A medical image interactive segmentation method using Gaussian process classification

Abstract

The application provides a medical image interactive segmentation method applying Gaussian process classification, and the method comprises the following steps: (1) introducing a to-be-segmented image into a feature extraction network to perform pixel depth feature extraction; (2) a user performs interaction on the to-be-segmented image to obtain user labeling information; (3) a Gaussian process model on a pixel classification function is constructed, and a prediction distribution of a pixel classification function value of an unmarked pixel is obtained according to the extracted pixel depth feature and the user labeling information; (4) a prediction label of the unmarked pixel is obtained according to the prediction distribution of the pixel classification function value of the unmarked pixel, and an image segmentation result is generated; (5) the user judges the image segmentation result, confirms whether the segmentation result meets the requirements, if the segmentation result does not meet the requirements, steps (2)-(5) are repeated until the segmentation result meets the requirements, and the segmentation result is output.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of medical image segmentation, and particularly relates to a medical image interactive segmentation method applying Gaussian process classification. BACKGROUND

[0002] The medical image interactive segmentation task is an important research direction in the field of medical image processing. Through the use of user interaction information, accurate segmentation of the structure of interest or lesion area in the medical image is realized. This interactive method provides users with higher control ability, thereby effectively improving the accuracy and reliability of segmentation. With the improvement of computer hardware performance and the continuous improvement of deep learning algorithms, the development of medical image interactive segmentation methods has made new breakthroughs, providing more valuable information and support for medical diagnosis and treatment.

[0003] In recent years, deep learning-based methods have achieved remarkable success in the medical image interactive segmentation task. In 2019, Tomas Sakinis et al. proposed a medical image interactive segmentation structure based on a fully convolutional neural network, which achieved relatively good performance in existing medical image interactive segmentation methods. Such deep learning-based medical image interactive segmentation method structures usually encode user interaction as a click map, and then input the click map and the input image into a deep neural network to extract deep features for subsequent segmentation. However, when processing interactive tasks, such methods usually perform pixel-by-pixel classification to segment the image, lacking specific design of interactive features, resulting in the inability to accurately propagate the information contained in the clicked pixels to other pixels. The activation and classification of non-clicked regions cannot be accurately guaranteed, limiting the performance of the model. In 2021, Xi Chen et al. redivided the interactive segmentation module into a conditional diffusion network and a position diffusion module, further enhancing the diffusion and transmission of pixel information. However, this non-local-based design brings additional computational cost and interaction cost to the model, increasing the use burden of medical professionals. SUMMARY

[0004] The application aims to provide a medical image interactive segmentation method applying Gaussian process classification to address the deficiencies in the background art. The technical solution of the application improves segmentation accuracy while further reducing computational cost. At the same time, a dual spatial kernel function is proposed to accurately capture and model the relationship between pixels, accurately extract prior knowledge after segmentation function, and further improve segmentation accuracy.

[0005] Technical solution: In order to achieve the above application purpose, the application provides a medical image interactive segmentation method applying Gaussian process classification, which comprises the following steps:

[0006] (1) importing the image to be segmented into a feature extraction network to perform pixel depth feature extraction;

[0007] (2) a user interacts with the image to be segmented to obtain user annotation information;

[0008] (3) constructing a Gaussian process model on a pixel classification function, and obtaining a prediction distribution of the pixel classification function value of the unannotated pixel according to the extracted pixel depth feature and the user annotation information;

[0009] (4) obtaining the predicted label of the unannotated pixel according to the prediction distribution of the pixel classification function value of the unannotated pixel to generate an image segmentation result;

[0010] (5) the user judges the image segmentation result and confirms whether the segmentation result meets the requirements, if not, repeating steps (2)-(5) until the segmentation result meets the requirements, and outputting the segmentation result.

