Myocardial curved surface three-dimensional reconstruction method based on point constraint

Abstract

The invention provides a base point constrained myocardial curved surface three-dimensional reconstruction method, which comprises the following steps of: 1, performing myocardial segmentation, accurately segmenting a myocardial substructure by analyzing a cardiac movie magnetic resonance image sequence, and extracting boundary contour lines of inner and outer walls of a myocardial; step 2, establishing a point cloud model; step 3, determining a constraint point, determining a central point on the myocardial inner boundary contour of the last slice of the cardiac apex area, and moving the central point along the longitudinal direction of the heart towards the cardiac apex by a distance of one slice interval to form a reconstructed constraint point; and 4, performing curved surface reconstruction on the point cloud models of the internal and external walls of the myocardium by adopting a Poisson reconstruction method. The method has the advantages that by using the vertex to restrain the myocardial curved surface, it can be ensured that the reconstructed curved surface is closed and smooth, and the original topological structure of the myocardial can be accurately restored; and the reconstruction result does not depend on the distribution of the point cloud in the space, so that the method has general applicability to different crowds and various cases.

Description

Technical Field

[0001] The present invention relates to the technical field of cardiovascular medical image analysis, and particularly to a three-dimensional reconstruction method for myocardial surface based on apex point constraint. Background Art

[0002] The existing three-dimensional reconstruction technologies for myocardial surface face many challenges. The physiological structure of the heart is complex, and it is difficult for traditional methods to fully maintain the natural curvature and local features of the myocardial surface. In addition, the point cloud data obtained from cardiac magnetic resonance imaging is dense within layers and sparse between layers, which brings difficulties to the closed reconstruction of the surface and maintaining the original topological structure.

[0003] In the prior art, for example, the classic Marching Cube algorithm can extract isosurfaces from volume data, but it has deficiencies in dealing with noise and details, and the generated meshes need to be further optimized. The radial basis function method can handle irregular point clouds and generate smooth surfaces, but it has a high computational complexity and poor processing effect for uneven data distribution. The implicit surface method is suitable for complex geometries, but the process of solving implicit functions consumes a large amount of computing resources and has limited ability to handle noise and outliers. The deep learning-based method can automatically extract features and generate high-quality surfaces, but it relies on a large amount of labeled data, the training process is complex, and the model interpretability is poor.

[0004] In addition, Chinese Patent Application No. CN201910227014.X discloses a method for reconstructing a static three-dimensional model of the heart, including: Step 1, establishing a basic dataset of the model; Step 2, after determining the reference model, registering it with the heart model in the basic dataset to obtain the reference model after non-rigid transformation; Step 3, establishing a three-dimensional mathematical model of the heart by the principal component analysis method; Step 4, adjusting the parameters of the three-dimensional mathematical model of the heart according to the given image to generate a static three-dimensional model of the heart corresponding to the given image; Step 5, conducting a social evaluation on the static three-dimensional model of the heart according to medical knowledge, and using this as the basis for judging the quality of the reconstructed model. The present invention can realize the reconstruction of a static three-dimensional heart by using a general initial three-dimensional heart model and a few cardiac CT images.

[0005] When the above-mentioned prior art processes myocardial data with sparsity and hierarchical characteristics, it is often difficult to obtain satisfactory results, and there are still limitations in the reconstruction of the apex point by traditional methods.

[0006] The Poisson surface reconstruction method can convert point clouds into closed and smooth three-dimensional surfaces. For this reason, the present invention proposes an improved three-dimensional reconstruction method for myocardial surface. By introducing apex point constraint and combining with Poisson reconstruction technology, it aims to more accurately capture the geometric features of the myocardial surface, improve the reconstruction accuracy, especially the reconstruction effect in key regions such as the apex. Summary of the Invention

[0007] In view of the defects existing in the prior art, the purpose of the present invention is to provide a three-dimensional reconstruction method for myocardial surface with base point constraints.

[0008] In order to achieve the above purpose, the three-dimensional reconstruction method for myocardial surface with base point constraints of the present invention includes the following steps:

[0009] Step 1. Perform myocardial segmentation. By analyzing the cardiac cine magnetic resonance image sequence, accurately segment the myocardial substructure and extract the boundary contour lines of the inner and outer myocardial walls.

[0010] Step 2. Establish a point cloud model. According to the segmentation result, convert the boundary contours of the inner and outer myocardial walls into a point cloud model and calculate the normal vector of each point.

