CN111369662A - Method and system for reconstructing 3D model of blood vessels in CT images - Google Patents

Abstract

The invention discloses a three-dimensional model reconstruction method and system of blood vessels in CT images. The three-dimensional model reconstruction method includes: establishing an image segmentation model based on a neural network; the image segmentation model is used to segment blood vessels in CT images, and output a two-dimensional segmentation map of the blood vessels; Input to the image segmentation model to obtain a plurality of two-dimensional segmentation maps; perform three-dimensional reconstruction on the two-dimensional segmentation maps. The image segmentation model constructed by the invention can quickly and accurately segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels, thereby accurately constructing a three-dimensional model of the blood vessels.

Description

Method and system for reconstructing 3D model of blood vessels in CT images

technical field

The invention relates to the technical field of medical imaging, in particular to a method and system for reconstructing a three-dimensional model of blood vessels on CT (Computer Tomography) pictures.

Background technique

The current CT technology has enabled 2D (planar graphics) visualization of the diseased area in the human body. However, it is difficult to imagine the three-dimensional structure of the diseased tissue from the 2D CT image. The construction of three-dimensional CAD (computer-aided design) model can help doctors to make more accurate judgments on the disease.

For the three-dimensional reconstruction of CT images in the prior art, the method of artificial marking is often adopted: the CT images are artificially marked by personnel with certain professional experience, and further segmentation processing is performed with relevant software. The obvious drawback of this method lies in the additional manual labeling cost, manual labeling time and errors that may be caused by the labor itself. The latter two points may cause delay in medical diagnosis and affect the accuracy of medical diagnosis, thereby delaying further diagnosis and treatment of patients, resulting in more serious consequences.

In recent years, the technology of automatic image segmentation based on pixel contrast difference has developed rapidly, but it is suitable for images with obvious color and contrast differences between the segmented object and other surrounding objects. For blurry CT images, the segmented objects (such as blood vessels) may be blurred, so the method based on poor pixel contrast will be very poor, and even segment multiple unwanted objects.

It can be seen that, using the prior art automatic image segmentation technology to segment CT images with relatively blurred segmentation objects has very low accuracy and cannot meet the quality requirements for subsequent three-dimensional model reconstruction.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method and system for reconstructing a three-dimensional model of a blood vessel in a CT image, in order to overcome the defect of the prior art automatic image segmentation technology for segmenting a CT image with a relatively blurred segmentation object, and the accuracy is very low. .

The present invention solves the above-mentioned technical problems through the following technical solutions:

A method for reconstructing a three-dimensional model of a blood vessel in a CT image, the three-dimensional model reconstruction method comprising:

An image segmentation model is established based on a neural network; the image segmentation model is used to segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels;

Input the CT image to be modeled into the image segmentation model to obtain multiple two-dimensional segmentation maps;

A three-dimensional reconstruction is performed on the two-dimensional segmentation map.

Preferably, the step of establishing an image segmentation model based on a neural network specifically includes:

Obtain the identified CT images as training samples;

The training samples are input into a neural network model, and the neural network model is trained according to the loss function of the neural network model to obtain the image segmentation model.

Preferably, the loss function is:

SI=∑ _i,j M _predict (i,j)×M _true (i,j);

Sum(M _predict )=∑ _i,j |M _predict (i,j)|;

Sum(M _true )=∑ _i,j |M _true (i,j)|;

Wherein, L represents the loss function; M _true (i, j) represents the pixel value at the position (i, j) in the two-dimensional segmentation map of the training sample; M _predict (i, j) represents the output of the neural network model The pixel value at (i,j) position in the 2D segmentation map; η represents the smoothing parameter.

Preferably, the step of performing 3D reconstruction on the 2D segmentation map specifically includes:

Converting the two-dimensional segmentation map into a three-dimensional image in a three-dimensional binary Analyze format;

Performing 3D image reconstruction on the 3D image in the Analyze format based on the Propulsion Cube algorithm;

The reconstructed 3D images are fitted based on NURBS.

Preferably, before the step of fitting the reconstructed three-dimensional image, the method further includes:

Smoothing is performed on the reconstructed three-dimensional image.