[0011] Further, in step (1), the specific process of pixel depth feature extraction is as follows:

[0012] feed the image to be segmented I into the feature extraction network g ψ (·) to perform depth feature extraction and obtain the depth feature representation of each pixel:

[0013] g ψ (I)=X=[x1,…,x m ] T ∈R m×d

[0014] wherein g ψ (·) is a feature extraction network with ψ as a parameter, I is the image to be segmented; X∈R m×d is a full-pixel feature matrix composed of the depth features of all pixels contained in the image to be segmented I, which is an m-row d-column vector matrix, m is the total number of pixels contained in the image to be segmented I, d is the dimension of the pixel feature vector, i.e. the number of features contained in each pixel feature vector; x i ∈R d represents the feature vector of pixel i.

[0015] Further, the specific process of step (2) is as follows:

[0016] (2.1) the user interacts with the image to be segmented I, clicks and labels the foreground and background regions of the segmentation target to represent the segmentation target;

[0017] (2.2) obtaining the pixel coordinates corresponding to the user interaction position and the label annotated by the user, extracting the depth feature vector of the pixel corresponding to the user annotation position from the full-pixel feature matrix X, and collecting to obtain the annotated pixel feature matrix Xc ∈R n×d The corresponding user-labeled pixel label is put into a labeled pixel label vector y c , where n is the number of user-labeled pixels, and d is the dimension of the pixel feature vector; the depth feature vectors of the pixels in the full pixel feature matrix X corresponding to the pixels not labeled by the user are extracted, and the unlabeled pixel feature matrix X u ∈R (m-n)×d is obtained by summarizing. u

[0018] Further, the specific process of step (3) is as follows:

[0019] (3.1) defining a pixel classification function f:R d →R, which takes the feature vector x i ∈R d of pixel i as input, and outputs the binary classification score of pixel i, that is, the positive score of the pixel x i label is foreground and the negative score is background;

[0020] (3.2) constructing a Gaussian process model on the pixel classification function f, taking the pixel depth feature vectors in the labeled pixel feature matrix X c as training data with corresponding pixel labels in the labeled pixel label vector y c , and taking the pixel depth feature vectors in the unlabeled pixel feature matrix X u as test data, to estimate the probability distribution p(f u ∣X u ,X u ,y c ) of the pixel classification function value f c of the unlabeled pixel:

[0021] p(f u ∣X u ,X c ,y c )=∫p(f u ∣X u ,X c ,f c )p(f c ∣X c ,y c )df c

[0022] (3.3) p(f u ∣X u ,X c ,f c ) is the probability distribution of the pixel classification function value f u ​, labeled pixel feature matrix X c and the pixel classification function value f of the labeled pixel c In the case of unlabeled pixels, the pixel classification function value f u The probability distribution of follows a Gaussian distribution with μ(·,·) as the mean function and k(·,·) as the covariance function of the kernel function:

[0023] p(f u ∣X u ,X c , f c )=N(μ u∣c , K u，u∣c )

[0024] N(μ u∣c , K u，u∣c ) is μ u∣c is the mean function, K u,u∣c is the Gaussian distribution of the covariance matrix;

[0025]

[0026]

[0027] Among them, μ u∣c Indicates the given labeled pixel feature matrix X c and the pixel classification function value f of the labeled pixel c In this case, the pixel classification function value f of the unlabeled pixel u In the unlabeled pixel feature matrix X u The conditional mean of the pixel feature vectors contained in K u，c is the unlabeled pixel feature matrix X u and the labeled pixel feature matrix X c The covariance matrix between ; is the labeled pixel feature matrix X c The inverse matrix of the covariance matrix between the depth feature vectors of each pixel; K u，u∣c represents the conditional covariance matrix, K u,u is the unlabeled pixel feature matrix X u The covariance matrix between the depth feature vectors of each pixel, K c,u is the labeled pixel feature matrix X c and the unlabeled pixel feature matrix X u The covariance matrix between ;

