A 3D-2D vascular elasticity registration method based on CTA and DSA

Abstract

The present invention discloses a 3D-2D vascular elasticity registration method based on CTA and DSA; on the basis of the segmentation results of preoperative CTA and intraoperative DSA images, the present invention performs four steps of vascular centerline topological characterization, vascular curve extraction, rigid registration, and elastic registration, and elastically registers the 3D blood vessels in the preoperative CTA onto the 2D vascular projection in the intraoperative DSA. On the one hand, the present invention can be used to enhance intraoperative DSA angiographic images and avoid the influence caused by the absence of blood vessels in DSA images due to vascular stenosis; on the other hand, it can achieve the integration of diagnosis and treatment, fuse the surgical plan made by doctors for CTA images before surgery onto intraoperative DSA images, so as to assist doctors in making decisions during vascular intervention surgery.

Description

Technical Field

[0001] The present invention relates to a 3D-2D vascular elastic registration method based on CTA and DSA, and belongs to the field of medical image analysis and processing. Background Art

[0002] Currently, in conventional vascular interventional surgeries, doctors take CTA images of patients before the surgery for vascular lesion diagnosis and interventional surgery planning, and use real-time DSA imaging during the surgery to provide path navigation for catheter / wire intervention. This clinical scenario faces two problems: one is that the surgical planning performed on preoperative 3D CTA cannot be intuitively integrated into intraoperative 2D DSA images, and many vascular pseudo bifurcations caused by projection in DSA images will interfere with doctors' judgments, resulting in the surgery not being able to proceed smoothly according to the preoperative plan; the other is that vascular stenosis caused by vascular plaques will cause poor circulation of contrast agents, resulting in the absence of vascular segments in DSA images, leading to incomplete intraoperative navigation information, and further possibly causing doctors to puncture vascular plaques during catheter / wire intervention, bringing surgical complications to patients. Through 3D-2D vascular elastic registration, the 3D blood vessels in preoperative CTA images are registered onto the 2D blood vessels in intraoperative DSA images. On the one hand, the preoperative planning (such as intervention path, lesion location, etc.) information can be integrated into intraoperative images; on the other hand, since vascular stenosis does not affect CTA imaging, the absence of vascular segments in DSA blood vessels can be compensated through registration.

[0003] In current 3D-2D registration technologies applied to medical images, most only achieve rigid registration, that is, only solve the affine transformation, and are generally applied to bones or cerebral blood vessels because these anatomical structures usually do not undergo elastic deformation. For hepatic blood vessels or coronary blood vessels, due to the influence of breathing and heartbeat, elastic deformation will occur, so elastic registration algorithms are required. Existing 3D-2D elastic registration technologies usually solve elastic deformation parameters through iterative optimization or search methods, and the solution process is time-consuming and cannot meet the requirements of intraoperative real-time registration. Summary of the Invention

[0004] The purpose of the present invention is to design a 3D-2D vascular elastic registration method based on CTA and DSA. The 3D-2D vascular elastic registration method proposed by the present invention is realized through two stages. First, the translation deformation parameters with very few parameters are solved through iterative optimization, and then the corresponding relationship between the 3D blood vessels after elastic deformation and the 2D blood vessels is directly obtained through three-level matching of blood vessel curves - blood vessel segments - points, which can meet clinical requirements in terms of registration accuracy and running time.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A 3D-2D vascular elasticity registration method based on CTA and DSA, comprising the following steps:

[0007] Step 1, perform centerline extraction and topological relationship characterization on the vascular segmentation results of the preoperative CTA image and intraoperative DSA image of the same patient, that is, represent each vascular segment by the centerline and obtain the connection relationship between the vascular segments;

[0008] Step 2, obtain the vascular curves according to the topological relationship of the 3D / 2D vascular segments, that is, extract all the vascular curves from the root vascular segment to the terminal vascular segment;

[0009] Step 3, perform rigid registration on the 3D / 2D vascular centerlines, that is, solve the translation parameters for the 3D vascular centerlines so that all the 3D vascular centerlines can be roughly aligned with the 2D vascular centerlines after projection;

[0010] Step 4, perform elastic registration on the 3D / 2D vascular centerlines, that is, solve the elastic deformation field for the 3D vascular centerlines so that all the 3D vascular curves can be fused with the matching 2D vascular curves after projection.