A three-dimensional model reconstruction system of blood vessels in CT images, the three-dimensional model reconstruction system includes:

a modeling module for establishing an image segmentation model based on a neural network; the image segmentation model is used to segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels;

The three-dimensional reconstruction module is used to input the CT image to be modeled into the image segmentation model, obtain a plurality of two-dimensional segmentation maps, and perform three-dimensional reconstruction on the two-dimensional segmentation maps.

Preferably, the modeling module specifically includes:

a data acquisition unit for acquiring the identified CT images as training samples;

A model training unit, configured to input the training samples into a neural network model, and train the neural network model according to the loss function of the neural network model to obtain the image segmentation model.

Preferably, the loss function is:

SI=∑ _i,j M _predict (i,j)×M _true (i,j);

Sum(M _predict )=∑ _i,j |M _predict (i,j)|;

Sum(M _true )=∑ _i,j |M _true (i,j)|;

Wherein, L represents the loss function; M _true (i, j) represents the pixel value at the position (i, j) in the two-dimensional segmentation map of the training sample; M _predict (i, j) represents the output of the neural network model The pixel value at (i,j) position in the 2D segmentation map; η represents the smoothing parameter.

Preferably, the three-dimensional reconstruction module specifically includes:

A format conversion unit, for converting the two-dimensional segmentation map into a three-dimensional image of a three-dimensional binary Analyze format;

a three-dimensional reconstruction unit, configured to perform three-dimensional image reconstruction on the three-dimensional image in the Analyze format based on the advancing cube algorithm;

The fitting unit is used to fit the reconstructed 3D image based on NURBS.

Preferably, the three-dimensional reconstruction module further includes:

The smoothing processing unit is used for calling the fitting unit after smoothing the reconstructed three-dimensional image.

The positive improvement effect of the present invention is that the image segmentation model constructed by the present invention can quickly and accurately segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels, thereby accurately constructing a three-dimensional model of the blood vessels.

Description of drawings

FIG. 1 is a first flowchart of a method for reconstructing a three-dimensional model of a blood vessel in a CT image according to Embodiment 1 of the present invention.

FIG. 2 is a second flowchart of a method for reconstructing a three-dimensional model of a blood vessel in a CT image according to Embodiment 1 of the present invention.

FIG. 3 is a schematic block diagram of a system for reconstructing a three-dimensional model of a blood vessel in a CT image according to Embodiment 2 of the present invention.

Detailed ways

The present invention is further described below by way of examples, but the present invention is not limited to the scope of the described examples.

Example 1

This embodiment provides a method for reconstructing a three-dimensional model of a blood vessel in a CT image. As shown in FIG. 1 , the method for reconstructing a three-dimensional model includes the following steps:

Step 101 , establishing an image segmentation model based on a neural network.

Among them, the image segmentation model is used to segment the CT image, and output a two-dimensional segmentation map of the blood vessels in the CT image. In this embodiment, a fully convolutional neural network is used as the basic structure for automatic blood vessel segmentation for CT images.

Referring to Figure 2, the following describes the establishment process of the image segmentation model:

Step 101-1: Acquire an identified CT image as a training sample.

In step 101-1, a large number of relevant high-precision artificially labeled CT images are obtained, some of which are used as training samples of the neural network model for the training of the neural network model; some are used as test samples for testing after each iteration training. The accuracy of the neural network model.

Step 101-2: Input the training samples into the neural network model, train the neural network model according to the loss function of the neural network model, and obtain an image segmentation model.

In this embodiment, for the specific situation of blood vessel segmentation, a dedicated convolutional neural network loss function is designed, and the loss function L can be but is not limited to:

SI=∑ _i,j M _predict (i,j)×M _true (i,j);

Sum(M _predict )=∑ _i,j |M _predict (i,j)|;

Sum(M _true )=∑ _i,j |M _true (i,j)|;

Among them, M _true represents the real segmentation map (two-dimensional segmentation map) data of the CT image of the training sample, and the real segmentation map is obtained by the trained labeler marking the original CT image with the corresponding labeling software; M _predict represents the model training The predicted segmentation map (two-dimensional segmentation map) data output by the neural network model in the process; M _true (i, j) represents the pixel value at the position of (i, j) in the real segmentation map; M _predict (i, j) represents in the The pixel value at position (i, j) in the predicted segmentation map; SI represents the segmentation intersection of the real segmentation map and the predicted segmentation map; η represents the smoothing parameter.