[0028] (3.4)p(f c ∣X c ,y e ) is the given labeled pixel feature matrix X c and the annotated pixel label vector yc the pixel classification function value f c of the labeled pixel, is a Gaussian process posterior distribution; based on Bayes' theorem, the Gaussian process posterior distribution is proportional to the product of the likelihood function and the prior distribution, that is:

[0029] p(f c ∣X c ,y c )∝p(y c ∣X c ,f c )p(f c ∣X c )

[0030] wherein:

[0031]

[0032] p(f c ∣X c )=N(μ c ,K c,c )

[0033] wherein p(y c ∣X c ,f c ) is a likelihood function, n is the number of rows of the labeled pixel feature matrix X c , that is, the number of pixels labeled by the user, s(·) is a sigmoid function, y t and f t are the pixel label y c and the pixel classification function value f t corresponding to the tthpixel depth feature vector in the labeled pixel feature matrix X t ; the prior distribution p(f c ∣X c ) is the probability distribution of the pixel classification function value f c of the labeled pixel given the labeled pixel feature matrix X c ; N(μ c ,K c,c ) is a Gaussian distribution with a mean function μ c and a covariance matrix K c,c , wherein the mean function μ c is a zero mean function, and K c,c is a covariance matrix between the pixel depth feature vectors in the labeled pixel feature matrix X c ;

[0034] wherein the likelihood function does not satisfy a Gaussian distribution, further leading to p(f c ∣X c,y c ) cannot be calculated directly, so for p(f c ∣X c ,y c ) corresponds to the Gaussian process variational distribution q(f c ∣X c ,y c ) is calculated and then p(f c ∣X c ,y c ) and q(f c ∣X c ,y c ) to measure p(f c ∣X c ,y c ) to perform approximate calculations;

[0035] p(f c ∣X c ,y c )The corresponding Gaussian process variational distribution q(f c ∣X c ,y c )for:

[0036] q(f c ∣X c ,y c )=N(m ξ (X c ,y c ),σ 2 I c )

[0037] m ξ (X c ,y c )=Softplus(MLP ξ (X c ))*y c

[0038] Among them, N(m ξ (X c ,y c ),σ 2 I c ) is a multivariate Gaussian distribution, m ξ (X c ,y c ) is the mean function, σ 2 I c is the covariance matrix, σ 2 is the variance parameter, I c is the unit matrix, which is used to represent the variance of each dimension of the multivariate Gaussian distribution; Softplus(·) is the activation function, MLPξ (·) is a multilayer perceptron parameterized by ξ, which is used to transform the labeled pixel feature matrix X c From R n×d Convert to R n×1 ;

[0039] (3.5) u ∣X u ,X c ,f c ) and p(f c ∣X c ,y c )Substitute into p(f u ∣X u ,X c ,y c )=∫p(f u ∣X u ,X c ,f c )p(f c ∣X c ,y c )df c , get the pixel classification function value f of the unlabeled pixel u The probability distribution p(f u ∣X u ,X c ,y c ).

[0040] Furthermore, the specific process of step (4) is as follows:

[0041] Get the pixel classification function value f of the unlabeled pixel u The probability distribution p(f u ∣X u ,X c ,y c ), the pixel classification function value f for unlabeled pixels u To make predictions:

[0042]

[0043] in, is the pixel classification function value f of the unlabeled pixel u The predicted value, μ * and K * is the pixel classification function value f of the unlabeled pixel u The probability distribution p(f u ∣X u ,X c ,y c )’s mean and variance;

[0044] Prediction value of pixel classification function value of unlabeled pixel Obtain the unlabeled pixel label vector y u Prediction vector of the unlabeled pixel label vector y

[0045]

[0046] Wherein, s(·) is a sigmoid function;

[0047] According to the original spatial position of the pixel of the image to be segmented, the labeled pixel label vector y c Prediction vector of the unlabeled pixel label vector y Each pixel label corresponding to each pixel in the prediction vector is sequentially arranged to obtain the image segmentation result

[0048] Further, the specific process of step (5) is that the user judges the image segmentation result, confirms whether the contour accuracy, object integrity and segmentation precision of the segmentation result meet the requirements, if not, repeats steps (2)-(5), until the segmentation result meets the requirements, and outputs the segmentation result in the form of segmentation mask and superimposed image. The contour accuracy, object integrity and segmentation precision are greater than the preset value, and if all are greater than the preset value, the segmentation result meets the requirements.

