MRI paraspinal muscle segmentation method based on bayesian fusion and probability shape modeling

Abstract

The application discloses a MRI paravertebral muscle segmentation method based on Bayesian fusion and probability shape modeling, and comprises the following steps: a) a Fourier-Gaussian process probability shape model is established to parameterize the muscle shape, the Fourier-Gaussian process probability shape model comprises radial modeling based on a Fourier basis function to represent a muscle cross-section profile, and axial modeling based on a Gaussian process to capture the axial variation law of the muscle shape; b) a muscle edge feature model based on a convolutional neural network is constructed to perform multi-scale feature extraction on the muscle edge in the MRI image; and c) a Bayesian segmentation framework is designed, and based on a maximum posterior estimation principle, online segmentation of the paravertebral muscle in the MRI image is realized. The application is customized according to the characteristics of the paravertebral muscle segmentation task through the idea of fusing high-quality artificial labeling and a powerful learning model, so that the application can achieve high segmentation and reconstruction quality under a small amount of interaction, and has strong shape change description capability.

Description

Technical Field

[0001] This invention belongs to the fields of medical image processing, computer vision and machine learning technology, and specifically relates to an efficient segmentation method for paravertebral muscles in MRI based on Bayesian fusion and probabilistic shape modeling. Background Technology

[0002] Low back pain (LBP) occurs at all ages, from childhood to old age (Hartvigsene et al. 2018, Ferreira et al. 2023). Many countries incur significant social costs for treating LBP, including healthcare expenditures and lost productivity (Knezevic et al. 2021). The causes of LBP are complex, as various lumbar structures are susceptible to biochemical, degenerative, and traumatic stressors (Knezevic et al. 2021). However, macroscopically, LBP is often accompanied by muscle degeneration, such as a decrease in cross-sectional area and increased fatty infiltration in the paravertebral muscles (Gouberte et al. 2016). To better aid in the diagnosis and treatment of LBP, imaging segmentation and three-dimensional reconstruction of the paravertebral muscle groups can obtain muscle shape and volume, objectively assessing lumbar muscle function.

[0003] Image segmentation is a fundamental problem in the field of radiological analysis. Compared to bones, muscles are more difficult to segment due to their less defined edges, irregular shapes, and significant differences in shape among different populations. According to a recent review (D'Antonietal. 2021), existing literature reports that the segmentation accuracy of paravertebral muscles is on average 4%–5% lower than that of the spine. Currently, the main methods for muscle segmentation include:

[0004] 1) Traditional image processing methods require a lot of manual intervention in parameter adjustment and initial contour placement, and the segmentation effect is quite sensitive to the initial value.

[0005] 2) Probabilistic graph-based methods. These methods typically require more computation and may fail to register when muscle deformation is significant.

[0006] 3) Deep learning-based methods. When the amount of data is limited, deep learning methods are often more difficult to handle changes in the shape of muscle edges caused by fat infiltration compared to structures such as the spine and intervertebral discs.

[0007] 4) Methods based on statistical shape or anatomical feature models. Statistical shape models represent the shape changes of the muscle surface through dimensionality-reduced parameters, while computational anatomy-based models focus on higher-level features such as the overall direction of muscle movement and its connection to the skeleton.

[0008] Statistical shape modeling aims to capture shape variations of a set of objects and extract the main patterns of change (Ambellane et al. 2019). When applying such algorithms, two key considerations must be taken into account: 1. the choice of shape representation, and 2. how the shape model is combined with other features such as image appearance.

[0009] The most popular shape representation method originated from a series of studies by Cootes et al. (1992, 1995), which uses a set of points on a surface to represent the shape, called Point Distribution Models (PDMs). PDMs have the advantage of wide applicability, but they usually require initial alignment of the shapes in order to match the points of different shapes.

[0010] Shape models can describe the shape features of an object to be segmented. Image appearance information also contains rich features, such as grayscale, edges, and texture (local structure).