[0011] Step 3. Determine the constraint points. Determine the center point on the inner boundary contour of the myocardium in the last slice of the apex region and move it along the longitudinal direction of the heart towards the apex by a slice interval distance to form the reconstructed constraint points.

[0012] Step 4. Perform surface reconstruction based on point constraints. Under the above constraint conditions, use the Poisson reconstruction method to perform surface reconstruction on the point cloud models of the inner and outer myocardial walls, so as to obtain the myocardial surface with the correct topological structure.

[0013] Further, for the myocardial segmentation in Step 1, by analyzing the cardiac cine magnetic resonance image sequence, accurately segment the myocardial substructure and extract the boundary contour lines of the inner and outer myocardial walls. The specific steps are as follows:

[0014] Step 1.1 Use the nnU-Net framework to construct a myocardial segmentation model, select the cross-entropy loss function as the performance evaluation index, and use the Adam optimization algorithm for model training.

[0015] Step 1.2 Input the training data of the cardiac cine magnetic resonance image sequence into the nnU-Net model for model training and optimization.

[0016] Step 1.3 Use the trained model to automatically segment the unsegmented magnetic resonance image to obtain the segmentation result of the myocardial structure.

[0017] Step 1.4 Perform binary processing on the segmentation result for subsequent edge detection.

[0018] Step 1.5 Apply an edge detection algorithm, such as the Sobel operator or the Canny algorithm, to extract the contour lines of the inner and outer myocardial boundaries.

[0019] Furthermore, for the establishment of the point cloud model in Step 2, according to the segmentation result, the boundary contours of the inner and outer myocardial walls are converted into a point cloud model, and the normal vector of each point is calculated. The specific steps are as follows:

[0020] Step 2.1 Convert each point on the extracted inner and outer boundary contours of the myocardium into a point in three-dimensional space;

[0021] Step 2.2 Within the same scan layer, multiply the index value of the edge pixel by the in-layer resolution to obtain the x and y coordinates of the point cloud;

[0022] Step 2.3 Among different scan layers, assume that the z coordinate of the first scanned layer is 0, and the z coordinate of each subsequent layer is shifted down by one scan layer spacing;

[0023] Step 2.4 Assign a coordinate of the point cloud to each pixel on the edge to create an initial point cloud.

[0024] Furthermore, for the determination of the constraint points in Step 3, determine the center point on the inner boundary contour of the myocardium in the last slice of the apex region, and move it along the longitudinal direction of the heart towards the apex by a distance of one slice interval to form a reconstructed constraint point. The specific steps are as follows:

[0025] Calculate the average coordinate of the bottom layer of the myocardial wall point cloud and move it down by one scan interval as the constraint point for the apex during reconstruction. The calculation formula is as follows:

[0026]

[0027] In the above formula (1): The coordinate of the constraint point is (C x , C y , C z ), T , n is the number of edge points, and the coordinate of the i-th (1 ≤ i ≤ n) edge point is (x i , y i , z i ), z pixel is the scan interval between layers of cine magnetic resonance images. The role of the constraint point is to ensure the closure of the apex at the bottom of the myocardium during reconstruction and ensure that the reconstructed surface has the correct topological structure.

[0028] Furthermore, for the surface reconstruction based on point constraints in Step 4, under the constraint of the constraint points calculated in Step 3, use the Poisson reconstruction method to perform surface reconstruction on the point cloud model of the inner and outer myocardial walls, so as to obtain a myocardial surface with the correct topological structure. Specifically, it includes:

[0029] 4.1 Poisson reconstruction of the myocardial surface: The process of Poisson reconstructing the myocardial surface is to input the point cloud data containing normals to obtain the vector field of the myocardium M Assume that all points are located on or near the surface of M. There exists an indicator function

[0030]

[0031] In the above formula (2): p = p(x, y, z) is a point of the myocardial point cloud, and χ M (p) represents whether the point cloud is in the vector field of the myocardium M. Solving the Poisson equation using the gradient field represented by the indicator function includes:

[0032] 4.2 Establish the Poisson equation: The gradient of the indicator function is approximated to the vector field That is, the following formula (3):

[0033]

[0034] Act on both sides of formula (3) with the divergence operator The Poisson equation of the myocardial surface is obtained, as shown in the following formula (4):

[0035]

[0036] where Δ is the Laplace operator is the divergence operator In the operator and respectively represent the first-order partial derivative and the second-order partial derivative of the surface along the x-axis direction, and Similarly, χ is the function to be solved;

