Multi-view KAN brain MRI image registration method under edge information guidance

Abstract

The invention discloses a multi-view KAN brain MRI (Magnetic Resonance Imaging) image registration method under the guidance of edge information, and the method comprises the steps: converting a brain moving image and fixed image registration task into a non-iterative coarse-to-fine calculation process through the intensity robustness of the edge information and the powerful representation capability of the KAN in an intensive task; a channel redundancy reduction mechanism is introduced into a convolutional layer of an encoder to extract low-redundancy related features of two images, a decoder of a multi-view KAN structure pays attention to dependency of different distances of the features through three different views, the decoder generates an intermediate deformation field by using a non-iterative coarse-to-fine principle, and the low-redundancy related features of the two images are extracted. And the accuracy of processing the large deformation task by the model is improved. Besides, model training is guided through edge information, a deformed moving image and a deformation field with higher precision can be output through the method, the visual perception quality can be improved, and the method surpasses various current advanced algorithms in the aspect of quantitative evaluation.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image processing, and particularly relates to a method for registering brain MRI images of multi-field KAN guided by edge information. Background Art

[0002] Medical image registration aims to align the anatomical structures between a fixed image and a moving image by finding a dense non-linear spatial transformation. It can be divided into traditional registration methods and deep learning-based methods. Traditional methods formalize image registration as an iterative optimization problem, and obtain the deformed moving image by maximizing similarity or minimizing difference through an iterative process. Traditional registration methods have strong theoretical interpretability, but iterative optimization is required for each pair of images. Therefore, these methods have a long iterative time and non-sharable parameters, and face the challenge of high time consumption in large-scale image registration.

[0003] In recent years, deep learning (DL)-based methods have received extensive attention in the field of image registration due to their superior inference performance. In terms of network architecture, the U-shaped deep network is one of the most common network structures, and its typical representative is U-Net, which can effectively utilize the abstract features of images to complete medical image analysis tasks. Subsequently, various skip connection structures have emerged, such as Residual Network (ResNet) and Dense Connectivity Convolutional Network (DenseNet), which aim to alleviate the problems of gradient degradation and gradient disappearance in deep neural networks.

[0004] The performance of the registration network depends on the effectiveness of image feature extraction. To better extract image features, many researchers have proposed different feature extraction modules. Convolutional Neural Networks (CNNs) have an inherent inductive bias of translational invariance and locality, and their proposal has brought significant advantages to image processing tasks. Therefore, CNNs are widely and continuously used as the basis of deep registration networks in registration tasks. Visual Transformer (ViT) and its derivative model Swin Transformer have been widely used because of their great ability to capture long-range dependencies through the self-attention mechanism. However, the self-attention mechanism often brings larger parameter and computational amounts. To alleviate the computational complexity of the self-attention mechanism, MambaMorph with the Mamba module constructs a linear complexity long-range feature capture mechanism using SSM. It is worth noting that models based on Multi-layer Perceptron (MLPs) also show the ability to capture long-range dependencies without self-attention. A large number of studies have demonstrated the effectiveness of MLPs in processing full-resolution images, showing their ability to recognize complex spatial relationships. Meng et al. first studied the optimal strategy for using MLPs in deformable medical image registration and verified its superior performance.

[0005] Although Multi-layer Perceptron (MLPs) have advantages in processing full-resolution images, MLP-based models face limitations in modeling complex functions because the mathematical basis of MLPs stems from the Universal Approximation Theorem and uses non-learnable activation functions. Kolmogorov-Arnold Networks (KANs), based on the Kolmogorov-Arnold (KA) representation theorem, have attracted extensive attention in the field of deep learning because of their learnable activation functions and stronger representation ability. However, current researchers are still exploring the performance and applications of KANs in the registration field.

[0006] Medical image registration is a key technology in clinical diagnosis and treatment, and its goal is to align the anatomical structures of the moving image and the fixed image through a non-linear spatial transformation. Traditional methods (free-form deformation, large deformation diffeomorphic mapping) rely on iterative optimization, which is time-consuming and difficult to handle large deformation tasks. Although deep learning-based methods (such as PIViT, TransMatch) have improved efficiency, they still have the following problems:

[0007] (1) Limitations of the iterative structure: Existing methods need to perform iterative optimization on the low-resolution feature layer and cannot directly process full-resolution images, resulting in loss of details.