[0011] Finally, SSM-based segmentation and shape generation need to consider the fusion of shape model and image appearance information. Existing SSM methods in segmentation pipelines commonly employ the following four fusion approaches:

[0012] 1) Image appearance information guides the movement of SSM landmarks.

[0013] 2) Image appearance information controls SSM global parameters.

[0014] 3) SSM serves as prior knowledge for image appearance information-based methods.

[0015] 4) SSM correction is based solely on segmentation or generation results that are based on image appearance information.

[0016] Since MRI images contain multiple layers, the interaction processes that need to be considered mainly include the intra-layer annotation process and the automated propagation process of manual annotations between layers.

[0017] MRI paraspinal muscle segmentation is of great significance for the quantitative assessment and diagnosis of lumbar diseases such as low back pain. However, unclear boundaries and large shape variations of paraspinal muscles pose challenges to the effectiveness of segmentation algorithms. Existing segmentation methods have the following problems: 1) Traditional image processing methods are easily affected by parameters and initial values, resulting in poor robustness; 2) Probabilistic graph-based methods are computationally intensive and unsuitable for cases with large deformations; 3) Deep learning-based methods have high requirements for sample size and annotation quality; 4) Existing statistical shape model-based methods focus on geometric representation but are not intuitive enough to express anatomical semantic information.

[0018] In summary, to solve the above problems, it is necessary to develop a new method that has high requirements for both performance and efficiency in MRI paraspinal muscle segmentation. Summary of the Invention

[0019] To address the technical problems of unclear boundaries and large shape variations in MRI paraspinal muscle segmentation, the present invention aims to propose an MRI paraspinal muscle segmentation method. Its features include: 1) establishing a Fourier-Gaussian probabilistic shape model to parameterize muscle shape; 2) constructing a deep learning-based muscle edge feature model; and 3) designing a Bayesian framework to fuse shape model priors and edge features to achieve segmentation and 3D reconstruction.

[0020] To achieve the above objectives, the technical solution adopted in this invention is an MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling, comprising the following steps:

[0021] a) Establish a Fourier-Gaussian process probabilistic shape model to parametrically represent muscle shape. The Fourier-Gaussian process probabilistic shape model includes: radial modeling based on Fourier basis functions to represent the muscle cross-sectional contour, and axial modeling based on Gaussian process to capture the axial variation law of muscle shape.

[0022] b) Construct a muscle edge feature model based on a convolutional neural network to extract multi-scale features from muscle edges in MRI images;

[0023] c) Design a Bayesian segmentation framework based on the maximum a posteriori estimation principle, which integrates the prior of the Fourier-Gaussian process probability shape model, sparse manual annotation, and edge feature model to achieve online segmentation of paravertebral muscles in MRI images.

[0024] The process involves three steps: expanding the observation range through annotation diffusion, fusing manually annotated observations of the shape model, and fusing the shape model with the edge feature model.

[0025] The method requires only a small amount of manual annotation at the top, bottom, and key middle layers of the MRI sequence to achieve segmentation and three-dimensional reconstruction of the paraspinal muscles throughout the entire MRI sequence.

[0026] Furthermore, this MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling includes two processes: offline probabilistic shape modeling and online real-time inference.

[0027] The offline probabilistic shape modeling process refers to the construction of a Fourier-Gaussian-Process Probabilistic Shape Model (FGPM), including establishing an anatomical coordinate system and performing radial and axial modeling of paraspinal muscles. In radial modeling, the geometric parameters of the muscles are obtained through Fourier transform, while in axial modeling, the randomness and correlation of the parameters are established through a Gaussian process. The Gaussian process parameters are trained using historical data and serve as prior information in the inference process. During inference, the image input is manually annotated and annotation propagation (AP), outputting an annotated human observation; simultaneously, an edge confidence map is output based on a convolutional neural network (CNN) Edge Feature Model (EFM). Through the priors from FGPM and the observations from AP, an interactive posterior distribution is obtained, which is then fused with the edge confidence map from EFM, and the final posterior shape is inferred through maximum a posteriori estimation (MAP).