[0037] 4.3 Define point constraints: To introduce point constraints, add a constraint term g to the right side of the Poisson equation (4). The constraint term g is the Dirac delta function multiplied by a constant, and this constant constrains the value of the indicator function χ M at the apex point. Denote the coordinates at the apex point as x 0 , and if we want to constrain the value of the indicator function χ M = 1 at this point, then the constraint condition g is expressed as the following formula (5):

[0038] g = k δ(x - x 0 )...(5),

[0039] In the above formula (5): δ is the Dirac delta function, and k is a sufficiently large constant to ensure

[0040] 4.4 Constraint and solution of the Poisson equation: After introducing the apex point constraint, the Poisson equation becomes a partial differential equation with boundary conditions, as shown in the following formula (6):

[0041]

[0042] 4.5 Solve the Poisson equation: obtain the implicit function expression χ. Based on the corner values χ(p) and the isosurface γ of the myocardium M, the isosurface is obtained, and the triangular mesh is output. The triangular mesh is the three-dimensional surface of the myocardium reconstructed under point constraints.

[0043] Compared with the prior art in this technical field, the superior technical effects of the present invention are as follows:

[0044] 1. For the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention, by using vertex constraints on the myocardial surface, the present invention can ensure that the reconstructed surface is both closed and smooth, and can accurately restore the original topological structure of the myocardium;

[0045] 2. For the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention, the reconstruction result does not depend on the distribution of the point cloud in space, so it has universal applicability for different populations and various cases.

[0046] 3. For the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention, the reconstruction has a high tolerance for the sparsity of the point cloud. Using a very small number of vertices can maintain the integrity and correctness of the reconstructed topological structure, with small resource overhead in the reconstruction process and accurate reconstruction results;

[0047] 4. For the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention, the acquisition of the point cloud can be extracted from the results of cardiac magnetic resonance scans, without relying on the information collection of external devices, and the operation is simple. Description of the Drawings

[0048] Figure 1 It is a schematic flow chart of the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention. Detailed Embodiments

[0050] In order to more clearly understand the above objects, features and advantages of the present invention, the technical solution of the present application will be described in detail below in conjunction with the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other. Embodiment

[0051] As Figure 1 shown, the method for three-dimensional reconstruction of the myocardial surface based on point constraints of the present invention includes the following steps:

[0052] Step 1. Perform myocardial segmentation. By analyzing the cine magnetic resonance image sequence of the heart, the myocardial substructure is accurately segmented, and the boundary contour lines of the inner and outer walls of the myocardium are extracted: specifically including:

[0053] Step 1.1: Build a myocardial segmentation model using the nnU-Net framework, select the cross-entropy loss function as the performance evaluation metric, and use the Adam optimization algorithm for model training;

[0054] Step 1.2: Input the training data of the cardiac cine magnetic resonance image sequence into the nnU-Net model for model training and optimization;

[0055] Step 1.3: Use the trained model to automatically segment the unsegmented magnetic resonance images to obtain the segmentation results of the myocardial structure;

[0056] Step 1.4: Perform binary processing on the segmentation results for subsequent edge detection;

[0057] Step 1.5: Apply edge detection algorithms such as the Sobel operator or the Canny algorithm to extract the contour lines of the inner and outer boundaries of the myocardium;

[0058] Step 2. Build a point cloud model. According to the segmentation results, convert the boundary contours of the inner and outer walls of the myocardium into a point cloud model and calculate the normal vector of each point. The specific steps are as follows:

[0059] Step 2.1: Convert each point on the extracted inner and outer boundary contours of the myocardium into a point in three-dimensional space;

[0060] Step 2.2: Within the same scan layer, multiply the index value of the edge pixels by the in-layer resolution to obtain the x and y coordinates of the point cloud;

[0061] Step 2.3: Between different scan layers, assume that the z coordinate of the first scan layer is 0, and the z coordinate of each subsequent layer is shifted down by a scan layer spacing;

[0062] Step 2.4: Assign a point cloud coordinate to each pixel on the edge to create an initial point cloud;

[0063] Step 3. Determine the constraint point. Determine the center point on the inner boundary contour of the myocardium in the last slice of the apex region and move it along the longitudinal direction of the heart towards the apex by a slice interval distance to form a reconstructed constraint point:

[0064] Calculate the average coordinate of the bottom layer of the myocardial wall point cloud and move it down by a scan interval as the constraint point for the apex during reconstruction. The calculation formula is as follows:

[0065]