[0008] (2) Feature extraction redundancy: The features extracted by traditional convolutional networks have high redundancy, which affects the model's ability to capture key anatomical structures.

[0009] (3) Similarity measurement deviation: Existing loss functions (such as normalized cross - correlation) are vulnerable to image gray - level distribution interference and are difficult to accurately evaluate the edge alignment effect.

[0010] (4) Insufficient smoothness of the deformation field: The directly generated deformation field is prone to local distortion, affecting the physiological rationality of the registration result.

[0011] In view of the above problems, the present invention proposes a multi - field - of - view KAN - based brain MRI image registration method guided by edge information, which significantly improves the registration accuracy and efficiency of brain MRI images. Summary of the Invention

[0012] To overcome the problems in the background technology, the present invention provides a multi - field - of - view KAN - based brain MRI image registration method guided by edge information.

[0013] To achieve the above object, the present invention is implemented by the following technical solutions:

[0014] I. Data pre - processing

[0015] S1: Use the public datasets LPBA40 and Mindboggle. After pre - processing such as skull removal, a brain MRI dataset to be registered required by the present invention is formed, including a fixed image I fixed and a moving image I moving ;

[0016] S2: Use a redundancy - reducing encoder to extract features from the fixed image I fixed and the moving image I moving respectively, to obtain the fixed - image features and the moving - image features

[0017] II. Implementation of the redundancy - reducing encoder

[0018] 1. The input feature V is sliced along the channel dimension into V up and V low ;

[0019] 2. V up passes through group convolution and point convolution and then is summed to obtain F1, and V low passes through point convolution and is concatenated with the original data to obtain F2;

[0020] 3. Global pooling is performed on F1 and F2 to obtain the saliency weights S1 and S2;

[0021] 4. Weighted fusion outputs low - redundancy features:

[0022]

[0023] III. Fusion of Multi-View KAN Module and Hierarchical Correlation

[0024] S3: Starting from the low-resolution feature map and calculate the cross-view correlation dependencies at distances of 3, 5, and 7 pixels to generate the initial deformation field correlation map Among them, the multi-view KAN module structure:

[0025] (1) Implement feature correlation calculation based on grouped rational functions:

[0026]

[0027] where Ω is the linear coefficient matrix, is the grouped rational function;

[0028] (2) Introduce a spatial gating unit to optimize feature fusion:

[0029] s(F) = F1⊙(WF2 + b)

[0030] where W is the learnable weight matrix and b is the bias term.

[0031] S4: Adopt a non-iterative coarse-to-fine strategy to generate the deformation field layer by layer The deformation field of the i-th layer is generated by the registration head according to the deformation field correlation map and perform spatial transformation on the moving image features of the previous layer after upsampling where i = 4, 3, 2, 1, and finally output the full-resolution deformation field

[0032]

[0033] to obtain the deformed features Based on and the fixed image features generate a new correlation map through the multi-view KAN module and pass it to the previous layer for processing.

[0034] S5. Fusion of the deformation field correlation map between levels, and calculate the cross-level correlation dependencies through the multi-view KAN module to enhance the consistency of the deformation field.

[0035] IV. Deformation Field Generation and Edge-Guided Optimization

[0036] S6. Integrate the multi-level deformation fields to generate the final deformation field​​ Convert the multi-channel feature map into a three-channel displacement field through a registration head:

[0037]

[0038] where the initial weight ensures smooth deformation.

[0039] S7. Extract the edge information E of the fixed image and the deformed moving image based on the Grünwald-Letnikov fractional differential theorem f and E m ′, construct the target edge registration error (TERE) loss function:

[0040]

[0041] and combine the normalized cross-correlation loss and the deformation field regularization loss to construct the total loss function:

[0042]

[0043] The extraction of the edge information in the TERE loss function is based on the Grünwald–Letnikov (GL) fractional differential operator:

[0044]

[0045] where O x , O y and O z are gradient operators, ω i is the GL fractional coefficient, and * is the convolution operation..