It should be noted that η can be set by itself according to actual requirements. In this embodiment, the "smoothing parameter" is set to 1 for consideration of numerical calculation. For the neural network model, the architecture of the training model can be selected according to the actual needs (such as CT pictures of different cases, accuracy, etc.), and the corresponding model parameters are also different.

Taking a training sample (2D CT image, the size is W×L, W represents the width of the CT image, and T represents the length of the CT image) as an example, the segmented area (that is, the area where the blood vessel is located) in the “real segmentation map” is Pixels are white, and pixels outside the segmented area are black. Denote the "true segmentation map" as a matrix M _true ∈ R ^W×L , then M _true (i,j)=1 represents the pixels of the segmented area in the true segmentation map, that is, the white pixels; M _true (i, j)=0 represents the pixels outside the segmented area in the real segmentation map, that is, the black pixels. Similarly, the "predicted segmentation map" output by the neural network model is represented as M _predict ∈R ^W×L , then M _predict (i,j)=1 indicates the pixels of the segmented area in the predicted segmentation map, that is, the white pixels point; M _true (i, j)=0 indicates that the pixel points outside the segmentation area in the prediction segmentation map, that is, the black pixel points.

During the model training process in step 101-2, the structure in the convolutional neural network is adjusted with reference to the accuracy observed during the entire training and testing process (the accuracy of the model is calculated according to the identified test samples). The iteration stops when the function converges to a local optimum and satisfactory performance is observed on the test data, thereby improving the training accuracy.

Step 102: Input the CT image to be modeled into the image segmentation model to obtain a two-dimensional segmentation map of multiple blood vessels.

Step 103: Perform three-dimensional reconstruction on the two-dimensional segmentation map.

In this embodiment, step 103 specifically includes:

Step 103-1: Convert each two-dimensional segmentation map into a three-dimensional image in a three-dimensional binary Analyze format (a medical image format).

Specifically, ITK (an image analysis extension software tool) is used to convert each two-dimensional segmentation map into a three-dimensional image in a three-dimensional binary Analyze format.

Among them, the generated 3D image contains a plurality of divided areas that are not connected to each other. ITK is used to calculate the connected area with the largest volume and remove the other pixels that are not connected to the largest segmented area, that is, to remove the isolated pixels in the image. Pixels, only the part of the image to be reconstructed with 3D geometry is retained, which is a 3D image.

Step 103-2, performing three-dimensional image reconstruction on the three-dimensional image in the Analyze format based on the Marching Cubes algorithm.

In this embodiment, the advancing cube algorithm is mainly divided into two parts:

The first part is to use a divide-and-conquer method to select the surface position of the segmented object in the image. Each cube determines how the object's surface intersects it and moves to the next cube position. The vertices of each cube are assigned 1 and 0 respectively depending on whether they are inside or outside the split object. A cube has 6 vertices, and different assignment combinations to the 6 vertices represent different secant states of the object surface and the cube. Excluding the symmetry, there are a total of 14 different secant modes. For each secant method, the algorithm determines which edge intersects the surface by interpolating the pixel values of the vertices.

The second part of the advancing cube algorithm is to calculate the unit normal vector of the triangle formed by the object and the cube. The normal vector can be used to determine the inside and outside of the surface. In order to determine the normal vector of the triangle, the algorithm interpolates the gradient vector of the vertices of the cube. The gradient vector of each vertex is obtained by the central difference method:

Among them, D(i,j,k) represents the pixel value at the position (i,j,k) in the 3D image. Δx, Δy, and Δz represent the side lengths of the cube, respectively. G _x (i, j, k), G _y (i, j, k) and G _z (i, j, k) represent the gradient values in the x, y and z directions at the vertex, respectively. The algorithm obtains the gradient vector of the intersection point by interpolating the two vertices of the intersecting edge to the edge, and finally obtains the surface of the entire segmented object by advancing the cube in the whole field of the image, and obtains the node coordinate information of the three-dimensional grid.

Step 103-3, smoothing the reconstructed three-dimensional image.

In this embodiment, in order to make the surface of the generated segmentation object smoother or to reduce the change of the large curvature of the surface, in this embodiment, two consecutive Gaussian smoothing steps are used to realize the smoothing processing algorithm.