[0011] Further, the centerline extraction and topological relationship characterization based on the 3D / 2D vascular segmentation results in Step 1 specifically include the following steps:

[0012] Step 1.1, use the image skeletonization algorithm to process the binary 3D / 2D vascular segmentation results, that is, continuously erode the edge pixel points on the image to refine the segmentation area until the 3D / 2D vascular centerline with a single-pixel width is obtained;

[0013] Step 1.2, divide all pixel points into three categories according to the adjacency relationship of the pixel points in the vascular centerline: branch points, intermediate points, and termination points; there will be only one intermediate point in the 3×3 neighborhood of the termination point; there are at most two non-adjacent intermediate points and at most one branch point in the 3×3 neighborhood of the intermediate point; there will be no other branch points in the 3×3 neighborhood of the branch point;

[0014] Step 1.3, extract the centerlines of all vascular segments. Each independent vascular segment takes the branch point and the termination point as endpoints, and the branch point and the termination point can only be used as the endpoints of the vascular segment. The vascular segment with the termination point as the endpoint is called the terminal vascular segment;

[0015] Step 1.4, obtain the connection relationship between the vascular segments. The centerlines of adjacent vascular segments have the same endpoints.

[0016] Further, the obtaining of the vascular curves according to the topological relationship of the 3D / 2D vascular segments in Step 2 specifically includes the following steps:

[0017] Step 2.1: Select the vascular segment with the longest average radius among all the terminal vascular segments as the root vascular segment. The average radius of a 3D / 2D vascular segment is the average of the radius values of all the voxel points / pixel points within the centerline of this vascular segment. The radius value of a voxel point / pixel point is the shortest distance from this point along the normal vector direction of the centerline to the blood vessel wall.

[0018] Step 2.2: Use depth-first traversal to continuously expand adjacent vascular segments starting from the root vascular segment until no further expansion is possible, obtaining multiple vascular curves.

[0019] Step 2.3: Since the projection during DSA imaging may cause different vascular segments to overlap each other, loops may appear in the 2D vascular centerline. Delete the curves in the vascular segment curves obtained in the previous step that do not end with terminal vascular segments to avoid the influence of loops.

[0020] Furthermore, the rigid registration of the 3D / 2D vascular centerline in Step 3 specifically includes the following steps:

[0021] Step 3.1: Obtain the angle of the device during intraoperative imaging, the distance from the radiation source to the detector plane (Source Image Receptor Distance, SID), and the position of the radiation source relative to the object (SourceObject Distance, SOD) from the header file of the DSA image; rotate the centerline of the preoperative 3D blood vessel according to the angle information to simulate the orientation of the intraoperative imaging device relative to the patient; construct a projection matrix P based on SID and SOD to simulate the projection imaging process of the intraoperative imaging device.

[0022] Step 3.2: Solve the translation parameters through rigid registration and set the registration loss function:

[0023]

[0024] where n represents the number of points on the 3D vascular centerline; the matrix T is the displacement matrix, indicating the movement of the patient from preoperative to intraoperative relative to the imaging device; x i represents the points on the 3D vascular centerline, and PTx i represents the 2D point obtained after translating and projecting this point; y i represents the point in the 2D vascular centerline that is closest to PTx i .

[0025] Step 3.3: Solve the translation parameters. Through the Powell optimization method based on search, solve for the optimal deformation parameters to minimize the value of the loss function D, and apply the solved translation parameters to the 3D vascular centerline.

[0026] Step 3.4, find the nearest matching point pairs, and find the point u in the 2D blood vessel centerline that is closest to the projection point with a distance of x i the point u closest to the projection point i ;

[0027] Step 3.5, continuously iterate the above two steps until convergence (the decrease value of the loss function D is less than the threshold or the number of iteration steps reaches the threshold).