[0028] Furthermore, in the Fourier-Gaussian process probabilistic shape model, Fourier basis functions and Gaussian processes are fused to parameterize the three-dimensional shape information of the paraspinal muscles in the MRI sequence, serving as geometric prior knowledge for segmentation. Specifically, this includes the following:

[0029] a) Establishment of anatomical coordinate system: Establish an anatomical coordinate system in which the z-coordinate is converted to the axial anatomical height associated with the vertebra, and a polar coordinate system is used to describe the cross-sectional shape.

[0030] b) Radial modeling: Fourier series decomposition is used to represent the contour of paraspinal muscles on a single MRI cross section.

[0031] c) Axial modeling: Each Fourier coefficient is used to construct an independent one-dimensional Gaussian process to describe the variation of the coefficient in the axial MRI sequence.

[0032] Furthermore, the online real-time inference framework for Bayesian segmentation includes: fusing online manual annotation, shape model, and image appearance information to achieve segmentation and three-dimensional reconstruction of paraspinal muscles.

[0033] a) Annotation propagation to expand the observation range: Annotations are made on key MRI planes, and based on the annotations on key planes, observation annotations on adjacent planes are automatically generated through local plane image registration.

[0034] b) Fusion of manually labeled observations: Manually labeled and generated labels from adjacent layers are fed into the FGPM model for hyperparameter optimization to obtain the posterior distribution of the shape model, which is called interactive posterior.

[0035] c) Fusion of shape model and edge feature model: Interactive posterior and muscle edge features are jointly used to perform maximum a posteriori estimation, and the final segmentation result is output to achieve maximum a posteriori estimation optimization.

[0036] Compared with existing technologies, this invention, through the fusion of high-quality manual annotation and a powerful learning model, is customized for the characteristics of paraspinal muscle segmentation tasks, enabling high segmentation and reconstruction quality with minimal interaction. This invention offers high segmentation accuracy and efficiency, is easy to deploy, and achieves excellent results with only a minimal amount of manual annotation.

[0037] Compared with existing technologies, the Fourier-Gaussian process probabilistic shape model established in this invention intuitively expresses anatomical features, has fewer parameters, and has a strong ability to describe shape changes. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall implementation process of this method.

[0039] Figure 2 Here is a flowchart of the anatomical feature extraction process. (a) Schematic diagram of the lumbar spine area; (b) Flowchart of feature extraction.

[0040] Figure 3 The flowchart for modeling muscle shape shows radial modeling on the left and axial modeling on the right.

[0041] Figure 4 The flowchart shows the fusion optimization process. (a) Interaction and inference region partitioning for a specific test sample. (b) Prior distribution of a geometric parameter in the training set. (c) Interaction posterior mean and uncertainty interval for parameter (b). (d) Global geometric adjustment and fine-tuning of all parameters. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0043] Segmentation of paraspinal muscles in magnetic resonance imaging (MRI) images can be used to reconstruct 3D muscle geometry, which is crucial for the quantitative assessment of nonspecific low back pain. However, challenges such as blurred muscle boundaries, significant shape variations, and sparse labeled data lead to poor performance of existing segmentation methods.

[0044] To address these issues, a novel MRI muscle segmentation method is proposed. First, a Statistical Shape Model (SSM) based on Fourier basis functions and Gaussian processes (GPs) is designed to encode 3D muscle shapes, with the model's geometric parameters assigned anatomical meaning. Variations and correlations in muscle shape are described by Gaussian processes of the geometric parameters, resulting in a relatively small overall parameter count. Second, a Bayesian framework is developed to segment the entire muscle through posterior estimation. This framework fuses the geometric prior of the SSM with observations from automatic edge detection and sparse manual annotation, thereby compensating for issues related to blurred boundaries and shape variations. The technical solution adopted in this invention is an efficient MRI paravertebral muscle segmentation method (based on Bayesian fusion and probabilistic shape modeling), the overall framework of which is as follows: Figure 1 As shown.

