# US 12,602,788 B2 · Method and system for fully automatically segmenting cerebral cortex surface based on graph network

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- Number: US 12,602,788 B2
- Document ID: US12602788B2
- Status: Granted
- Kind: B2
- Application number: 18/279,316
- Filed: 2022-12-29
- Published: 2025-03-06
- Granted: 2026-04-14
- Earliest claimed: 2022-07-27
- Assignees: Shandong University
- Applicants: Shandong University
- Inventors: Ying Wei; Xinyu Liu; Zhi Liu; Yankun Cao
- Web page: https://patentgrep.com/patent/US12602788B2

## CPC

- G06T 7/10: Segmentation; Edge detection (motion-based segmentation G06T7/215)
- G06T 7/11: Region-based segmentation
- G06T 7/344: {involving models}
- G06T 17/20: Finite element generation, e.g. wire-frame surface description, {tesselation}
- G06T 19/20: Editing of three-dimensional [3D] images, e.g. changing shapes or colours, aligning objects or positioning parts
- G06T 2207/10088: Magnetic resonance imaging [MRI]
- G06T 2207/20081: Training; Learning
- G06T 2207/20084: Artificial neural networks [ANN]
- G06T 2207/30016: Brain
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

A method and a system for fully automatically segmenting a cerebral cortex surface based on a graph network, the method including: registering a cerebral magnetic resonance image to a standard template space; performing cerebral cortex surface reconstruction on the registered cerebral magnetic resonance image based on a deep neural network; calculating adjacency matrices among the vertexes of the reconstructed cerebral cortex; acquiring corresponding distinguishing features of each grid vertex of the cerebral cortex surface as corresponding feature vectors of the point so as to obtain a cerebral cortex surface segmentation result; and mapping the cerebral cortex surface segmentation result back to the original coordinate space from the standard template space. Graph structure modeling is performed on the reconstructed cerebral cortex surface, and the global topological structure features are learned based on the graph network, thus realizing the accurate segmentation of the cerebral cortex surface.

## Claims

### Claim 1

A method for fully automatically segmenting a cerebral cortex surface based on a graph network, comprising:
registering a cerebral magnetic resonance image to a standard template space;
performing cerebral cortex surface reconstruction on the registered cerebral magnetic resonance image based on a deep neural network, and acquiring triangular patch grid representations of the cerebral cortex surface;
performing a 4× down-sampling on cerebral cortex surface grid data;
calculating adjacency matrices in a corresponding convolution process of the graph network;
calculating feature description vectors of vertexes of the cerebral cortex surface, and generating corresponding feature matrices of all vertexes of the cerebral cortex surface;
inputting the adjacency matrices and the feature matrices to a trained graph network model to obtain a cerebral cortex surface segmentation result; and
performing post-processing and space mapping on the segmentation result to complete the segmentation of the cerebral cortex surface, wherein
the calculating adjacency matrices in a corresponding convolution process of the graph network comprises:
calculating a Euclidean distance and a geodesic distance among the cerebral cortex vertexes according to a connection relationship among the cerebral cortex surface grid vertexes after down-sampling and corresponding Euclidean space coordinates of the vertexes, and acquiring corresponding adjacency matrices of three convolution layers in the graph network according to a weight calculation formula and by virtue of three Gaussian kernels initialized by pre-training parameters, and
specifically, the calculating 3 adjacency matrices among the cerebral cortex vertexes for the corresponding convolution process of the graph network according to the connection relationship among the vertexes and the geodesic distance comprises: calculating a Euclidean distance d and a geodesic distance ρ among the cerebral cortex vertexes according to the connection relationship among the down-sampled cerebral cortex surface grid vertexes and corresponding Euclidean space coordinates of the vertexes; acquiring the corresponding adjacency matrices Ā1, Ā2, Ā3 of the three convolution layers in the graph network according to a weight calculation formula and by virtue of the three Gaussian kernels initialized by pre-training parameters; and giving coordinates of two vertexes, shown as:
vi=(xi, yi, zi) and vj=(xj, yj, zj), the calculation formula of the Euclidean distance di,j being:
d
i
,
j
=