[0028] Furthermore, the elastic registration of the 3D / 2D blood vessel centerlines in step 4 specifically includes the following steps:

[0029] Step 4.1, on the basis of rigid registration, find the 2D blood vessel curve X that is most similar to each 3D blood vessel curve C C :

[0030]

[0031] where PC represents the projection curve of C, χ represents the set of 2D blood vessel curves, and the function F represents the Fréchet distance; if the Fréchet distance between curve C and all 2D blood vessel curves is greater than the threshold, it is considered that X does not exist C ;

[0032] Step 4.2, for the 3D curve C for which the matching curve is found, let the set of all endpoints of the blood vessel segments in it be {p0, p1, …, p m}, and the set of all endpoints of the matching 2D curve X C be {q0, q1, …, q n}, and the endpoints are arranged in topological order in the set; for each endpoint p i in C, find the matching endpoint q C in X j :

[0033]

[0034] where I(p i-1 ) represents the subscript of the point in X i-1 that matches p C ; according to the matching situation of the branch points, each independent blood vessel segment |p i p i+1 |, (0 ≤ i < m) in the 3D curve C can obtain the matching blood vessel segment |q C q u |, (u = I(p v ), v = I(p i )) in the 2D curve X i+1 ), and |q u q v | is composed of XC is composed of an independent blood vessel segment or multiple adjacent blood vessel segments in

[0035] Step 4.3, use the Dynamic Time Warping (DWT) algorithm to find the projection of |p i p i+1 | and the minimum distance cost matching of each point in |q u q v |; Let x i ∈|p i p i+1 | and its matching point be y i ∈|q u q v |, indicating that the point x i on the 3D blood vessel centerline will finally coincide with the point y i on the 2D blood vessel centerline after displacement and projection;

[0036] Step 4.4, if there is a matching curve X C for the 3D blood vessel curve C, then for each point x i on C, a corresponding 2D blood vessel centerline point y i can be found. Project x i and then displace it to y i ; If there is no matching curve X C for the 3D blood vessel curve C, then some points on C cannot find corresponding 2D points. Take the points on C that can find matching points as control points, and perform Thin-Plane Spline (TPS) interpolation on the projection curve of C to calculate the deformed positions of the points on C that cannot find matching points.

[0037] The present invention has the following effective benefits: (1) The present invention provides a 3D-2D blood vessel elastic registration method based on CTA and DSA, which can quickly and accurately integrate the blood vessel structure in the preoperative CTA image into the intraoperative DSA image, realizing the intuitive integration of the preoperative planning of the blood vessel intervention surgery into the intraoperative scene, and providing more auxiliary information for the path navigation of the catheter / guide wire during the operation; (2) The present invention elastically registers the blood vessel structure in CTA onto the DSA image. Since CTA imaging is not affected by blood vessel stenosis, it can effectively solve the problem of blood vessel loss due to blood vessel stenosis in the intraoperative DSA image; (3) The present invention realizes elastic registration through two stages. First, it iteratively optimizes and solves the translation deformation parameters with very few parameters, and then directly obtains the corresponding relationship between the 3D blood vessel after elastic deformation and the 2D blood vessel through three-level matching of blood vessel curve - blood vessel segment - point, which can meet the clinical requirements in terms of registration accuracy and running time. Description of the Drawings

[0038] Figure 1 is the flowchart of the present invention;

[0039] Figure 2 (a) and (b) are the vascular segmentation result and centerline extraction result of the preoperative CTA image;

[0040] Figure 3 (a), (b), and (c) are the intraoperative DSA image, vascular segmentation result, and centerline extraction result respectively;

[0041] Figure 4 is the rough registration result. The black ones are the projections of the 3D vascular centerlines, and the white ones are the 2D vascular centerlines;

[0042] Figure 5 are three groups of mutually matching 3D vascular curve projections (black) and 2D vascular curves (white);

[0043] Figure 6 is the schematic diagram of the fine registration result. Detailed implementation manners

[0044] The present invention will be further clarified below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art to the present invention all fall within the scope defined by the appended claims of this application.

[0045] Embodiment 1: As Figure 1 shown, a 3D-2D vascular elastic registration method based on CTA and DSA specifically includes the following steps:

[0046] Step 1: Perform centerline extraction and topological relationship characterization on the vascular segmentation results of the preoperative CTA image and intraoperative DSA image of the same patient, that is, represent each vascular segment by the centerline and obtain the connection relationship between the vascular segments.