[0049] Beneficial effects: compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0050] (1) The medical image interactive segmentation task is constructed as a Gaussian process classification problem of the pixel of the image to be segmented, the Gaussian process model is effectively combined with the deep learning mechanism, the advantages of deep learning feature extraction and representation learning are used to approximate the posterior distribution of the Gaussian process, and it is ensured that the information contained in the clicked area can be accurately propagated to the entire image. While improving the segmentation accuracy, the calculation cost is further reduced;

[0051] (2) A double spatial kernel function is proposed, which accurately captures and models the relationship between pixels, accurately extracts the prior knowledge after segmentation, and further improves the segmentation accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 The method flowchart of the present application. DETAILED DESCRIPTION

[0053] As Figure 1 shown, the present application proposes a medical image interactive segmentation method applying Gaussian process classification, which comprises the following steps:

[0054] ​(1) importing the image to be segmented into a feature extraction network to perform pixel depth feature extraction;

[0055] (2) a user interacts with the image to be segmented to obtain user annotation information;

[0056] (3) constructing a Gaussian process model on a pixel classification function, and obtaining a prediction distribution of the pixel classification function value of the unannotated pixel according to the extracted pixel depth feature and the user annotation information;

[0057] (4) obtaining a predicted label of the unannotated pixel according to the prediction distribution of the pixel classification function value of the unannotated pixel to generate an image segmentation result;

[0058] (5) the user judges the image segmentation result to determine whether the segmentation result meets the requirements, if not, repeating steps (2)-(5) until the segmentation result meets the requirements, and outputting the segmentation result.

[0059] Further, in step (1), the specific process of pixel depth feature extraction is as follows:

[0060] feed the image to be segmented I into the feature extraction network g ψ (·) to perform depth feature extraction and obtain a depth feature representation of each pixel:

[0061] g ψ (I)=X=[x1,…,x m ] T ∈R m×d

[0062] wherein g ψ (·) is a feature extraction network with ψ as a parameter, I is the image to be segmented; X∈R m×d is a full-pixel feature matrix composed of depth features of all pixels contained in the image to be segmented I, which is a vector matrix of m rows and d columns, m is the total number of pixels contained in the image to be segmented I, and d is the dimension of the pixel feature vector, i.e. the number of features contained in each pixel feature vector; x i ∈R d , represents the feature vector of pixel i.

[0063] Further, the specific process of step (2) is as follows:

[0064] (2.1) the user interacts with the image to be segmented I, and clicks on the foreground and background regions of the segmentation target to mark the segmentation target;

[0065] (2.2) obtaining the pixel coordinates corresponding to the user interaction position and the label annotated by the user, extracting the depth feature vector of the pixel corresponding to the user annotation position from the full-pixel feature matrix X, and collecting to obtain the annotated pixel feature matrix Xc ∈R n×d The corresponding user-labeled pixel label is put into a labeled pixel label vector y c , where n is the number of user-labeled pixels, and d is the dimension of the pixel feature vector; the depth feature vectors of the pixels in the full pixel feature matrix X corresponding to the pixels not labeled by the user are extracted, and the unlabeled pixel feature matrix X u ∈R (m-n)×d is obtained by summarizing. u

[0066] Further, the specific process of step (3) is as follows:

