation area, use the pipe with the largest pipe diameter as the carrier plate And cut and pave along the direction of the skeleton line, other branches are projected onto the carrier board in turn, as each small panel, and select and determine the projection center point on the skeleton line of each projected branch as the equivalent center point of the small panel; S4: Use the method based on the subdivision of the cavity area to fill the two-dimensional topological plane, and reconstruct the surface of the vessel bifurcation area. The method is as follows: S41: Establishing an equivalent topological plan of the bifurcation area; S42: Establish an opposite relationship, the opposite relationship refers to the opposite relationship between the boundaries of the small panels and between the boundaries of the small panels and the boundary of the cavity of the carrier board, and the condition that the opposite relationship satisfies is: In the process of equivalently enlarging two small panels, in the direction of the line connecting the middle points of the small panels, the boundary where the boundary of any small panel intersects for the first time must be the boundary of another small panel; S43: Find multiple points on the boundary of the cavity on the carrier board, where the multiple points refer to boundary points where there are two opposite boundaries; S44: Establish a triangulation, using the opposite relationship established in step S42, connect the center points of each small panel and the multiple points on the carrier board to form a triangulation, if any three small panels or carrier boards form a pairwise opposite relationship , then connect their corresponding center points or multiple points into a triangle, and mark the intersection points of the sides of the triangle and the border of the panel; S45: Fill the triangular void, using irregular quadrilaterals to fill the void; S5: Reconstruct the entire vascular tree by using the hole area triangulation filling method. 2. the blood vessel bifurcation surface reconstruction method based on cavity area triangulation as claimed in claim 1, is characterized in that, also has the following steps between described step S4 and step S5: Use the Loop subdivision method to subdivide the surface of the vessel bifurcation area.