[0047] Specifically, it includes the following steps:

[0048] Step 1.1: Use the image skeletonization algorithm to process the binary 3D / 2D vascular segmentation results (as Figure 2 (a) and Figure 3 (b) shown), that is, continuously erode the edge pixel points on the image to refine the segmentation area until a single-pixel-width 3D / 2D vascular centerline is obtained (as Figure 2 (b) and Figure 3 (c) shown);

[0049] Step 1.2: According to the adjacency relationship of the pixel points in the blood vessel centerline, all pixel points are divided into three categories: branch points, intermediate points, and termination points. There is only one intermediate point in the 3×3 neighborhood of the termination point. There are at most two non-adjacent intermediate points and at most one branch point in the 3×3 neighborhood of the intermediate point. There will be no other branch points in the 3×3 neighborhood of the branch point.

[0050] Step 1.3: Extract the centerlines of all blood vessel segments. Each independent blood vessel segment has branch points and termination points as its endpoints, and branch points and termination points can only be used as the endpoints of the blood vessel segment. The blood vessel segment with a termination point as an endpoint is called the terminal blood vessel segment.

[0051] Step 1.4: Obtain the connection relationship between blood vessel segments. The centerlines of adjacent blood vessel segments have the same endpoints.

[0052] Step 2: Obtain the blood vessel curves according to the topological relationship between 3D / 2D blood vessel segments, that is, extract all blood vessel curves from the root blood vessel segment to the terminal blood vessel segment. The specific steps are as follows:

[0053] Step 2.1: Take the blood vessel segment with the longest average radius among all terminal blood vessel segments as the root blood vessel segment. The average radius of a 3D / 2D blood vessel segment is the average of the radius values of all voxel points / pixel points in the centerline of the blood vessel segment. The radius value of a voxel point / pixel point is the shortest distance from this point along the normal vector direction of the centerline to the blood vessel wall.

[0054] Step 2.2: Use depth-first traversal to continuously expand adjacent blood vessel segments starting from the root blood vessel segment until no further expansion is possible, and obtain multiple blood vessel curves.

[0055] Step 2.3: Since the projection during DSA imaging may cause different blood vessel segments to overlap each other, there may be loops in the 2D blood vessel centerline. Delete the curves that do not end with the terminal blood vessel segment in the blood vessel segment curves obtained in the previous step to avoid the influence of loops.

[0056] Step 3: Perform rigid registration on the 3D / 2D blood vessel centerline, that is, solve the translation parameters for the 3D blood vessel centerline so that all 3D blood vessel centerlines can be roughly aligned with the 2D blood vessel centerline after projection. The specific steps are as follows:

[0057] Step 3.1: Obtain the angle of the device during intraoperative imaging, the distance between the X-ray source and the detector plane (Source Image Receptor Distance, SID), and the position of the X-ray source relative to the object (SourceObject Distance, SOD) from the header file of the DSA image; rotate the centerline of the preoperative 3D blood vessel according to the angle information to simulate the orientation of the intraoperative imaging device relative to the patient; construct a projection matrix P based on SID and SOD to simulate the projection imaging process of the intraoperative imaging device.

[0058] Step 3.2: Solve the translation parameters through rigid registration and set the registration loss function:

[0059]

[0060] where n represents the number of points on the centerline of the 3D blood vessel; the matrix T is the displacement matrix, representing the movement of the patient from preoperative to intraoperative relative to the imaging device; x i represents the points on the centerline of the 3D blood vessel, and PTx i represents the 2D point obtained after translating and projecting this point; y i represents the point in the 2D blood vessel centerline that is closest to PTx i ;

[0061] Step 3.3: Solve the translation parameters. Through the Powell optimization method based on search, solve the optimal deformation parameters to minimize the value of the loss function D, and apply the obtained translation parameters to the centerline of the 3D blood vessel.

[0062] Step 3.4: Find the nearest matching point pairs. Find the point u i in the 2D blood vessel centerline that is closest to the projection point of x i ;

[0063] Step 3.5: Continuously iterate the above two steps until convergence (the decrease value of the loss function D is less than the threshold or the number of iteration steps reaches the threshold), and the final rough registration result is as Figure 4 shown.

