Spectral embedding approximation and feature extraction method for three-dimensional jaw-face volume images

Abstract

The application discloses a spectrum embedding approximation and feature extraction method of a three-dimensional jaw face body image, establishes a spectrum embedding approximation and feature extraction network of the three-dimensional jaw face body image for dense corresponding features of the three-dimensional jaw face medical image, reduces the spectrum embedding calculation cost in the spectrum corresponding process of the body image, and automatically extracts the body image features of the body image corresponding task. The method can effectively calculate the spectrum embedding of the body image hyper-voxel graph, can reduce the time cost of the spectrum embedding calculation and extract the body image features specific to the corresponding task, extracts the body image features suitable for the corresponding task and calculates the body image hyper-voxel correspondence; the spectrum mapping-based image correspondence can avoid the interference caused by the patient posture and the tissue structure change, the spectrum embedding base function of the internal structure of the body image can improve the semantic correspondence of the body image, the three-dimensional jaw face medical body image correspondence is quickly established, and the image correspondence can be used for further image attribute migration.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of medical image processing and computer vision, in particular to a spectral embedding approximation and feature extraction method for three-dimensional jaw-face volume images. BACKGROUND

[0002] Volume image registration and dense correspondence are important problems in the field of medical image processing. Based on voxel dense correspondence or volume image deformation field, automatic image attribute transfer can be performed, which can avoid the cost and error of manual annotation. Most existing methods achieve image registration by measuring alignment in the spatial domain, which is easily affected by patient posture or structural changes and falls into local extremum. Spectral space function correspondence method can be used to calculate the voxel dense correspondence of volume images. Using graph Laplacian spectral basis function, the high-dimensional image voxel correspondence can be converted into low-dimensional spectral function correspondence, reducing the computational cost of volume image correspondence. Spectral space function correspondence method calculates image correspondence by aligning image features in spectral space. Manually designed volume image features are not specific to image correspondence tasks, and it is difficult to obtain the best image correspondence when applied to spectral space function correspondence method. Learning-based methods usually require manually annotated paired landmark points to assist in learning image features specific to volume image correspondence tasks. Unsupervised feature extraction methods for volume image correspondence tasks still have challenges. Spectral space function correspondence method calculates image correspondence in the spectral space spanned by graph Laplacian eigenvectors. The computational cost of spectral embedding increases with the expansion of the graph size, limiting the application of spectral space function correspondence method to large-scale graphs.

[0003] In recent years, learning-based methods have been applied in graph embedding and representation learning. For example, spectral graph convolution network using Chebyshev polynomial approximation does not need to perform eigenvalue decomposition, but this spectral graph convolution cannot guarantee to obtain orthogonal graph embedding, making it difficult to be directly applied to spectral basis function calculation of spectral space function correspondence algorithm. Existing technologies lack unsupervised volume image feature learning and efficient graph embedding approximation methods specific to volume image correspondence tasks. SUMMARY

[0004] In order to overcome the deficiencies of the above-mentioned prior art, the present application provides a spectral embedding approximation and feature extraction method for three-dimensional jaw-face volume images, which can reduce the time cost of spectral embedding calculation and extract volume image features specific to the correspondence task. Image correspondence based on spectral mapping can avoid the interference caused by patient posture and tissue structure changes, and the spectral embedding basis function of the internal structure of the volume image can improve the semantic correspondence of the volume image.