[0067] (3.1) defining a pixel classification function f: R d →R, which takes the feature vector x i ∈R d of pixel i as input, and outputs the binary classification score of pixel i, that is, the positive score of the pixel x i labeling the foreground and the negative score of the background;

[0068] (3.2) constructing a Gaussian process model on the pixel classification function f, taking the pixel depth feature vectors in the labeled pixel feature matrix X c as training data with corresponding pixel labels in the labeled pixel label vector y c , taking the pixel depth feature vectors in the unlabeled pixel feature matrix X u as test data, and estimating the probability distribution p(f u ∣X u ,X c ,y c ) of the pixel classification function value f u of the unlabeled pixel:

[0069] p(f u ∣X u ,X c ,y c )=∫p(f u ∣X u ,X c ,f c )p(f c ∣X c ,y c )df c

[0070] (3.3) p(f u ∣X u ,X c ,f c ) is the probability distribution of the pixel classification function value f u ​, the pixel classification function value f c of the labeled pixels c , the pixel classification function value f u of the unlabeled pixels, follows a Gaussian distribution with the mean function μ(·,·) and the covariance function k(·,·):

[0071] p(f u ∣X u ,X c ,f c )=N(μ u∣c ,K u,u∣c )

[0072] N(μ u∣c ,K u,u∣c ) is a Gaussian distribution with the mean function μ u∣c and the covariance matrix K u,u∣c ;

[0073]

[0074]

[0075] wherein μ u∣c represents the conditional mean at the pixel feature vector contained in the unlabeled pixel feature matrix X c with the given labeled pixel feature matrix X c and the pixel classification function value f u of the labeled pixels; K u,c is the covariance matrix between the unlabeled pixel feature matrix X u and the labeled pixel feature matrix X c ; is the inverse matrix of the covariance matrix between the pixel depth feature vectors of the labeled pixel feature matrix X c ; K u,u∣c represents the conditional covariance matrix, K u,u is the covariance matrix between the pixel depth feature vectors of the unlabeled pixel feature matrix X u , and K c,u is the covariance matrix between the unlabeled pixel feature matrix X c and the labeled pixel feature matrix X u ;

[0076] (3.4) p(f c ∣X c ,y c ) is the pixel classification function value f c of the unlabeled pixels with the given labeled pixel feature matrix X c and the labeled pixel label vector yc the pixel classification function value f c of the labeled pixel, is a Gaussian process posterior distribution; based on Bayes' theorem, the Gaussian process posterior distribution is proportional to the product of the likelihood function and the prior distribution, that is:

[0077] p(f c ∣X c ,y c )∝p(y c ∣X c ,f c )p(f c ∣X c )

[0078] wherein:

[0079]

[0080] p(f c ∣X c )=N(μ c ,K c,c )

[0081] wherein p(y c ∣X c ,f c ) is a likelihood function, n is the number of rows of the labeled pixel feature matrix X c , that is, the number of pixels labeled by the user, s(·) is a sigmoid function, y t and f t are the pixel label y c and the pixel classification function value f t corresponding to the tthpixel depth feature vector in the labeled pixel feature matrix X t ; the prior distribution p(f c ∣X c ) is the probability distribution of the pixel classification function value f c of the labeled pixel given the labeled pixel feature matrix X c ; N(μ c ,K c,c ) is a Gaussian distribution with a mean function μ c and a covariance matrix K c,c , wherein the mean function μ c is a zero mean function, and K c,c is a covariance matrix between the pixel depth feature vectors in the labeled pixel feature matrix X c ;

[0082] wherein the likelihood function does not satisfy a Gaussian distribution, further leading to p(f c ∣X c,y c ) cannot be directly computed, so the Gaussian process variational distribution q(f c ∣X c ,y c ) corresponding to p(f c ∣X c ,y c ) is computed, and then p(f c ∣X c ,y c ) is approximated by minimizing the KL divergence between p(f c ∣X c ,y c ) and q(f c ∣X c ,y c );