[0045] The muscle segmentation method proposed in this invention is particularly suitable for paraspinal muscles with significant variability, such as... Figure 1 As shown, this method mainly includes two processes: probabilistic shape modeling and inference. The probabilistic shape modeling process refers to the construction of the FGPM, including establishing an anatomical coordinate system and performing radial and axial modeling of the paraspinal muscles. In radial modeling, the geometric parameters of the muscles are obtained through Fourier transform, while in axial modeling, the randomness and correlation of the parameters are established through a Gaussian process. The Gaussian process parameters are trained using historical data and serve as prior information in the inference process. During inference, the image input is manually annotated and annotated through AP, outputting labeled human observations; simultaneously, an edge confidence map is output based on a CNN-based edge feature model (EFM). Through the priors of the FGPM and the observations of AP, an interactive posterior distribution is obtained, which is then fused with the edge confidence map of the EFM, and the final posterior shape is inferred through maximum a posteriori estimation (MAP).

[0046] Step 1: Probabilistic shape modeling;

[0047] The goal of FGPM is to characterize the overall geometry of a muscle. Considering the shape characteristics of a muscle, it is represented as a sequence of slices, with each cross-sectional profile represented as a Fourier basis function in polar coordinates, a process called radial modeling. Since the axial spacing between slices is typically large, available data is insufficient for shape fitting. Gaussian processes are used to describe the axial correlation of the cross-sectional shapes, a process called axial modeling. This model can generate new muscle shapes after training.

[0048] Step 11: Anatomical coordinate system

[0049] Medical images are typically represented using a Cartesian coordinate system in standard units. The coordinates of a point on a muscle contour can be represented as P(x,y,z), where x and y are coordinates in the horizontal plane, and z is the axial coordinate. However, this coordinate system lacks anatomical significance due to individual variations in muscle length. Therefore, an anatomical coordinate system is proposed, where the z-coordinate is transformed into coordinates in anatomical units associated with the vertebrae, and a polar coordinate system is used to describe the cross-sectional shape. The establishment of the anatomical coordinate system is as follows: Figure 2 As shown, it includes two steps:

[0050] Step 111: Axial coordinate transformation

[0051] First, lumbar vertebral cross sections from L1 (L1) to S1 (S1) are obtained from MR images through vertebral segmentation. In the sagittal view, the spinal centerline L is obtained in a standard unit Cartesian coordinate system via spline interpolation. sp (z), such as Figure 2 As shown in (a). In the new anatomical coordinate system, the heights of the superior endplates of L1 and S1 are defined as h, respectively. L =1 and h S =6. By transforming (hh) S ) / (hh L )=(zz S ) / (zz L ), where z L and z S The axial Cartesian coordinates of the superior endplates of L1 and S1 can be used to determine h, which is called the anatomical height variable. h is only related to the vertebral position and is independent of the actual slice height. The anatomical axial coordinate transformation is applied to all slices.

[0052] Step 112: Polar coordinate transformation

[0053] On any slice of height h, the muscle contour point P(x,y,z) can be represented in polar coordinates as:

[0054]

[0055] Among them O v and O m These represent the 2D coordinates of the vertebral body center and the muscle center, respectively. Indicates the relative position of the muscle center. θ represents the radius of the muscle edge. Angle relative to the polar axis.

[0056] Step 12: Radial modeling;

[0057] like Figure 3As shown, the muscle edge radius r(θ; h) in formula (1) can be regarded as a periodic function of θ with a period of 2π, and the edge contour can be parameterized using a Fourier series:

[0058]

[0059] Where n is the Fourier order, a0, a n ,b n These are the coefficients of the basis functions. Given a truncation order N, r(θ; h) can be considered a smooth approximation of the muscle shape; the higher the order, the better it reflects the detailed shape features of the muscle. The geometric parameter vector Ψ of the muscle contour at height h. h Including the 2N+1 shape parameters a0…a in formula (2) N b N And the two positional parameters x in Equation 1 c ,y c ,

[0060]

[0061] Where ψ j (h) is Ψ h The j-th parameter in the equation.