[0046] V. Model Optimization and Effect Verification

[0047] S8. Use the Adam optimizer to optimize the model parameters and output the optimal deformation field ψ and the registered image Verify the registration accuracy through comparative experiments. This method is compared with four advanced methods in 2024. The Dice coefficient is increased by 2.875% (LPBA40) and 3.775% (Mindboggle) on average, the HD95 is reduced by 0.440 (LPBA40) and 0.308 (Mindboggle) on average, and the number of model parameters is reduced by 28.475M on average.

[0048] Advantages of the present invention:

[0049] 1. High efficiency of the redundancy reduction encoder: By channel splitting and saliency weighting, reduce the interference of redundant features and improve the recognition accuracy of key anatomical structures.

[0050] 2. Strong representation ability of the multi-field KAN module: The combination of grouped rational functions and spatial gating units enhances the modeling of cross-distance and cross-level feature dependencies.

[0051] 3. Optimization efficiency of the non-iterative strategy: The deformation field between levels is directly transmitted, avoiding low-resolution iterative calculations.

[0052] 4. Edge-guided fast convergence: The TERE loss function suppresses noise through fractional-order differentiation, accelerating the model training iteration times by about 20%.

[0053] 5. Industrial application value: Tested in a surgical navigation system, the registration result error is less than 1.5 mm, meeting the clinical accuracy requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other accompanying drawings can be obtained based on these drawings without creative efforts.

[0055] Figure 1 It is a schematic diagram of the brain MRI medical image registration process provided by the present invention;

[0056] Figure 2 It is a schematic diagram of the edge-guided multi-field KAN registration model architecture provided by the present invention;

[0057] Figure 3 It is a comparison diagram of the registration effects with the 7 most advanced medical image registration methods provided by the present invention;

[0058] Figure 4 It is a schematic diagram of the interpretability of the multi-field KAN module provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0060] Embodiment 1

[0061] Refer to Figures 1 to 4 , the present invention discloses a method for registering brain MRI images with multi-field KAN guided by edge information, including the following steps:

[0062] S1. Using the publicly available datasets LPBA40 and Mindboggle, after preprocessing such as skull stripping, a brain MRI dataset to be registered required by the present invention is formed, including a fixed image I fixed and a moving image I moving . As Figure 3 shown in the first two columns, the images under brain MRI-T1 weighting have large spatial differences, including but not limited to parts of the posterior cingulate cortex and precentral gyrus structures.

[0063] S2. Use a redundancy reduction encoder to extract features from the fixed image I fixed and the moving image I moving respectively, to obtain the fixed image features and the moving image features

[0064] Among them, the principle of the redundancy reduction encoder is: using the cascaded operations of convolution-normalization-redundancy reduction-convolution-normalization to complete the extraction of low-redundancy features of the image pair. The redundancy reduction operation can be expressed as:

[0065]

[0066] where V up and V up are obtained by splitting the input image in the channel dimension, and are the weight matrices of group convolution and point convolution respectively, D, H, and W are the depth, height, and width of the input image, and S n is the feature saliency vector obtained by pooling F n . This part performs saliency normalization and weighting processing on the input image to extract low-redundancy and more significant image features.

[0067] S3. According to the processing of F fixed and F moving in S2, starting from the low-resolution feature maps and , through the multi-field KAN module, focus on the correlation dependencies of the maps in the window fields with distances of 3, 5, and 7, and obtain the deformation field correlation maps

[0068] Among them, the principle of extracting multi-field correlation dependencies is: using convolution to calculate the correlation between the fixed image features and the moving image features of the input, and connecting it to the middle of the two features. The present invention uses windows of three sizes, 3×3×3, 5×5×5, and 7×7×7, to segment the input and calculate the feature dependency relationships within the windows. The correlation dependency is expressed as:

[0069]

[0070] Among them, is the correlation mapping of the same-level deformation field, is is i is the number of levels, is the deformation field identifier. The correlation dependence calculation CorrDep(*) is based on the Kolmogorov - Arnold representation theorem:

[0071]

[0072] Among them, and are continuous functions, and v p is the element value of the input vector. The original KAN is based on spline functions and is difficult to calculate efficiently on the GPU. Therefore, the present invention uses a grouped rational function KAN:

[0073]

[0074] as its continuous function, where Ω is the linear coefficient matrix, is the grouped rational function. The present invention uses a spatial gating unit:

[0075] s(F) = F1⊙(WF2 + b)

[0076] to further optimize the representational ability of the module. Among them, F1 and F2 are the equally divided components of the input feature F on the channel, and W and b are the learnable linear weight matrix and bias matrix respectively.