In the Gaussian smoothing process, the positions of the vertices of the triangular elements of each 3D mesh are recalculated by the vertices of its neighboring triangular elements. The coordinate vector V _m of a vertex is the vertex coordinate vector V _n of the adjacent triangle elements, which refers to all the triangle element vertices that are on the same side as V _m or on the same triangle element, and does not include the vertex V _m . If the vertices of the triangular elements adjacent to V _m are defined as S _m ={V _n :n=1,2,3,...,p}, where p is the total number of adjacent vertices, an average vector ΔV _m is calculated as:

1≤o≤p；顶点V_m的坐标被更新为：where w _mo is a trade-off parameter whose value is set as

1≤o≤p; the coordinates of vertex V _m are updated as:

V _m ′=V _m +λΔV _m ;

Among them, the value of the extension parameter λ is in the range of 0 to 1.

In this embodiment, the first step of the Gaussian smoothing process adopts a positive extension parameter λ. The second step of Gaussian smoothing uses a negative spread parameter μ. And the two parameters satisfy the relation 0<λ<-μ<1. Assuming that the vertex coordinates obtained by the first Gaussian smoothing process are V _m ′, the second Gaussian smoothing process is:

V _m ″=V _m ′+μΔV _m ′;

Among them, ΔV _m ′ is the average vector obtained based on the coordinates of the new vertexes after the first smoothing process, and V _m ″ is the new vertex of the second smoothing process obtained based on the coordinates of the new vertexes after the first smoothing process Coordinates. By continuing to apply the above continuous two-step Gaussian smoothing process to the surface after smoothing, the obtained surface can be sufficiently smooth.

Step 103-4: Fitting the smoothed three-dimensional image based on NURBS.

The process of image fitting is further described below:

(1) Main direction analysis of point cloud in three-dimensional space

For the convenience of expression, the 3D point cloud set V _m ″ of the smoothed 3D image is redefined as point cloud X{X ₁ ,X ₂ ,...,X _r }∈R ³ , and defined at the beginning of NURBS CAD 3D reconstruction The first three principal directions obtained by PCA (Principal Component Analysis) decomposition are the point cloud coordinate system E{E ₁ , E ₂ , E ₃ }. The solution process is briefly described as follows:

其中

对伴随矩阵进行特征值分解，即求解∑E＝λE。取E的前3个特征向量为点云初始坐标系E{E₁,E₂,E₃}。build adjoint matrix

in

Perform eigenvalue decomposition on the adjoint matrix, that is, solve ∑E=λE. Take the first three eigenvectors of E as the point cloud initial coordinate system E{E ₁ , E ₂ , E ₃ }.

(2) Rigid body rotation of point cloud in three-dimensional space

其中

H可认为是一个奇异值矩阵。则其可被分解为H＝U∑V^T。通过分解相似伴随阵H，转动矩阵R可由UV^T求得。刚体位移t则可通过

求得。于是，转动点云x{x₁,x₂,…,x_r}∈R³为x＝RX+t。Due to the different shooting conditions of the reconstructed point cloud of blood vessels, the spatial orientation and position are uncertain when starting the 3D reconstruction of NURBS CAD. In order to ensure that the surfaces have the same coordinate system when entering the surface reconstruction stage, the point cloud rigid body must be rotated to a unified global coordinate system. The method adopted in this embodiment is SVD (Singular-valuedecomposition). Assuming that the global coordinate system is e{e ₁ ,e ₂ ,e ₃ }, the similar adjoint matrix is constructed as follows:

in

H can be thought of as a singular value matrix. Then it can be decomposed into H=UΣV ^T . By decomposing the similar adjoint matrix H, the rotation matrix R can be obtained by UV ^T. The rigid body displacement t can be obtained by

beg. Therefore, the rotation point cloud x{x ₁ ,x ₂ ,...,x _r }∈R ³ is x=RX+t.

(3) NURBS curve fitting of 2D point cloud

This patent adopts the fitting of layered NURBS surfaces. Each stratum was fitted as a circular NURBS curve. The curve equation is:

Among them, P _i is the control point coordinate vector, and ω _i and ω _j are their corresponding weight values. The basis function N is obtained by the following recursive function:

Among them, u={u ₀ ,..., _um } is the node vector, which is a set of non-negative, uniform and monotonically increasing node vectors arbitrarily selected; p is the curve order, and the value of p can be set according to actual needs. , for example, p=2 in this embodiment. The fitted curve for each layer uses the same set of nodal vectors. By constructing the least squares equation system N ^t NP=N ^t X, the control point P _i can be obtained by solving.