[0005] The core of the present application is that the present application provides a spectral embedding approximation and feature extraction method of a three-dimensional jaw face body image. For the dense correspondence problem of a three-dimensional jaw face medical image, the present application establishes a spectral embedding approximation and feature extraction network of a three-dimensional jaw face body image, which can reduce the spectral embedding calculation cost in the spectral correspondence process of the body image and automatically extract the body image features suitable for the body image correspondence task. The spectral embedding approximation and feature extraction network of the three-dimensional jaw face body image designs a multi-path spectral embedding module based on GCN, which can approximate the multi-band spectral basis function of the body image hyper voxel graph, and enhances the orthogonality of the spectral basis function using orthogonal constraints. The network converts the correspondence between the hyper voxels of the body image into the correspondence between the spectral space basis functions, aligns the image features in the spectral space to obtain the image spectral correspondence, and restores the body image spatial domain correspondence. Unlike the manually designed body image features, the spectral space body image correspondence network (i.e. the spectral embedding approximation and feature extraction network of the three-dimensional jaw face body image) proposed by the present application can automatically extract the body image features suitable for the body image correspondence task, and calculate the body image correspondence using the spectral embedding of the body image hyper voxel graph, thereby enhancing the semantic correspondence of the body image. The network optimizes the network parameters by aligning the body image probe function in the spectral space and constraining the orthogonality of the spectral correspondence. In the online test stage, the spectral embedding approximation and feature extraction network of the three-dimensional jaw face body image proposed by the present application can effectively calculate the spectral embedding of the body image hyper voxel graph, extract the body image features suitable for the correspondence task, and calculate the body image hyper voxel correspondence.

[0006] The parameters in the present application are defined as follows:

[0007] X and Y: cone beam CT images;

[0008] Hyper voxel graph, including hyper voxel set and edge set;

[0009] n X And n Y : the number of hyper voxels of X and Y;

[0010] L: hyper voxel graph Laplacian matrix;

[0011] K: spectral space dimension, number of spectral space orthogonal basis functions;

[0012] Z: body image hyper voxel graph spectral embedding, spectral basis function;

[0013] Q: hyper voxel feature dimension extracted by the network;

[0014] Body image hyper voxel feature output by the network;

[0015] Spectral space expression of hyper voxel feature, spectral space orthogonal basis function coefficient;

[0016] C: spectral correspondence of hyper voxel;

[0017] C * : optimal C;

[0018] P: permutation matrix of super voxel;

[0019] loss function;

[0020] F p : volume image probe function;

[0021] γ1 and γ2: weight coefficients in the loss function;

[0022] The three-dimensional jaw-facial volume image spectrum embedding approximation and feature extraction method provided by the application comprises the following steps:

[0023] 1) Calculate the super voxel map of the three-dimensional jaw-facial volume image:

[0024] The SLIC (Simple Linear Iterative Clustering) algorithm is applied to super voxel decomposition of the three-dimensional jaw-facial volume image to obtain a super voxel map comprising super voxels and super voxel adjacency relationships, and a super voxel map Laplacian matrix is calculated. Specifically, the simple linear iterative clustering SLIC algorithm recorded in document 1 (Achanta, R., Shaji, A., Smith, K., Lucchi, A., Fua, P., Süssstrunk, S.: Slic superpixels compared to state-of-the-art superpixel methods. IEEE Trans. PAMI 34, 2274-2282 (2012)) is used.

[0025] 2) Build and train a three-dimensional jaw-facial volume image spectrum embedding approximation and feature extraction network;

[0026] The three-dimensional jaw-facial volume image spectrum embedding approximation and feature extraction network comprises a spectrum embedding module and a volume image feature extraction module. The volume image feature extraction module uses a three-dimensional U-shaped convolutional network 3D U-net to extract multi-scale features of the image. The spectrum embedding module builds a multi-path spectrum embedding network based on a GCN (graph convolutional networks) to extract multi-band spectrum basis functions of the super voxel map. The volume image super voxel features extracted by the network are projected into a spectrum space using the spectrum basis functions, and the spectral space expression of the super voxel features is aligned to obtain the spectrum correspondence between the volume images. The spectrum correspondence of the volume images can restore the spatial domain correspondence of the volume images.

[0027] Specifically, document 2 (Wang, Y., Liu, Y., Liu, Y., Wang, Z., Zuo, W., Zhang, Z., Wang, X.: Deep metric learning with image-set validation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5400-5409 (2017)) is used. 3D U-net described in document 1 (Abdulkadir, A., Lienkamp, S.S., Brox, T., Ronneberger, O.: 3d u-net: learning dense volumetric segmentation from sparse annotation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 424-432 (2016)); and GCN described in document 3 (Kipf, T., Welling, M.: Semi-supervised classification with graph convolutional networks. ArXiv abs / 1609.02907 (2017)).