[0064] Step 4: Perform elastic registration on the 3D / 2D blood vessel centerlines, that is, solve the elastic deformation field for the 3D blood vessel centerlines so that all 3D blood vessel curves can be fused with the corresponding 2D blood vessel curves after projection. Specifically, it includes the following steps:

[0065] Step 4.1: On the basis of rigid registration, find the 2D blood vessel curve X C that is most similar to each 3D blood vessel curve C:

[0066]

[0067] Among them, PC represents the projection curve of C, χ represents the set of 2D vascular curves, and the function F represents the Fréchet distance; if the Fréchet distance between curve C and all 2D vascular curves is greater than the threshold, it is considered that X does not exist. C ; Figure 5 are three groups of mutually matching 3D vascular curve projections (purple) and 2D vascular curves (black);

[0068] Step 4.2, for the 3D curve C for which the matching curve is found, let the set of all endpoints of the vascular segments be {p0, p1, …, p m}}, and the set of all endpoints of the matching 2D curve X C be {q0, q1, …, q n}}, and the endpoints are arranged in topological order in the set; for each endpoint p i in C, find the matching endpoint q C in X j according to the distance:

[0069]

[0070] where I(p i-1 ) represents the subscript of the point in X i-1 that matches p C ; according to the matching situation of the branch points, each independent vascular segment |p i p i+1 |, (0 ≤ i < m) in the 3D curve C can obtain the matching vascular segment |q C q u q v |, (u = I(p i ), v = I(p i+1 )) in the 2D curve X C ; |q u q v | is composed of an independent vascular segment or multiple adjacent vascular segments in X C ;

[0071] Step 4.3, use the Dynamic Time Warping (DWT) algorithm to find the minimum distance cost matching between the projection of |p i p i+1 | and each point in |q u q v |; let x i ∈|p i p i+1 | and the matching point be y i ∈|q u q v|, indicating the point x on the 3D blood vessel centerline i After displacement and projection, it will finally coincide with the point y on the 2D blood vessel centerline i ;

[0072] Step 4.4, if there is a matching curve X for the 3D blood vessel curve C C , then for each point x on C i a corresponding 2D blood vessel centerline point y can be found i . Project x i and then displace it to y i ; if there is no matching curve X for the 3D blood vessel curve C C , then some points on C cannot find corresponding 2D points. Take the points on C that can find matching points as control points, perform Thin-Plane Spline (TPS) interpolation on the projection curve of C, and calculate the deformed positions for the points on C that cannot find matching points; The final fine registration result is as Figure 6 shown

[0073] It should be noted that the above embodiments are only preferred embodiments of the present invention and do not limit the protection scope of the present invention. Equivalent replacements or substitutions made on the basis of the above technical solutions all fall within the protection scope of the present invention