[0062] Step 13: Axial modeling;

[0063] The three-dimensional muscle shape is represented by a sequence of interconnected slices. To describe the axial correlation and randomness of the muscle cross-sectional shape, the variation in muscle shape and position relative to h is modeled as including all parameters Ψ. h The joint Gaussian process. These parameters are independent, thus 2N+3 independent Gaussian processes can be obtained. In formula (3), ψ j The Gaussian process of (h) is represented as follows:

[0064]

[0065] Where ∈ j This is the observation noise of an MRI device that conforms to an independent Gaussian distribution. It is the noise variance, while f j (h) corresponds to a noiseless Gaussian process:

[0066]

[0067] Where m j (h) is the mean function that determines the general trend of the Gaussian process, while k j (h,h') represents f j The kernel function for the covariance of heights h and h'. Considering simplicity and flexibility, m j(h) is defined as a polynomial function.

[0068]

[0069] Where α d,j The coefficients of the mean function are denoted by , and D represents the highest polynomial degree. The Matérn kernel, known for its adaptability and computational efficiency, was chosen as the kernel function, defined as .

[0070]

[0071] Where δh=h-h', ν=3 / 2, Γ(ν) represents the gamma function, and K v It is a modified Bessel function, with kernel parameter σ. f,j ,l j A value greater than 0 controls the smoothness of the kernel and adapts it to different data scales. Ultimately, the parameters of the mean, kernel, and noise function form the parameter set of the Gaussian process:

[0072]

[0073] Step 14: Model training and reconstruction process;

[0074] GP parameters Estimate from a training dataset of S samples with manual annotations. Let t s Let be the number of slices in the s-th sample (s=1,…,S). This is the height vector of sample s. The training dataset for the cross-sectional geometry;

[0075]

[0076] The muscle shapes labeled in all slices were obtained by performing a Fourier transform, where... Let h train =[h (1)T ,…,h (S)T ] T , GP parameters Including the mean polynomial α obtained through least squares curve fitting d,j The coefficients, and the parameters of the kernel and noise function estimated by maximizing the logarithmic marginal likelihood.

[0077]

[0078] Where K j It is the GP covariance matrix, μ j Through m j (h train The mean vector obtained. Best estimate of GP parameters. It is derived using the quasi-Newton method.

[0079] Use the trained parameters A generative model of 3D muscle shape can be obtained. In the height vector h', the j-th geometric parameter is...

[0080] ψ′ j =μ′ j +A j Z, (11)

[0081] Where μ' j It is by The obtained mean vector, A j yes The Cholesky decomposition, where Z is sampled from a standard Gaussian distribution. Based on formulas (1) and (2), ψ' can be used. j Robustly reconstruct 3D muscle shapes.

[0082] Step 2: Inference based on posterior estimation;

[0083] An efficient Bayesian framework for inference of muscle shape in MRI is established, in which the posterior distribution of geometric parameters is obtained by fusing labeled data and a trained FGPM, and the final 3D shape is estimated by MAP using observations from EFM.

[0084] Step 21: Edge Feature Model

[0085] A muscle edge feature model (EFM) using a CNN edge detector is constructed to generate a confidence distribution C of curve L as the muscle boundary, called the edge confidence map. The CNN architecture is the same as that of UAED [@zhou2023treasure] to automatically extract multi-scale muscle edge features and handle annotation ambiguity. Define event I. edge (u,v) represents the pixel (u,v) and the event at the muscle edge. The CNN output at (u,v) is I. edge The probability of (u,v) is denoted as P. β (I edge (u,v))∈(0,1), where β is the weight of the CNN. Given the height h, let Represented by geometric parameter Ψ h The set of pixels for the generated closed curve. The overall confidence of the curve as a muscle boundary is defined as:

[0086]

[0087] Where q is the curve Upper pixel (u q The index of (vx). Represents a set The number of pixels and the weight β were pre-trained on a large-scale natural image dataset and fine-tuned on an MR image dataset of the lumbar spine.