[0028] The spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial body image spectrum restricts the orthogonality of the spectral embedding, and restricts the spectral embedding approximation to the eigenvector of the hyper-voxel graph Laplacian matrix. The training data includes synthetic cone beam CT images and real cone beam CT images. During the training process, the difference between the hyper-voxel output by the network and the true value is calculated for the synthetic data set, and the loss function is calculated by aligning the body image probe function for the real data set. The training of this network does not require manual labeling and matrix eigenvalue decomposition.

[0029] 3) Online test of the three-dimensional maxillofacial body image spectral embedding approximation and feature extraction network.

[0030] The three-dimensional maxillofacial body image to be processed and its hyper-voxel are segmented (or decomposed), and are input into the three-dimensional maxillofacial body image spectral embedding approximation and feature extraction network. The network outputs the spectral embedding of the body image hyper-voxel graph, the hyper-voxel feature, and the hyper-voxel correspondence between the body images.

[0031] The beneficial effects of the present application are:

[0032] The three-dimensional maxillofacial body image spectral embedding approximation and feature extraction method provided by the present application can effectively calculate the body image hyper-voxel graph spectral embedding, extract the body image features suitable for the corresponding task, and calculate the body image hyper-voxel correspondence. The technical solution provided by the present application can quickly establish the correspondence of the three-dimensional maxillofacial medical body image. The image correspondence can be used for further image attribute transfer. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a flowchart of the method of the present application. DETAILED DESCRIPTION

[0034] The present application will be further described by examples in connection with the accompanying drawings, but the scope of the present application is not limited in any way.

[0035] The present application establishes a spectral embedding approximation and feature extraction network of three-dimensional jaw-facial medical volume images, effectively calculates the spectral embedding of volume image super voxel, extracts volume image features suitable for corresponding tasks, and outputs volume image super voxel correspondence. According to the super voxel correspondence between volume images, further image attribute migration can be carried out to obtain automatic volume image attribute labeling based on image attribute migration.

[0036] The present application will be further described by examples in connection with the accompanying drawings, but the scope of the present application is not limited in any way. 3 The actual size of the voxel is 1.5 3 mm 3 .As shown in the flow, the specific implementation steps of the spectral embedding approximation and feature extraction of the three-dimensional jaw-facial medical volume image are as follows: Figure 1

[0037] Step one: for cone beam CT image, calculate super voxel decomposition and super voxel graph Laplace matrix

[0038] For cone beam CT images X and Y, use SLIC algorithm for super voxel decomposition, respectively get n X and n Y super voxels, for the cone beam CT image with a size of 128 3 , it can be decomposed into 15000 super voxels, get super voxel graph and and are the super voxel sets of images X and Y respectively, ε X and ε Y are the super voxel graph edge sets of images X and Y respectively. According to the super voxel graph, calculate the super voxel graph Laplace matrix L X and L Y of cone beam CT images X and Y.

[0039] Step two: establish and train the spectral embedding approximation and feature extraction network of three-dimensional jaw-facial medical volume images

[0040] 21) Volume image feature extraction module

[0041] The spectral embedding approximation and feature extraction network of three-dimensional jaw-facial medical volume images is based on 3D U-net to build volume image feature extraction module, 3D U-net and two linear layers together realize the volume image super voxel feature extraction function F s =h θ ​(X), where θ is the spectral embedding approximation and feature extraction network parameters of the three-dimensional jaw-facial volume image. The network has a hierarchical encoder-decoder, which is able to extract multi-scale volume image features. The decoder is able to extract five different resolution volume image features, which are 256x8 3 , 128x16 3 , 64x32 3 , 32x64 3 , 4x128 3 , the above volume image features are resampled and concatenated to form the volume image feature with feature channel number q = 484. The super voxel feature of the volume image is defined as the mean of the voxel features inside the super voxel, the l-th dimensional feature of the super voxel s is denoted as F s,l , which is calculated as equation (1):

[0042]

[0043] where F l is the l-th dimensional volume image feature, δ s is the delta function of the super voxel s, which is 1 at voxels inside the super voxel s and 0 at other voxels. The volume image super voxel features output by the volume image feature extraction module will be used in the corresponding computation of the volume image.