Claims

1. A 3D-2D vascular elasticity registration method based on CTA and DSA, characterized in that, It includes the following steps: Step 1: For the vascular segmentation results of the preoperative CTA image and intraoperative DSA image of the same patient, perform centerline extraction and topological relationship characterization respectively, that is, represent each vascular segment by the centerline and obtain the connection relationship between vascular segments; Step 2: Obtain vascular curves according to the topological relationship of 3D / 2D vascular segments, that is, extract all vascular curves from the root vascular segment to the terminal vascular segment; Step 3: Perform rigid registration on the 3D / 2D vascular centerlines, that is, solve the translation parameters for the 3D vascular centerlines so that all 3D vascular centerlines can be aligned with the 2D vascular centerlines after projection; Step 4: Perform elastic registration on the 3D / 2D vascular centerlines, that is, solve the elastic deformation field for the 3D vascular centerlines so that all 3D vascular curves can be fused with the matching 2D vascular curves after projection; Among them, the centerline extraction and topological relationship characterization based on the 3D / 2D vascular segmentation results in Step 1 specifically include the following steps: Step 1.1: Use the image skeletonization algorithm to process the binary 3D / 2D vascular segmentation results, that is, continuously erode the edge pixel points on the image to refine the segmentation area until a single-pixel-width 3D / 2D vascular centerline is obtained; Step 1.2: According to the adjacency relationship of pixel points in the vascular centerline, divide all pixel points into three categories: branch points, intermediate points, and termination points; Step 1.3: Extract the centerlines of all vascular segments. Each independent vascular segment has branch points and termination points as endpoints, and branch points and termination points can only be used as endpoints of vascular segments. The vascular segment with a termination point as an endpoint is called the terminal vascular segment; Step 1.4: Obtain the connection relationship between vascular segments. The centerlines of adjacent vascular segments have the same endpoints; The obtaining of vascular curves according to the topological relationship of 3D / 2D vascular segments in Step 2 specifically includes the following steps: Step 2.1: Take the one with the longest average radius among all terminal vascular segments as the root vascular segment. The average radius of a 3D / 2D vascular segment is the average of the radius values of all voxel points / pixel points within the centerline of the vascular segment. The radius value of a voxel point / pixel point is the shortest distance from this point along the normal vector direction of the centerline to the vascular wall; Step 2.2: Use depth-first traversal to continuously expand adjacent vascular segments starting from the root vascular segment until no further expansion is possible, and obtain multiple vascular curves; Step 2.3: Since the projection during DSA imaging may cause different vascular segments to overlap each other, loops may appear in the 2D vascular centerline. Delete the curves in the vascular segment curves obtained in the previous step that do not end with the terminal vascular segment to avoid the influence of loops; The rigid registration of the 3D / 2D vascular centerlines in Step 3 specifically includes the following steps: Step 3.1: Obtain the angle of the device during intraoperative imaging, the distance between the X-ray source and the detector plane (Source Image Receptor Distance, SID), and the position of the X-ray source relative to the object (SourceObject Distance, SOD) from the header file of the DSA image; rotate the centerline of the preoperative 3D blood vessel according to the angle information to simulate the orientation of the intraoperative imaging device relative to the patient; construct a projection matrix P based on SID and SOD to simulate the projection imaging process of the intraoperative imaging device. Step 3.2: Solve the translation parameters through rigid registration and set the registration loss function: Among them, n represents the number of points on the 3D blood vessel centerline; the matrix T is the displacement matrix, representing the movement of the patient relative to the imaging device from before surgery to during surgery; x i represents a point on the 3D blood vessel centerline, and PTx i represents the 2D point obtained after translating and projecting this point; y i represents the point in the 2D blood vessel centerline that is closest to PTx i the closest point; Step 3.3: Solve the translation parameters. Through the Powell optimization method based on search, solve the optimal deformation parameters to minimize the value of the loss function D, and apply the solved translation parameters to the 3D blood vessel centerline. Step 3.4, find the nearest matching point pair, and find the point u in the 2D blood vessel centerline that is closest to the projection point with a distance of x i the point u closest to the projection point i ; Step 3.5: Continuously iterate the above two steps until convergence. The elastic registration of the 3D / 2D blood vessel centerline in Step 4 specifically includes the following steps: Step 4.1, on the basis of rigid registration, find the 2D vascular curve X that is most similar to each 3D vascular curve C C : Wherein, PC represents the projection curve of C, X represents the set of 2D vascular curves, and the function F represents the Fréchet distance; if the Fréchet distance between curve C and all 2D vascular curves is greater than the threshold, it is considered that X does not exist C ; Step 4.2, for the 3D curve C for which the matching curve is found, let the set of all the endpoints of the blood vessel segments therein be {p0, p1,..., p m}, and the set of all the endpoints of the blood vessel segments in the matching 2D curve X C be {q0, q1,..., q n}, and the endpoints are arranged in topological order in the set; for each endpoint p i in C, find the matching endpoint q C in X j according to the distance: where I(p i-1 ) represents the subscript of the midpoint of X i-1 that matches p C ; according to the matching situation of the branch points, each independent blood vessel segment |p i p i+1 |, 0 ≤ i < m in the 2D curve X C is obtained, and the blood vessel segment |q u q v | that matches it in X i is composed of an independent blood vessel segment or multiple adjacent blood vessel segments in X i+1 . Let u = I(p u ) and v = I(p i+1 ), and |q u q v | is composed of an independent blood vessel segment or multiple adjacent blood vessel segments in X C ; Step 4.3, use the Dynamic Time Warping (DWT) algorithm to find the minimum distance cost matching between the projection of |p i p i+1 | and each point in |q u q v |; Let x i ∈|p i p i+1 | have a matching point y i ∈|q u q v |, indicating that the point x i on the 3D blood vessel centerline will finally coincide with the point y i on the 2D blood vessel centerline after displacement and projection; Step 4.4, if there is a matching curve X for the 3D blood vessel curve C C , then for each point x on C i , a corresponding 2D blood vessel centerline point y that matches it can be found i . Project x i and then displace it to y i ; if there is no matching curve X for the 3D blood vessel curve C C , then some points on C cannot find corresponding 2D points. Take the points on C that find matching points as control points, perform Thin-Plane Spline (TPS) interpolation on the projection curve of C, and calculate the deformed positions for the points on C that cannot find matching points.

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