(4) Constructing NURBS surface by tensor product

Since each curve of each layer uses the same node vector, for the same node, a new set of node directions v={v ₀ ,..., _vm } can be established along the layer number direction. NURBS surfaces are calculated by multiplying NURBS curves in two directions by tensors. Its surface equation is:

P_i,j为在新构建v方向，第j层，第i个控制点的值；n，m分别为u和v方向的曲线阶数。n，m的数值可根据实际需求自行设置，例如本实施例中n＝2，m＝2。in,

P _i,j is the value of the i-th control point at the j-th layer in the newly constructed v direction; n, m are the curve orders in the u and v directions, respectively. The values of n and m can be set according to actual requirements. For example, in this embodiment, n=2, m=2.

In this embodiment, the constructed image segmentation model can quickly and accurately segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels, thereby realizing the accurate construction of a three-dimensional model of the blood vessels.

Example 2

As shown in FIG. 3 , the system for reconstructing a three-dimensional model of a blood vessel in a CT image in this embodiment includes: a modeling module 1 and a three-dimensional reconstruction module 2 .

The modeling module 1 is used to establish an image segmentation model based on a neural network. The image segmentation model is used to segment the blood vessels in the CT image, and outputs a two-dimensional segmentation map of the blood vessels in the CT image. In this embodiment, a fully convolutional neural network is used as the basic structure for automatic blood vessel segmentation for CT images.

In this embodiment, the modeling module 1 specifically includes: a data acquisition unit 11 and a model training unit 12 .

The data acquisition unit 11 is used for acquiring the identified CT images as training samples. Specifically, the data acquisition unit 11 acquires a large number of relevant high-precision artificially labeled CT images, some of which are used as training samples of the neural network model for training the neural network model; and some are used as test samples for testing each iteration of training accuracy of the neural network model.

The model training unit 12 is configured to input the training samples into the neural network model, and train the neural network model according to the loss function of the neural network model to obtain an image segmentation model.

In the process of model training, the model training unit 12 adjusts the structure in the convolutional neural network with reference to the accuracy observed during the entire training and testing process (calculating the accuracy of the model according to the identified test samples), and when the loss of The iteration stops when the function converges to a local optimum and satisfactory performance is observed on the test data, thereby improving the training accuracy.

In this embodiment, for the specific situation of blood vessel segmentation, a dedicated convolutional neural network loss function is designed, and the loss function L can be but is not limited to:

SI=∑ _i,j M _predict (i,j)×M _true (i,j);

Sum(M _predict )=∑ _i,j |M _predict (i,j)|;

Sum(M _true )=∑ _i,j |M _true (i,j)|;

Among them, M _true represents the real segmentation map (two-dimensional segmentation map) data of the CT image of the training sample, and the real segmentation map is obtained by the trained labeler marking the original CT image with the corresponding labeling software; M _predict represents the model training The predicted segmentation map (two-dimensional segmentation map) data output by the neural network model in the process; M _true (i, j) represents the pixel value at the position of (i, j) in the real segmentation map; M _predict (i, j) represents in the The pixel value at position (i, j) in the predicted segmentation map; SI represents the segmentation intersection of the real segmentation map and the predicted segmentation map; η represents the smoothing parameter.

It should be noted that η can be set by itself according to actual requirements. In this embodiment, the "smoothing parameter" is set to 1 for consideration of numerical calculation. For the neural network model, the architecture of the training model can be selected according to the actual needs (such as CT pictures of different cases, accuracy, etc.), and the corresponding model parameters are also different.

Taking a training sample (2D CT image, the size is W×L, W represents the width of the CT image, and T represents the length of the CT image) as an example, the segmented area (that is, the area where the blood vessel is located) in the “real segmentation map” is Pixels are white, and pixels outside the segmented area are black. Denote the "true segmentation map" as a matrix M _true ∈ R ^W×L , then M _true (i,j)=1 represents the pixels of the segmented area in the true segmentation map, that is, the white pixels; M _true (i, j)=0 represents the pixels outside the segmented area in the real segmentation map, that is, the black pixels. Similarly, the "predicted segmentation map" output by the neural network model is represented as M _predict ∈R ^W×L , then M _predict (i,j)=1 indicates the pixels of the segmented area in the predicted segmentation map, that is, the white pixels point; M _true (i, j)=0 indicates that the pixel points outside the segmentation area in the prediction segmentation map, that is, the black pixel points.