[0044] 22) Volume image spectral embedding approximation module

[0045] To avoid the computational cost of spectral embedding based on eigenvalue decomposition of graph Laplacian matrix, a multi-path spectral embedding approximation module based on GCN is proposed in this method. The Laplacian matrix of the super voxel graph of the volume image is defined as L = D - A, where A is the symmetric similarity matrix and D is the diagonal degree matrix. The convolution of GCN is defined as:

[0046] Z (l+1) = σ(D -1 / 2 AD -1 / 2 Z (l) W (l) ) (2)

[0047] where Z (l) denotes the input of the l-th layer convolution, Z (0) = F s is the volume image feature output by the feature extraction module. W (l) is the learnable parameter of this layer convolution. Z (l+1) denotes the output of the l-th layer convolution, which contains the approximate spectral embedding that is able to minimize tr(Z T LZ). To ensure the orthogonality of the approximate spectral embedding, the loss function contains the measurement of the orthogonality of the spectral embedding, and the loss function of the spectral embedding module is defined as:

[0048]

[0049] where I k is the identity matrix. The first term of the loss function can enhance the orthogonality of the spectral embedding. The second term is used to guarantee that Z T approximates the eigenvectors of the Laplacian matrix L. α is a hyper-parameter to balance the two constraints. The spectral embedding approximation module uses a three-path GCN network to approximate the spectral basis functions Z1, Z2 and Z3 of different frequency bands. With the increase of network layers, it can approximate the spectral basis functions of lower frequency of the super-voxel graph Laplacian matrix. Connecting the three spectral basis functions corresponding to different frequency bands can obtain the low-dimensional spectral embedding of the super-voxel graph, which can be used as the spectral space basis function of the volume image.

[0050] 23) Based on the spectral space corresponding to the volume image corresponding

[0051] Based on the super-voxel features of the volume images X and Y obtained in step 21) and and the spectral embedding Z obtained in step 22) X and Z Y The low-dimensional spectral correspondence C can be calculated k is the dimension of the spectral basis function. Since k << min(m X ,m Y ), the calculation cost of the spectral correspondence is less than that of directly calculating the super-voxel spatial correspondence between the two volume images. By using the spectral basis function, the super-voxel feature of the volume image can be mapped to the spectral space to obtain the spectral space expression of the super-voxel feature and satisfying and The spectral correspondence C should be aligned with the spectral space expression of the super-voxel feature and that is

[0052]

[0053] The optimal spectral correspondence C can be obtained by using linear least squares * .

[0054] In the training process, synthetic cone beam CT image datasets and real cone beam CT image datasets are used to train the spectral embedding approximation and feature extraction network of three-dimensional maxillofacial medical volume images. The synthetic cone beam CT image data is obtained by random non-rigid image deformation, and has the voxel correspondence ground truth between images. The real cone beam CT image data has not been artificially labeled. For synthetic data, the difference between the network output super-voxel correspondence and the ground truth is constrained. For real data, the spectral correspondence output by the network is aligned with the volume image probe function F pThe probe function is a set of pre-computed functions defined on the super voxel, including the super voxel gray scale distribution histogram, the apparent difference between the super voxel and the context super voxel, and the spatial difference. The super voxel context is a certain number of super voxels randomly extracted around the super voxel, the apparent difference between the super voxels is defined as the chi-square distance of the gray scale distribution histogram, and the spatial difference is defined as the Euclidean distance of the center of the super voxel. The image correspondence loss function of the network is defined as:

[0055]

[0056] where P is the super voxel displacement matrix between the volume images, which can be obtained by spectral correspondence, that is, , represents the pseudo-inverse of the matrix. Orthogonal constraints are used to enhance the orthogonality of spectral correspondence and spatial correspondence:

[0057]

[0058] The loss function of the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical volume image is:

[0059]

[0060] where γ1 and γ2 are used to adjust the weights of the image correspondence loss function, the spectral embedding loss function and the regularization term, and the optimal three-dimensional maxillofacial volume image feature extraction and spectral embedding approximation network parameters can be obtained by minimizing the loss function

[0061] Step three: online test of the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical volume image

[0062] The cone beam CT image V i and V j to be processed are decomposed into super voxels, and the image and super voxel decomposition label are input into the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical volume image, and the network outputs the super voxel displacement matrix P of the two cone beam CT images, P contains the probability of the corresponding relationship between the super voxels of the two cone beam CT images. Based on the cone beam CT image super voxel, further image attribute transfer can be carried out.

[0063] In order to verify the effect of the spectral embedding approximation and feature extraction method of the three-dimensional maxillofacial medical volume image, experiments were carried out on the clinically collected maxillofacial cone beam CT images, the structure segmentation label transfer based on the super voxel correspondence between the cone beam CT images was tested, and the transfer of the maxillary bone, mandibular bone, zygomatic bone, frontal bone, temporal bone, sphenoid bone and occipital bone segmentation labels was tested respectively. The DICE similarity coefficient between the mandibular bone segmentation label transfer result and the true value reaches 0.9, the DICE similarity coefficient between the maxillary bone and temporal bone segmentation label transfer result and the true value reaches 0.85, and the segmentation label annotation accuracy is good. ​

[0064] The method of the present application can quickly obtain the spectral embedding and super voxel features of the three-dimensional jaw face body image, and calculate the super voxel correspondence between the body images. The spectral embedding module can reduce the computational cost and save the calculation time compared with the spectral embedding method using eigenvalue decomposition. Compared with the manually designed body image features, the feature extraction module can obtain the body image features more suitable for the correspondence problem. The training process of the method does not require manual annotation.

[0065] The above embodiments are only used to illustrate the present application, but not to limit the present application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application. Therefore, all equivalent technical solutions belong to the scope of the present application, and the patent protection scope of the present application should be defined by the claims.

Claims

1. A spectral embedding approximation and feature extraction method for three-dimensional maxillofacial images, characterized by: For the dense correspondence problem of three-dimensional maxillofacial medical images, a spectral embedding approximation and feature extraction network for three-dimensional maxillofacial images is established to reduce the spectral embedding calculation cost in the spectral correspondence process of the volume image and automatically extract the volume image features of the volume image correspondence task; comprising the following steps: 1) Calculate the super voxel map of the three-dimensional maxillofacial volume image: Using the simple linear iterative clustering algorithm SLIC, the super voxel decomposition of the three-dimensional maxillofacial volume image is carried out to obtain the super voxel map including super voxels and super voxel adjacency relationship, and the super voxel map Laplacian matrix is calculated; 2) Build and train the three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network; The three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network includes a spectral embedding module and a volume image feature extraction module; wherein the volume image feature extraction module uses 3D U-net to extract multi-scale features of the image; the spectral embedding module builds a multi-path spectral embedding network based on GCN to extract multi-band spectral basis functions of the super voxel map; the spectral embedding module constrains the orthogonality of spectral embedding and calculates the approximation degree of spectral embedding to the characteristic vector of the super voxel map Laplacian matrix; The three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network automatically extracts the volume image features of the volume image correspondence task, and uses the volume image super voxel map spectral embedding to calculate the volume image correspondence, and enhances the semantic correspondence of the volume image; The volume image super voxel features extracted by the three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network are projected into the spectral space using the spectral basis function, the spectral correspondence between the volume images is obtained by aligning the spectral space expression of the super voxel features, and the volume image spatial correspondence is restored based on the spectral correspondence of the volume image; Specifically, the correspondence between the volume image super voxels is converted into the correspondence between the spectral space basis functions, the image spectral correspondence is obtained by aligning the image features in the spectral space, and the volume image spatial correspondence is restored; The three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network optimizes the network parameters by aligning the volume image probe function in the spectral space and constraining the orthogonality of the spectral correspondence; the training data of the three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network includes synthetic cone beam CT images and real cone beam CT images; During training, the difference between the super voxel correspondence calculated by the network output and the true value is calculated for the synthetic data set, and the loss function is calculated by aligning the volume image probe function for the real data set; Training the three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network does not require manual annotation and matrix eigenvalue decomposition; 3) Online test of the three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network to realize the spectral embedding approximation and feature extraction of the three-dimensional maxillofacial volume image; including: Super voxel decomposition of the three-dimensional maxillofacial volume image to be processed; The three-dimensional maxillofacial volume image to be processed and its super voxels are respectively input into the trained three-dimensional maxillofacial volume image spectral embedding approximation and feature extraction network; The spectral embedding of the network output body image super voxel graph, the super voxel feature and the super voxel correspondence between the body image are extracted, the body image feature corresponding to the task is extracted, and the spectral embedding approximation and feature extraction of the three-dimensional maxillofacial body image are realized.