v
i
-
v
j

2
2
=
(
x
i
-
x
j
)
2
+
(
y
i
-
y
j
)
2
+
(
z
i
-
z
j
)
2
2
,
wherein the geodesic distance ρ is calculated by using a classical Dijkstra algorithm; a relationship vector between any two vertexes vi and vj is ui,j=(di,j,ρi,j)T, i≠j; and the calculation of adjacency weight coefficients of two non-overlapped vertexes is generated by inputting the relationship vectors into the Gaussian kernel functions, and the specific calculation formula is as follows:
w
i
,
j
=
exp
⁡
(
-
1
2
⁢
(
u
-
u
_
i
,
j
)
T
⁢
(
σ
¯
d
2
σ
¯
ρ
2
)
-
1
⁢
(
u
-
u
_
i
,
j
)
)
and i≠j, an adjacency coefficient between any two vertexes is shown as:
a
i
,
j
=
a
j
,
i
=
{
w
i
,
j
i
≠
j
1
i
=
j
;
the adjacency matrix à can be shown as:
A
_
=
(
1
a
1
,
2
…
a
1
,
N
a
2
,
1
1
…
a
2
,
N
⋮
⋮
⋱
⋮
a
N
,
1
a
N
,
2
…
1
)
;
and the cerebral cortex surface formed by points and edges is shown as G=(V, E), V representing a set of all the vertexes, and E representing a set corresponding to all the edges; (xi, yi, zi) represents position coordinates of the edge v; in a three-dimensional template space; and the obtained adjacency matrices are square matrices having a dimension of N*N, N representing the number of the vertexes of the cortex surface.

### Claim 2 (depends on 1)

The method for fully automatically segmenting a cerebral cortex surface based on a graph network according to claim 1, wherein the registering a cerebral magnetic resonance image to a standard template space specifically comprises:
specifying the standard template space to be registered, and performing affine and nonlinear registration through an image registration open source library.

### Claim 3 (depends on 1)

The method for fully automatically segmenting a cerebral cortex surface based on a graph network according to claim 1, wherein the performing cerebral cortex surface reconstruction on the inputted registered cerebral magnetic resonance image based on a deep neural network, and acquiring triangular patch grid representations of the cerebral cortex surface comprises:
inputting a registered MRI cerebral image for the adopted network structure, and predicting implicit surface representations of the inner and outer surfaces of the cerebral cortex;
then eliminating topological deformation caused by singular points by means of topological correction to a sphere; and
finally, acquiring the triangular patch grid structure data of the reconstructed cerebral cortex surface by a contour surface grid extraction algorithm.

### Claim 4 (depends on 1)

The method for fully automatically segmenting a cerebral cortex surface based on a graph network according to claim 1, wherein the calculating feature description vectors of vertexes of the cerebral cortex surface, and generating corresponding feature matrices of all vertexes of the cerebral cortex surface comprises: calculating an average curvature, a groove depth, a shape index, a curvature and maximum and minimum main curvatures of the cerebral cortex surface; fusing the geometric quantities for describing cortex wrinkle information and Euclidean space position coordinate information to serve as description feature vectors of the vertexes; and combining the corresponding feature vectors of all the vertexes to form cerebral cortex surface feature matrices.

### Claim 5 (depends on 1)

The method for fully automatically segmenting a cerebral cortex surface based on a graph network according to claim 1, wherein in the step of inputting the adjacency matrices and the feature matrices to a trained graph network model to obtain a cerebral cortex surface segmentation result, a neighborhood combination mode and a message propagation rule f of the graph network are as follows:
H
i
+
1
=
f
⁡
(
H
i
,
A
¯
i
)
=
σ
⁡
(
A
¯
i
⁢
H
i
⁢
W
i
)
;
O
=
softmax
⁢
(
A
¯
3
⁢
H
3
⁢
W
3
)
;
wherein, Hi represents the weight matrix of an ith layer, a nonlinear activation function o is a Relu function, and i=1, 2; the graph convolution network comprises three convolution layers and a softmax layer; the first layer of input comprises a feature matrix X=H1 and an adjacency matrix Ā1, Ā representing an adjacency matrix added with self-loop and normalization operation; the output is a category matrix O of the vertex, and the matrix has the size of N×C, C representing a number of categories in vertex prediction; and Wi is a hidden layer learnable parameter of the graph convolution; and
the step includes: determining categories of all vertexes in the template space according to the output category matrix O so as to complete the segmentation of the cerebral cortex surface in the template space.

### Claim 6 (depends on 1)

The method for fully automatically segmenting a cerebral cortex surface based on a graph network according to claim 1, wherein the performing post-processing and space mapping on the segmentation result to complete the segmentation of the cerebral cortex surface comprises: applying a spatial consistency to the cerebral cortex surface segmentation result based on a graph segmentation algorithm, and correcting a possible prediction error of a single singular point; and
performing up-sampling on the corrected segmentation result, and mapping the segmentation of the cerebral cortex surface back to an original coordinate space from the standard template space to complete the segmentation of the cerebral cortex surface.

### Claim 7 (depends on 1)

A computer apparatus, comprising a memory, a processor, and a computer program stored on the memory and runnable on the processor, wherein the processor executes the steps of the method according to claim 1 when executing the program.

### Claim 8 (depends on 1)

A non-transitory computer-readable storage medium with a computer program stored thereon, wherein the program executes the steps of the method according to claim 1 when being executed by the processor.