The three-dimensional reconstruction module 2 is used to input the CT image to be modeled into the image segmentation model, obtain a plurality of two-dimensional segmentation maps, and perform three-dimensional reconstruction on the two-dimensional segmentation maps.

In this embodiment, the three-dimensional reconstruction module 2 specifically includes: a format conversion unit 21 , a three-dimensional reconstruction unit 22 , a smoothing processing unit 23 and a fitting unit 24 .

The format conversion unit 21 is configured to convert the two-dimensional segmentation map into a three-dimensional image in a three-dimensional binary Analyze format, and output it to the three-dimensional reconstruction unit 22 . Specifically, the format conversion unit 21 uses ITK (an image analysis extension software tool) to convert each two-dimensional segmentation map into a three-dimensional image in a three-dimensional binary Analyze format.

Among them, the generated 3D image contains a plurality of divided areas that are not connected to each other. ITK is used to calculate the connected area with the largest volume and remove the other pixels that are not connected to the largest segmented area, that is, to remove the isolated pixels in the image. Pixels, only the part of the image to be reconstructed with 3D geometry is retained, which is a 3D image.

The three-dimensional reconstruction unit 22 is configured to perform three-dimensional image reconstruction on the three-dimensional image in the Analyze format based on the advancing cube algorithm, and output the three-dimensional image to the smoothing processing unit 23 .

In this embodiment, the advancing cube algorithm is mainly divided into two parts:

The first part is to use a divide-and-conquer method to select the surface position of the segmented object in the image. Each cube determines how the object's surface intersects it and moves to the next cube position. The vertices of each cube are assigned 1 and 0 respectively depending on whether they are inside or outside the split object. A cube has 6 vertices, and different assignment combinations to the 6 vertices represent different secant states of the object surface and the cube. Excluding the symmetry, there are a total of 14 different secant modes. For each secant method, the algorithm determines which edge intersects the surface by interpolating the pixel values of the vertices.

The second part of the advancing cube algorithm is to calculate the unit normal vector of the triangle formed by the object and the cube. The normal vector can be used to determine the inside and outside of the surface. In order to determine the normal vector of the triangle, the algorithm interpolates the gradient vector of the vertices of the cube. The gradient vector of each vertex is obtained by the central difference method:

Among them, D(i,j,k) represents the pixel value at the position (i,j,k) in the 3D image. Δx, Δy, and Δz represent the side lengths of the cube, respectively. G _x (i, j, k), G _y (i, j, k) and G _z (i, j, k) represent the gradient values in the x, y and z directions at the vertex, respectively. The algorithm obtains the gradient vector of the intersection point by interpolating the two vertices of the intersecting edge to the edge, and finally obtains the surface of the entire segmented object by advancing the cube in the whole field of the image, and obtains the node coordinate information of the three-dimensional grid.

The smoothing processing unit 23 is used to call the fitting unit 24 after smoothing the reconstructed three-dimensional image.

In this embodiment, in order to make the surface of the generated segmentation object smoother or to reduce the change of the large curvature of the surface, in this embodiment, two consecutive Gaussian smoothing steps are used to realize the smoothing processing algorithm.

In the Gaussian smoothing process, the positions of the vertices of the triangular elements of each 3D mesh are recalculated by the vertices of its neighboring triangular elements. The coordinate vector V _m of a vertex is the vertex coordinate vector V _n of the adjacent triangle elements, which refers to all the triangle element vertices that are on the same side as V _m or on the same triangle element, and does not include the vertex V _m . If the vertices of the triangular elements adjacent to V _m are defined as S _m ={V _n :n=1,2,3,...,p}, where p is the total number of adjacent vertices, an average vector ΔV _m is calculated as:

ΔV _m =∑ _Vo∈sm w _mo (V _o -V _m );

1≤o≤p；顶点V_m的坐标被更新为：where w _mo is a trade-off parameter whose value is set as

1≤o≤p; the coordinates of vertex V _m are updated as:

V _m ′=V _m +λΔV _m ;

Among them, the value of the extension parameter λ is in the range of 0 to 1.