[0083] The Gaussian process variational distribution q(f c ∣X c ,y c ) corresponding to p(f c ∣X c ,y c ) is:

[0084] q(f c ∣X c ,y c ) = N(m ξ (X c ,y c ), σ 2 I c )

[0085] m ξ (X c ,y c ) = Softplus(MLP ξ (X c ))*y c

[0086] where N(m ξ (X c ,y c ), σ 2 I c ) is a multivariate Gaussian distribution, m ξ (X c ,y c ) is the mean function, σ 2 I c is the covariance matrix, σ 2 is the variance parameter, I c is the identity matrix, used to represent the variance in each dimension of the multivariate Gaussian distribution; Softplus(·) is an activation function, MLPξ (·) is a multi-layer perceptron parameterized by ξ, which is used to map the labeled pixel feature matrix X c From R n×d to R n×1 ;

[0087] (3.5) Substitute p(f u | X u , X c , f c ) and p(f c | X c , y c ) into p(f u | X u , X c , y c ) = ∫p(f u | X u , X c , f c ) p(f c | X c , y c ) df c , to obtain the probability distribution p(f u | X u , X u , y c ) of the pixel classification function value f c of the unlabeled pixel.

[0088] Further, the specific process of step (4) is:

[0089] Obtain the probability distribution p(f u | X u , X u , y c ) of the pixel classification function value f c of the unlabeled pixel, and predict the pixel classification function value f u of the unlabeled pixel:

[0090]

[0091] wherein f u is the predicted value of the pixel classification function value f * of the unlabeled pixel, μ * and K u are the mean and variance of the probability distribution p(f u | X u , X c , y c ) of the pixel classification function value f u of the unlabeled pixel;

[0092] Predicted value of pixel classification function value of unlabeled pixels Get the unlabeled pixel label vector y u The prediction vector

[0093]

[0094] Where s(·) is the sigmoid function;

[0095] Annotate the pixel label vector y according to the original spatial position of the pixel in the image to be segmented c The predicted vector with the unlabeled pixel label vector The pixel labels corresponding to each pixel in the image are arranged in order to obtain the image segmentation results.

[0096] Furthermore, the specific process described in step (5) is as follows: the user judges the image segmentation result to confirm whether the contour accuracy, object integrity, and segmentation accuracy of the segmentation result meet the requirements. If not, repeat steps (2) to (5) until the segmentation result meets the requirements, and then perform segmentation mask and superimpose image on the segmentation result. Output. Determine whether the contour accuracy, object integrity, and segmentation accuracy are all greater than preset values. If they are all greater than the preset values, the segmentation result meets the requirements.