[0066] In the above formula (1): The coordinates of the constraint point are (C x , C y , C z ) T, where n is the number of edge points, and the coordinates of the i-th (1 ≤ i ≤ n) edge point are (x i , y i , z i ), and z pixel is the inter-slice scanning spacing of cine magnetic resonance images. The role of the constraint points is to ensure the closure of the myocardial base and apex during reconstruction and to ensure that the reconstructed surface has the correct topological structure;

[0067] Step 4. Surface reconstruction based on point constraints. Under the above constraint conditions, the Poisson reconstruction method is used to perform surface reconstruction on the point cloud models of the inner and outer myocardial walls, so as to obtain a myocardial surface with the correct topological structure. The specific steps are as follows:

[0068] 4.1 Poisson reconstruction of the myocardial surface: The process of Poisson reconstructing the myocardial surface is to input the point cloud data containing normals and obtain the vector field of the myocardium M Assume that all points are located on or near the surface of M, and there is an indicator function

[0069]

[0070] In the above formula (2): p = p(x, y, z) is a point in the myocardial point cloud, and χ M (p) represents whether the point cloud is in the vector field of the myocardium M. The gradient field characterized by the indicator function is used to solve the Poisson equation, including:

[0071] 4.2 Establish the Poisson equation: The gradient of the indicator function is approximated to the vector field That is, the following formula (3):

[0072]

[0073] The divergence operator · is applied to both sides of formula (3) to obtain the Poisson equation of the myocardial surface, as shown in the following formula (4):

[0074]

[0075] where Δ is the Laplace operator is the divergence operator In the operator and respectively represent the first-order partial derivative and the second-order partial derivative of the surface along the x-axis direction, and Similarly, χ is the function to be solved;

[0076] 4.3 Definition of point constraint: To introduce the point constraint, a constraint term g is added to the right side of Poisson's equation (4). The constraint term g is the Dirac delta function multiplied by a constant, and this constant constrains the value of the indicator function χ at the apex point. Denote the coordinates of the apex point as x M . 0 If we want to constrain the value of the indicator function χ to be 1 at this point, then the constraint condition g is expressed as the following equation (5): M g = kδ(x - x

[0077] )......(5), 0 In the above equation (5): δ is the Dirac delta function, and k is a sufficiently large constant to ensure

[0078]

[0079] 4.4 Constraint and solution of Poisson's equation: After introducing the apex point constraint, Poisson's equation becomes a partial differential equation with boundary conditions, as shown in the following equation (6):

[0080]

[0081] 4.5 Solve this Poisson's equation: Obtain the implicit function expression χ. Based on the corner values χ(p) and the isosurface γ of the myocardium M, the isosurface is obtained, and the triangular mesh is output. The triangular mesh is the three-dimensional surface of the myocardium reconstructed under the point constraint.

[0082] This invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principle of this invention. Without departing from the spirit and scope of this invention, this invention will have various changes and improvements, and these changes and improvements all fall within the scope of this invention claimed. The scope of protection claimed by this invention is defined by the appended claims.​

Claims

1. A method for three-dimensional reconstruction of myocardial surface with base point constraints, comprising the following steps: Step 1. Perform myocardial segmentation by analyzing cardiac movie magnetic resonance image sequences to accurately segment the myocardial substructures and extract the boundary contours of the inner and outer walls of the myocardium; Step 2. Establish a point cloud model. According to the segmentation results, convert the boundary contours of the inner and outer walls of the myocardium into a point cloud model, and calculate the normal vector of each point. Step 3. Determine the constraint point, determine the center point on the inner boundary contour of the myocardium of the last slice in the apex region, and move it along the longitudinal direction of the heart toward the apex by a distance of a slice interval to form a reconstructed constraint point; Step 4. Surface reconstruction based on point constraints. Under the above constraints, the Poisson reconstruction method is used to reconstruct the point cloud model of the inner and outer walls of the myocardium, thereby obtaining a myocardial surface with a correct topological structure.

2. According to the method for three-dimensional reconstruction of myocardial curved surface with base point constraints as claimed in claim 1, the myocardial segmentation is performed as described in step 1, and the myocardial substructures are accurately segmented by analyzing the cardiac movie magnetic resonance image sequence, and the boundary contour lines of the inner and outer walls of the myocardium are extracted. The specific steps are as follows: Step 1.1 Use the nnU-Net framework to build a myocardial segmentation model, select the cross entropy loss number as the performance evaluation indicator, and use the Adam optimization algorithm for model training; Step 1.2: Input the training data of the cardiac cine MRI sequence into the nnU-Net model to train and optimize the model; Step 1.3: Use the trained model to automatically segment the unsegmented magnetic resonance image to obtain the segmentation result of the myocardial structure; Step 1.4 performs binarization processing on the segmentation results to facilitate subsequent edge detection; Step 1.5: Apply an edge detection algorithm, such as the Sobel operator or the Canny algorithm, to extract the contour lines of the inner and outer boundaries of the myocardium.