[0088] Step 22: Annotation and Dissemination - General;

[0089] Manual annotation can be considered high-quality observation. To reduce manual intervention, the number of annotated slices is increased using an annotation propagation (AP) algorithm based on non-rigid registration. Since shape variations between adjacent slices are insignificant, the shapes obtained through AP have high confidence. The algorithm consists of three stages:

[0090] 1) Select the manually annotated slice (H1) and the adjacent unannotated slice (H2).

[0091] 2) Expand the bounding box of the annotation by (w) pixels to define a region of interest (ROI), and register (H1) to (H2) within the ROI to derive the deformation field.

[0092] 3) Use deformation fields to transform geometric parameters The boundary pixels are mapped from (H1) to (H2), thus the geometric parameters of (H2) can be obtained. As a supplementary note.

[0093] Step 23: Bayesian Fusion Optimization

[0094] By performing Bayesian fusion of the FGPM prior and finite observations, the posterior of the geometric parameters on all slices was estimated, such as... Figure 4 As shown in (a), the fusion process consists of two steps to obtain the interactive posterior and the final posterior. The interactive posterior distribution of the geometric parameters can be calculated by updating the GP parameters based on the annotated observations. The interactive posterior and the marginal confidence distribution of the EFM are fused through MAP estimation to obtain the final posterior inference of the 3D muscle shape.

[0095] set up For noisy annotation observations, For in (h * The geometric parameters are generated at (). The conditional distribution properties of the multivariate Gaussian distribution [@murphy2012machine] are utilized. The interactive posterior distribution is in

[0096]

[0097] annotation (h) * The top, bottom, and center key slices c in the ) are used as These slices are equally spaced. When c=1, the prior and interactive posterior of a0 are as follows: Figure 4 As shown in (b) and (c).

[0098] It not only relies on interactive posterior but also incorporates image features from EFM into the optimized inference results. This is to find the maximum posterior distribution. of (Ψ) h The Bayesian optimization objective for inference is:

[0099]

[0100] The first term can be obtained using formula 10, where... These are the final estimated GP parameters from the interactive posterior, and the second term can be obtained through Equation 12, where... These are the training CNN weights for EFM. To accelerate the global optimum search, the Hooke-Jeeves pattern search algorithm is used.

[0101] The process is divided into two stages, such as Figure 4 As shown in (d). First, (Ψ) h The shape parameters in ((a0,a1,b1,…,a) N Grouping (bx) into (Ψh-shape) and scaling by a factor (η). This reduces the optimization dimension to 3D space ((η,x)). c ,y c This allows for a rapid approximation of the target muscle image. Next, the (Ψ) h All parameters in the ) are fine-tuned and constrained within the range of [μ-σ,μ+σ] in the interactive posterior to obtain the final inference result.

[0102] In summary, muscle shape segmentation is a challenging task, primarily due to its geometric variability, the lack of rare case samples, and the blurring of edges in images. Therefore, fusing image information with geometric priors represented by Fourier basis functions (SSMs) is an effective method to improve the reliability of muscle segmentation. However, current SSMs mainly focus on geometric details but lack descriptions of muscle anatomical features and their correlations. Global correlation and confidence are also frequently neglected in muscle feature fusion. This invention proposes a geometric shape model of paraspinal muscles based on Fourier basis functions, where geometric parameters can intuitively represent anatomical features. Based on the geometric model, a Gaussian process model is constructed to describe the individual variability and global correlation of geometric parameters. This combined model is called the Fourier-Gaussian process probabilistic shape model (FGPM). Furthermore, a Bayesian fusion framework is designed to obtain the maximum a posteriori estimate of the FGPM, which fuses sparse, high-quality annotations and automatically extracted image features into a model prior derived from historical data. This approach fully utilizes the correlation of the data, allowing low-confidence estimates under local observations to be corrected through high-quality data and a reliable model. Experiments on lumbar paravertebral muscle datasets from healthy individuals and patients demonstrate that the segmentation results obtained by the posterior estimation of this invention are more accurate than other methods and provide higher inference efficiency.