Claims

1. A medical image interactive segmentation method using Gaussian process classification, characterized in that: The method comprises the following steps: (1) Import the image to be segmented into the feature extraction network to extract pixel depth features; (2) The user interacts with the image to be segmented and obtains user annotation information; (3) Construct a Gaussian process model on the pixel classification function and obtain the predicted distribution of the pixel classification function value of unlabeled pixels based on the extracted pixel depth features and user annotation information; (4) Obtain the predicted labels of the unlabeled pixels based on the predicted distribution of the pixel classification function values ​​of the unlabeled pixels and generate the image segmentation results; (5) The user judges the image segmentation result and confirms whether the segmentation result meets the requirements. If not, repeat steps (2) to (5) until the segmentation result meets the requirements and outputs the segmentation result; The process of pixel depth feature extraction in step (1) is as follows: Feed the image to be segmented I to the feature extraction network g ψ (·) Perform deep feature extraction to obtain the deep feature representation of each pixel: g ψ (I)=X=[x1,…,x m ] T ∈R m×d Among them, g ψ (·) is a feature extraction network with ψ as a parameter, I is the image to be segmented; X∈R m×d The full pixel feature matrix is ​​a summary of the depth features of all pixels contained in the image to be segmented I. It is a vector matrix with m rows and d columns, where m is the total number of pixels contained in the image to be segmented I, and d is the dimension of the pixel feature vector, that is, the number of features contained in each pixel feature vector; i ∈R d , represents the feature vector of pixel i, where i ranges from 1 to m; The specific process of step (2) is as follows: (2.1) The user interacts with the image to be segmented I and clicks on the foreground and background areas of the segmentation target to mark the segmentation target; (2.2) Obtain the pixel coordinates corresponding to the user interaction position and the user-annotated label, extract the depth feature vector of the pixel corresponding to the user-annotated position from the full pixel feature matrix X, and summarize it to obtain the annotated pixel feature matrix X c ∈R n×d The corresponding user-annotated pixel labels are put into the annotated pixel label vector y c Where n is the number of pixels annotated by the user, and d is the dimension of the pixel feature vector; the depth feature vectors corresponding to the pixels not annotated by the user in the full pixel feature matrix X are extracted and summarized to obtain the unannotated pixel feature matrix X u ∈R (m-n)×d , let the label data set corresponding to the unlabeled pixels be the unlabeled pixel label vector y u ; The specific process of step (3) is as follows: (3.1) Define a pixel classification function f:R d →R, which is the feature vector x of pixel i i ∈R d As input, the output is the binary classification score of pixel i, that is, pixel x i The labels are positive scores for foreground and negative scores for background; (3.2) Construct a Gaussian process model on the pixel classification function f, and label the pixel feature matrix X c The pixel depth feature vector in is regarded as the annotated pixel label vector y c The training data with corresponding pixel labels is represented by the unlabeled pixel feature matrix X u The pixel depth feature vector in is the test data, and the pixel classification function value f for unlabeled pixels is u The probability distribution p(f u ∣X u ,X c ,y c ) to estimate: p(f u ∣X u ,X c ,y c )=∫p(f u ∣X u ,X c ,f c )p(f c ∣X c ,y c )df c (3.3)p(f u ∣X u ,X c ,f c ) is the given unlabeled pixel feature matrix X u , labeled pixel feature matrix X c and the pixel classification function value f of the labeled pixel c In the case of unlabeled pixels, the pixel classification function value f u The probability distribution of follows a Gaussian distribution with μ(·,·) as the mean function and k(·,·) as the covariance function of the kernel function; p(f u ∣X u ,X c ,f c )=N(μ u∣c ,K u,u∣c ) N(μ u∣c ,K u,u∣c ) is μ u∣c is the mean function, K u,u∣c is the Gaussian distribution of the covariance matrix; Among them, μ u∣c Indicates the given labeled pixel feature matrix X c and the pixel classification function value f of the labeled pixel c In this case, the pixel classification function value f of the unlabeled pixel u In the unlabeled pixel feature matrix X u The conditional mean of the pixel feature vectors contained in K u,c is the unlabeled pixel feature matrix X u and the labeled pixel feature matrix X c The covariance matrix between ; is the labeled pixel feature matrix X c The inverse matrix of the covariance matrix between the depth feature vectors of each pixel; K u,u∣c