In this embodiment, the first step of the Gaussian smoothing process adopts a positive extension parameter λ. The second step of Gaussian smoothing uses a negative spread parameter μ. And the two parameters satisfy the relation 0<λ<-μ<1. Assuming that the vertex coordinates obtained by the first Gaussian smoothing process are V _m ′, the second Gaussian smoothing process is:

V _m ″=V _m ′+μΔV _m ′;

Among them, ΔV _m ′ is the average vector obtained based on the coordinates of the new vertexes after the first smoothing process, and V _m ″ is the new vertex of the second smoothing process obtained based on the coordinates of the new vertexes after the first smoothing process Coordinates. By continuing to apply the above continuous two-step Gaussian smoothing process to the surface after smoothing, the obtained surface can be sufficiently smooth.

The fitting unit 24 is used for fitting the reconstructed three-dimensional image based on NURBS.

The working principle of the image fitting performed by the fitting unit 24 is further described below:

(1) Main direction analysis of point cloud in three-dimensional space

For the convenience of expression, the 3D point cloud set V _m ″ of the smoothed 3D image is redefined as point cloud X{X ₁ ,X ₂ ,...,X _r }∈R ³ , and defined at the beginning of NURBS CAD 3D reconstruction The first three principal directions obtained by PCA (Principal Component Analysis) decomposition are the point cloud coordinate system E{E ₁ , E ₂ , E ₃ }. The solution process is briefly described as follows:

其中

对伴随矩阵进行特征值分解，即求解∑E＝λE。取E的前3个特征向量为点云初始坐标系E{E₁,E₂,E₃}。build adjoint matrix

in

Perform eigenvalue decomposition on the adjoint matrix, that is, solve ∑E=λE. Take the first three eigenvectors of E as the point cloud initial coordinate system E{E ₁ , E ₂ , E ₃ }.

(2) Rigid body rotation of point cloud in three-dimensional space

其中

H可认为是一个奇异值矩阵。则其可被分解为H＝U∑V^T。通过分解相似伴随阵H，转动矩阵R可由UV^T求得。刚体位移t则可通过

求得。于是，转动点云x{x₁,x₂,…,x_r}∈R³为x＝RX+t。Due to the different shooting conditions of the reconstructed point cloud of blood vessels, the spatial orientation and position are uncertain when starting the 3D reconstruction of NURBS CAD. In order to ensure that the surfaces have the same coordinate system when entering the surface reconstruction stage, the point cloud rigid body must be rotated to a unified global coordinate system. The method adopted in this embodiment is SVD (Singular-valuedecomposition). Assuming that the global coordinate system is e{e ₁ ,e ₂ ,e ₃ }, the similar adjoint matrix is constructed as follows:

in

H can be thought of as a singular value matrix. Then it can be decomposed into H=UΣV ^T . By decomposing the similar adjoint matrix H, the rotation matrix R can be obtained by UV ^T. The rigid body displacement t can be obtained by

beg. Therefore, the rotation point cloud x{x ₁ ,x ₂ ,...,x _r }∈R ³ is x=RX+t.

(3) NURBS curve fitting of 2D point cloud

This patent adopts the fitting of layered NURBS surfaces. Each stratum was fitted as a circular NURBS curve. The curve equation is:

Among them, P _i is the control point coordinate vector, and ω _i and ω _j are their corresponding weight values. The basis function N is obtained by the following recursive function:

Among them, u={u ₀ ,..., _um } is the node vector, which is a set of non-negative, uniform and monotonically increasing node vectors arbitrarily selected; p is the curve order, and the value of p can be set according to actual needs. , for example, p=2 in this embodiment. The fitted curve for each layer uses the same set of nodal vectors. By constructing the least squares equation system N ^t NP=N ^t X, the control point P _i can be obtained by solving.

(4) Constructing NURBS surface by tensor product

Since each curve of each layer uses the same node vector, for the same node, a new set of node directions v={v ₀ ,..., _vm } can be established along the layer number direction. NURBS surfaces are calculated by multiplying NURBS curves in two directions by tensors. Its surface equation is:

P_i,j为在新构建v方向，第j层，第i个控制点的值；n，m分别为u和v方向的曲线阶数。n，m的数值可根据实际需求自行设置，例如本实施例中n＝2，m＝2。in,

P _i,j is the value of the i-th control point at the j-th layer in the newly constructed v direction; n, m are the curve orders in the u and v directions, respectively. The values of n and m can be set according to actual requirements. For example, in this embodiment, n=2, m=2.