[0103] Segmentation results on public and clinical datasets demonstrate that the proposed method achieves a Dice similarity coefficient exceeding 90% using only three manually labeled slices, outperforming other methods. This method achieves fast inference speed with only a small training dataset, showcasing its potential clinical applicability. Furthermore, this method is more accurate, efficient, and easier to deploy.

Claims

1. A method for segmenting paraspinal muscles in MRI based on Bayesian fusion and probabilistic shape modeling, characterized in that, Includes the following steps: a) Establish a Fourier-Gaussian process probabilistic shape model to parametrically represent muscle shape. The Fourier-Gaussian process probabilistic shape model includes: radial modeling based on Fourier basis functions to represent the muscle cross-sectional contour, and axial modeling based on Gaussian process to capture the axial variation law of muscle shape. b) Construct a muscle edge feature model based on a convolutional neural network to extract multi-scale features from muscle edges in MRI images; c) Design a Bayesian segmentation framework based on the maximum a posteriori estimation principle, integrating the prior of the Fourier-Gaussian process probability shape model, sparse manual annotation, and edge feature model to achieve online segmentation of paravertebral muscles in MRI images; The process involves three steps: expanding the observation range through annotation diffusion, fusing manually annotated observations of the shape model, and fusing the shape model with the edge feature model. Manual annotations were performed at the top, bottom, and key intermediate layers of the MRI sequence to achieve segmentation and three-dimensional reconstruction of the paraspinal muscles throughout the MRI sequence.

2. The MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling according to claim 1, characterized in that, This MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling includes two processes: offline probabilistic shape modeling and online real-time inference. The offline probabilistic shape modeling process refers to the construction of the Fourier-Gaussian process probabilistic shape model (FGPM), which includes establishing an anatomical coordinate system and performing radial and axial modeling of paraspinal muscles. In radial modeling, the geometric parameters of the muscles are obtained through Fourier transform. In axial modeling, the randomness and correlation of the parameters are established through Gaussian processes. The Gaussian process parameters are obtained through training with historical data and serve as prior information in the inference process. During the inference process, the image input is processed through manual annotation and annotation diffusion (AP), and the output is an annotated human observation. The edge feature model EFM, based on a convolutional neural network (CNN), outputs an edge confidence map. An interactive posterior distribution is obtained through the prior of the FGPM and the observations of AP. This distribution is then fused with the edge confidence map of EFM, and the final posterior shape is inferred through maximum a posteriori estimation (MAP).

3. The MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling according to claim 1, characterized in that, The Fourier-Gaussian process probabilistic shape model integrates Fourier basis functions and Gaussian processes to parameterize the three-dimensional shape information of paraspinal muscles in MRI sequences, serving as geometric prior knowledge for segmentation. Specifically, this includes the following: a) Establishment of anatomical coordinate system: Establish an anatomical coordinate system in which the z-coordinate is converted to the axial anatomical height associated with the vertebra, and a polar coordinate system is used to describe the cross-sectional shape; b) Radial modeling: Fourier series decomposition is used to represent the contour of the paravertebral muscles on a single MRI cross section; c) Axial modeling: Each Fourier coefficient is used to construct an independent one-dimensional Gaussian process to describe the variation of the coefficient in the axial MRI sequence.

4. The MRI paravertebral muscle segmentation method based on Bayesian fusion and probabilistic shape modeling according to claim 1, characterized in that, The online real-time inference framework for Bayesian segmentation includes: fusing online manual annotation, shape model, and image appearance information to achieve segmentation and three-dimensional reconstruction of paraspinal muscles; a) Annotation propagation extends the observation range: Annotations are performed on key MRI layers, based on annotations at key layers. By using local layer image registration, observation labels on adjacent layers are automatically generated; b) Fusion of manually labeled observations: Manually labeled and generated labels from adjacent layers are fed into the FGPM model for hyperparameter optimization to obtain the posterior distribution of the shape model, which is called interactive posterior. c) Fusion of shape model and edge feature model: Interactive posterior and muscle edge features are jointly used to perform maximum a posteriori estimation, and the final segmentation result is output to achieve maximum a posteriori estimation optimization.

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