represents the conditional covariance matrix, K u,u is the unlabeled pixel feature matrix X u The covariance matrix between the depth feature vectors of each pixel, K c,u is the labeled pixel feature matrix X c and the unlabeled pixel feature matrix X u The covariance matrix between ; (3.4)p(f c ∣X c ,y c ) is the given labeled pixel feature matrix X c and the annotated pixel label vector y c In the case of c The probability distribution of is the Gaussian process posterior distribution; based on Bayes' theorem, the Gaussian process posterior distribution is proportional to the product of the likelihood function and the prior distribution, that is: p(f c ∣X c ,y c )∝p(y c ∣X c ,f c )p(f c ∣X c ) in: p(f c ∣X c )=N(μ c ,X c,c ) Among them, p(y c ∣X c ,f c ) is the likelihood function, n is the labeled pixel feature matrix X c The number of rows, that is, the number of pixels annotated by the user, s(·) is the sigmoid function, y t 、f t is the labeled pixel feature matrix X c The pixel label y corresponding to the t-th pixel depth feature vector t and pixel classification function value f t ; Prior distribution p(f c ∣X c ) is the given labeled pixel feature matrix X c In the case of c The probability distribution of N(μ c ,K c,c ) is μ c is the mean function, with K c,c is the Gaussian distribution of the covariance matrix, where the mean function μ c is a zero-mean function, K c,c is the labeled pixel feature matrix X c The covariance matrix between the depth feature vectors of each pixel; Among them, the likelihood function Does not satisfy the Gaussian distribution, p(f c ∣X c ,y c ) cannot be calculated directly, for p(f c ∣X c ,y c ) corresponds to the Gaussian process variational distribution q(f c ∣X c ,y c ) is calculated by minimizing p(f c ∣X c ,y c ) and q(f c ∣X c ,y c ) between the KL divergence of p(f c ∣X c ,y c ) to perform approximate calculations; p(f c ∣X c ,y c )The corresponding Gaussian process variational distribution q(f c ∣X c ,y c )for: q(f c ∣X c ,y c )=N(m ξ (X c ,y c ),σ 2 I c ) m ξ (X c ,y c )=Softplus(MLP ξ (X c ))*y c Among them, f c is the pixel classification function value of the labeled pixel, X c is the labeled pixel feature matrix, y c is the labeled pixel label vector; N(m ξ (X c ,y c ),σ 2 I c ) is a multivariate Gaussian distribution, m ξ (X c ,y c ) is the mean function, σ 2 I c is the covariance matrix, σ 2 is the variance parameter, I c is the unit matrix, which is used to represent the variance of each dimension of the multivariate Gaussian distribution; Softplus(·) is the activation function, MLP ξ (·) is a multilayer perceptron parameterized by ξ, which is used to transform the labeled pixel feature matrix X c From R n×d Convert to R n ×1 ; (3.5) u ∣X u ,X c ,f c ) and p(f c ∣X c ,y c ) into p(f u ∣X u ,X c ,y c )=∫p(f u ∣X u ,X c ,f c )p(f c ∣X c ,y c )df c , to obtain the pixel classification function value f of the unlabeled pixels u The probability distribution p(f u ∣X u ,X c ,y c ); The specific process of step (4) is as follows: Get the pixel classification function value f of the unlabeled pixel u The probability distribution p(f u ∣X u ,X c ,y c ), the pixel classification function value f for unlabeled pixels u To make predictions: in, is the pixel classification function value f of the unlabeled pixel u The predicted value, μ * and K * is the pixel classification function value f of the unlabeled pixel u The probability distribution p(f u ∣X u ,X c ,y c )’s mean and variance; Predicted value of pixel classification function value of unlabeled pixels Get the unlabeled pixel label vector y u Prediction Where s(·) is the sigmoid function; Annotate the pixel label vector y according to the original spatial position of the pixel in the image to be segmented c Prediction of unlabeled pixel label vectors The pixel labels corresponding to each pixel in the image are arranged in order to obtain the image segmentation results.

2. The method for interactive segmentation of medical images using Gaussian process classification according to claim 1, characterized in that: The specific process described in step (5) is as follows: the user judges the image segmentation result to confirm whether the contour accuracy, object integrity and segmentation accuracy of the segmentation result meet the preset requirements. If not, repeat steps (2) to (5) until the segmentation result meets the requirements, and then perform segmentation mask and superimpose image on the segmentation result. Output.

3. The method for interactive segmentation of medical images using Gaussian process classification according to claim 2, characterized in that: The judgment of whether the preset requirements are met is as follows: determine whether the contour accuracy, object integrity, and segmentation accuracy are all greater than preset values. If they are all greater than the preset values, the segmentation result meets the requirements.

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