2. The method of spectral embedding approximation and feature extraction of three-dimensional dento-maxillofacial images according to claim 1, characterized in that, The spectral embedding module of the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial body image is a multi-path spectral embedding module, which is used to approximate the multi-band spectral basis function of the body image super voxel graph, and the orthogonality of the spectral basis function is enhanced by using orthogonal constraint.

3. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 1, characterized in that, In step 1), for the cone beam CT image, the super voxel decomposition and the super voxel graph Laplace matrix are calculated, specifically including: For cone beam CT images X and Y, superpixel decomposition is performed using the SLIC algorithm to obtain n X and n Y superpixels, respectively, to obtain superpixel maps and and are the superpixel sets of images X and Y, respectively, and ε X and ε Y are the superpixel map edge sets of images X and Y, respectively. According to the super voxel map, a super voxel map Laplacian matrix L of the cone beam CT image X and Y is calculated X and L Y .

4. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 3, characterized in that, A cone beam CT image of size 128 3 was decomposed into 15000 super voxels.

5. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 1, characterized in that, In step 2), in the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical body image, the body image feature extraction module is built based on 3D U-net, including: By using 3D U-net with two linear layers to realize the body image super voxel feature extraction function F s = h θ (X), where θ is the network parameter; The three-dimensional maxillofacial body image spectral embedding approximation and feature extraction network has a hierarchical encoder-decoder for extracting multi-scale body image features; Resampling and concatenating multi-scale volumetric image features to form volumetric image features q is the number of feature channels; The super voxel feature of the volume image is defined as the mean value of the voxel features inside the super voxel, and the lth dimensional feature F of the super voxel s is calculated by formula (1) s,l : where F l is the l-dimensional volume image feature, δ s is the delta function of super voxel s, which is 1 at voxels inside super voxel s and 0 elsewhere. The body image super voxel feature output by the body image feature extraction module is used for body image correspondence calculation.

6. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 5, characterized in that, The decoder is used to extract five different resolution volumetric image features, 256x8 3 , 128x16 3 , 64x32 3 , 32x64 3 , 4x128 3 , respectively. The volumetric image features are resampled and concatenated to form a volumetric image feature with q=484 channels.

7. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 5, characterized in that, In the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical body image, the spectral embedding module is a multi-path body image spectral embedding approximation module based on GCN, which is used to avoid the calculation cost caused by the spectral embedding based on the eigenvalue decomposition of the graph Laplace matrix; including: The Laplace matrix of the super voxel graph of the body image is defined as L=D-A, where A is a symmetric similarity matrix and D is a diagonal degree matrix; the convolution of GCN is defined as formula (2): Z (l+1) = σ(D -1 / 2 AD -1 / 2 Z (l) W (l) ) Equation (2) where Z (l) represents the input of the l-th layer convolution, Z (0) = F s is the volumetric image feature output by the feature extraction module; W (l) is the learnable parameter of the layer convolution; Z (l+1) represents the output of the l-th layer convolution, which contains an approximate spectral embedding that can minimize tr(Z T LZ). The loss function of the spectral embedding module contains the measurement of the orthogonality of the spectral embedding, which is used to ensure the orthogonality of the approximate spectral embedding; the loss function of the spectral embedding module is defined as: where I k is the identity matrix; the first term of the loss function is used to enhance the orthogonality of the spectral embedding; the second term is used to ensure that Z T LT is approximated as a diagonal matrix, so that the spectral embedding Z approximates the eigenvectors of the Laplacian matrix L; alpha is a hyperparameter used to balance the two constraints; the spectral embedding approximation module uses a three-way GCN network to approximate the spectral basis functions Z1, Z2 and Z3 of different frequency bands, and with the increase of the network layers, it approximates the spectral basis functions of lower frequencies of the super-voxel graph Laplacian matrix; connecting the three spectral basis functions corresponding to different frequency bands, a low-dimensional spectral embedding of the super-voxel graph is obtained, which can be used as a spectral space basis function of the body image.

8. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 7, characterized in that, The body image correspondence based on spectral space correspondence is carried out, including: based on the obtained hyperspectral features of the volume images X and Y and and the obtained spectral embedding Z X and Z Y , computing a low-dimensional spectral correspondence k is the dimension of the spectral basis functions; k « min(m X , m Y The computational cost of the spectral correspondence is less than that of directly computing the hyperspectral spatial correspondence between the two volume images. The body image super voxel features are mapped into a spectral space by using spectral basis functions to obtain spectral space expressions of the super voxel features and satisfy and spectrum corresponding to the spectral space expression of the C-aligned super voxel features and is expressed as formula (3): The optimal spectral correspondence C is obtained by solving the linear least squares problem * .

9. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 8, characterized in that, Using synthetic cone beam ct image data sets and real cone beam ct image data sets a spectral embedding approximation and feature extraction network for three-dimensional maxillofacial medical volume images is jointly trained; during the training process: The synthesized cone beam CT image data is obtained by random non-rigid image deformation, and has voxel correspondence truth value between images; the real cone beam CT image data does not need to be manually labeled; for the synthesized data, the difference between the super voxel correspondence output by the network and the true value is constrained; for the real data, the spectral correspondence output by the network is aligned with the body image probe function Fp; The probe function is a set of functions defined on the super voxel, including the super voxel gray level distribution histogram, the apparent difference between the super voxel and the context super voxel and the spatial difference; The context super voxel is a super voxel randomly extracted around the super voxel, the apparent difference between the super voxels is defined as the chi-square distance of the gray level distribution histogram, and the spatial difference is defined as the Euclidean distance of the super voxel center; The image correspondence loss function of the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical body image is defined as formula (4): where P is the super voxel permutation matrix between the body images, which can be obtained by spectral correspondence, i.e. denotes the pseudo-inverse of matrix; the orthogonal constraint is used to enhance the orthogonality of spectral correspondence and spatial correspondence, which is denoted as equation (5): The loss function of the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical body image is represented as formula (6): where γ1 and γ2 are used to adjust the weights of the image correspondence loss function, the spectral embedding loss function and the regularization term, by minimizing the loss function obtain optimal three-dimensional jaw facial body image feature extraction and spectral embedding approximation network parameters.

10. The method for spectral embedding approximation and feature extraction of three-dimensional maxillofacial images as claimed in claim 1, characterized in that, Step 3) performing spectral embedding approximation and online testing of a feature extraction network of the three-dimensional maxillofacial medical volume image, and inputting the cone beam CT image V i and V j performing hyper voxel decomposition, inputting the image and hyper voxel decomposition label into the spectral embedding approximation and feature extraction network of the three-dimensional maxillofacial medical volume image, and outputting a hyper voxel replacement matrix P of the two cone beam CT images by the network; P contains the probability that there is a corresponding relationship between the hyper voxels of the two cone beam CT images; further image attribute migration can be performed based on the hyper voxels of the cone beam CT image.

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