In this embodiment, the constructed image segmentation model can quickly and accurately segment the blood vessels in the CT image, and output a two-dimensional segmentation map of the blood vessels, thereby realizing the accurate construction of a three-dimensional model of the blood vessels.

Although the specific embodiments of the present invention are described above, those skilled in the art should understand that this is only an illustration, and the protection scope of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principle and essence of the present invention, but these changes and modifications all fall within the protection scope of the present invention.

Claims (10)

1. A three-dimensional model reconstruction method of a blood vessel in a CT image, the three-dimensional model reconstruction method comprising:

establishing an image segmentation model based on a neural network; the image segmentation model is used for segmenting blood vessels in the CT image and outputting a two-dimensional segmentation map of the blood vessels;

inputting a CT image to be modeled into the image segmentation model to obtain a plurality of two-dimensional segmentation maps;

and performing three-dimensional reconstruction on the two-dimensional segmentation map.

2. The method for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 1, wherein the step of establishing the image segmentation model based on the neural network specifically comprises:

acquiring the identified CT image as a training sample;

and inputting the training sample into a neural network model, and training the neural network model according to a loss function of the neural network model to obtain the image segmentation model.

3. The method of reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 2, wherein the loss function is:

SI＝∑_i,jM_predict(i,j)×M_true(i,j)；

Sum(M_predict)＝∑_i,j|M_predict(i,j)|；

Sum(M_true)＝∑_i,j|M_true(i,j)|；

wherein L represents the loss function; m_true(i, j) represents the pixel value of the (i, j) location in the two-dimensional segmentation map of the training sample; m_predict(i, j) represents the pixel value of the (i, j) position in the two-dimensional segmentation map output by the neural network model, and η represents the smoothing parameter.

4. The method for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 1, wherein the step of reconstructing the two-dimensional segmentation map in three dimensions specifically comprises:

converting the two-dimensional segmentation graph into a three-dimensional image in an Analyze format of a three-dimensional binary system;

carrying out three-dimensional image reconstruction on the three-dimensional image in the Analyze format based on a marching cube algorithm;

fitting the reconstructed three-dimensional image based on NURBS.

5. The method of reconstructing a three-dimensional model of a blood vessel in a CT image as set forth in claim 4, wherein the step of fitting the reconstructed three-dimensional image is preceded by the steps of:

and smoothing the reconstructed three-dimensional image.

6. A three-dimensional model reconstruction system for a blood vessel in a CT image, the three-dimensional model reconstruction system comprising:

the modeling module is used for establishing an image segmentation model based on a neural network; the image segmentation model is used for segmenting blood vessels in the CT image and outputting a two-dimensional segmentation map of the blood vessels;

and the three-dimensional reconstruction module is used for inputting the CT image to be modeled into the image segmentation model to obtain a plurality of two-dimensional segmentation maps and performing three-dimensional reconstruction on the two-dimensional segmentation maps.

7. The system for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 6, wherein the modeling module comprises:

the data acquisition unit is used for acquiring the identified CT image as a training sample;

and the model training unit is used for inputting the training samples into a neural network model, and training the neural network model according to the loss function of the neural network model to obtain the image segmentation model.

8. The system for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 7, wherein the loss function is:

SI＝∑_i,jM_predict(i,j)×M_true(i,j)；

Sum(M_predict)＝∑_i,j|M_predict(i,j)|；

Sum(M_true)＝∑_i,j|M_true(i,j)|；

wherein L represents the loss function; m_true(i, j) represents a two-dimensional segmentation of the training samplesPixel value at the (i, j) position in the figure; m_predict(i, j) represents the pixel value of the (i, j) position in the two-dimensional segmentation map output by the neural network model, and η represents the smoothing parameter.

9. The system for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 6, wherein the three-dimensional reconstruction module comprises:

the format conversion unit is used for converting the two-dimensional segmentation graph into a three-dimensional image in an Analyze format of a three-dimensional binary system;

the three-dimensional reconstruction unit is used for reconstructing a three-dimensional image in the Analyze format based on a marching cube algorithm;

and the fitting unit is used for fitting the reconstructed three-dimensional image based on NURBS.

10. The system for reconstructing a three-dimensional model of a blood vessel in a CT image according to claim 9, wherein the three-dimensional reconstruction module further comprises:

and the smoothing unit is used for calling the fitting unit after smoothing the reconstructed three-dimensional image.

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