3. According to the method for three-dimensional reconstruction of myocardial curved surface with base point constraints as claimed in claim 1, the point cloud model is established in step 2, and according to the segmentation result, the boundary contours of the inner and outer walls of the myocardium are converted into a point cloud model, and the normal vector of each point is calculated, and the specific steps are as follows: Step 2.1 converts each point on the extracted inner and outer boundary contour lines of the myocardium into a point in three-dimensional space; Step 2.2: In the same scanning layer, multiply the index value of the edge pixel by the resolution within the layer to obtain the x and y coordinates of the point cloud; Step 2.3: Between different scanning layers, assuming that the z coordinate of the first layer is 0, the z coordinate of each subsequent layer moves down by one scanning layer spacing; Step 2.4 assigns a point cloud coordinate to each pixel on the edge, thereby creating an initial point cloud.

4. According to the method for three-dimensional reconstruction of myocardial curved surface with base point constraints as claimed in claim 1, the step of determining the constraint point in step 3 is to determine the center point on the inner boundary contour of the myocardium of the last slice in the apex region, and move it along the longitudinal direction of the heart toward the apex by a distance of a slice interval to form a reconstructed constraint point, and the specific steps are as follows: Calculate the average coordinates of the bottom layer of the myocardial wall point cloud and move it down by one scanning interval as the constraint point of the apex during reconstruction. The calculation formula is as follows: In the above formula (1), the coordinates of the constraint point are (C x ,C y ,C z ) T , n is the number of edge points, the coordinates of the i-th (1≤i≤n) edge point are (x i ,y i ,z i ), z pixel is the inter-slice scanning distance of the cine MRI image. The function of the constraint point is to ensure the closure of the apex at the bottom of the myocardium during reconstruction and to ensure that the reconstructed surface has the correct topological structure.

5. According to the method for three-dimensional reconstruction of myocardial curved surface with base point constraints as claimed in claim 1, the curved surface reconstruction based on point constraints in step 4, under the constraint of the constraint points calculated in step 3, uses the Poisson reconstruction method to reconstruct the point cloud model of the inner and outer walls of the myocardium, thereby obtaining a myocardial curved surface with a correct topological structure, specifically comprising: 4.1 Poisson reconstruction of myocardial surface: The process of Poisson reconstruction of myocardial surface is to input point cloud data containing normal lines and obtain the vector field of myocardium M. Assume that all points are on or near the surface of M, and there exists an indicator function In the above formula (2), p = p(x, y, z) is a point in the myocardial point cloud, χ M (p) Indicate whether the point cloud is within the vector field of the myocardium M, and use the gradient field represented by the indicator function to solve the Poisson equation, including: 4.2 Establishing the Poisson equation: Gradient of the indicator function Approximation to a vector field That is, the following formula (3): The divergence operator acting on both sides of equation (3) is The Poisson equation of the myocardial surface is obtained as follows (4): Where Δ is the Laplace operator is the divergence operator In the operator and They represent the first-order partial derivative and the second-order partial derivative of the surface along the x-axis, respectively. and Similarly, χ is the function to be solved; 4.3 Definition of point constraint: To introduce the point constraint, a constraint term g is added to the right side of Poisson equation (4). The constraint term g is the Dirac delta function multiplied by a constant. The constant constrains the indicator function χ at the apex point. M The value of the indicator function is x0, and the coordinate of the apex point is x0. M =1, then the constraint condition g is expressed as the following formula (5): g=kδ(x-x0)......(5), In the above formula (5), δ is the Dirac delta function, and k is a constant large enough to ensure 4.4 Constraints and solutions of the Poisson equation: After the apex constraint is introduced, the Poisson equation becomes a partial differential equation with boundary conditions, as shown in equation (6): 4.5 Solve the Poisson equation: obtain the implicit function expression χ, based on the corner point value χ(p) and the isovalue γ of the myocardium M, obtain the isosurface, and output the triangular mesh. The triangular mesh is the three-dimensional surface of the myocardium reconstructed under point constraints.

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