[0077] S4. According to the processing of in S3, generates a low - resolution deformation field through the registration head using a non - iterative coarse - to - fine registration strategy to make the third - layer moving image feature map deform through the deformation field to obtain and then perform the processing as described in S3 to obtain The calculations for the second layer and the first layer are the same. deform through the deformation field to obtain and deform through the deformation field to obtain and

[0078] Among them, the principle of the non - iterative coarse - to - fine registration strategy is: converting the iteration within the low - resolution layer into the iteration between the full - resolution layers. Generating a low - resolution deformation field through the image features of a lower resolution:

[0079]

[0080] Among them, and are the feature maps of the fixed image and the moving image at the i-th layer respectively. The deformation field After upsampling, performs a deformation operation on the moving image features of the previous level:

[0081]

[0082] Among them, SpatialTransform(*) is to perform a specified spatial transformation on the input F using the spatial transformation grid. This step starts from the fourth layer and goes up gradually. Therefore, in the non-iterative process from coarse to fine, i = 4, 3, 2, 1.

[0083] S5. According to the processing of the low-resolution deformation field correlation mapping in S3 and the processing of the deformed moving image feature mapping in S4 and the correlation mapping of the same-level deformation field , using the multi-view KAN module, pays attention to the correlation dependencies of the correlation mappings between different levels at distances of 3, 5, and 7 pixels, and obtains the updated deformation field correlation mapping

[0084] Among them, the principle of paying attention to the correlation between different levels is: different from calculating the correlation between the fixed image features and the moving image features by the multi-view KAN module in S3, the multi-view KAN module in S5 calculates the correlation dependency between the correlation mapping of the same-level deformation field and the correlation mapping of the next-level deformation field , and obtains the correlation mapping of the previous-level deformation field That is:

[0085]

[0086] Among them, i is the number of levels, is the deformation field identifier. This step increases the attention of the method to the deformation field by supplementing the correlation of the deformation fields at different levels.

[0087] S6. According to the processing in S4 and S5, when the non-iterative calculation from coarse to fine reaches the top layer i = 0, the deformation field

[0088] Among them, the principle of generating the deformation field is as follows: Through a learnable registration head, the multi-channel feature map information is converted into three-channel information, respectively representing the displacement offsets of each pixel point on the x-axis, y-axis, and z-axis:

[0089]

[0090] Among them, Re g Head(*) is a convolution operation that converts multi-channel information into three-channel information, and its initial parameter ω is distributed as

[0091] S7. According to the processing of the deformation field in S6, using the fractional differential theorem, the implicit weighted edge information of the image is extracted, and thus the fixed image I is constructed. The similarity measure of the target edge registration error (TERE) between the fixed image I fixed and the deformed moving image is as follows. Among them, TERE is:

[0092]

[0093] Among them, E f is the edge information of the fixed image, and E m ′ is the edge information of the deformed moving image.

[0094] Among them, the principle of the target edge registration error is as follows: Based on the Grünwald–Letnikov (GL) fractional differential principle, the edge information of the image is implicitly weighted and extracted, and the target edge registration error is constructed using the coincidence rate of the fixed image edge and the deformed moving image edge. Among them, the GL fractional differential is expressed as:

[0095]

[0096] Among them, x0 is the lower bound of the independent variable x, α is a non-integer real number, s is a very small interval sampling number, and w i is the binomial coefficient. The binomial coefficient is expressed through the Euler gamma function:

[0097]

[0098] Among them, n is the order. The fractional derivative of the image edge on a single coordinate axis (taking the x-axis as an example) can be written as:

[0099]

[0100] Among them, f(x, y, z) is an image edge calculation function, and (x, y, z) represents the pixel point coordinates. Since the image is in units of 1 pixel point, s = 1 in the present invention. The α-order differential form:

[0101]

[0102] Among them, Δx, Δy, and Δz are the increments of the independent variables. It can be deduced that:

[0103]

[0104] Among them, O x , O y and O z respectively represent the gradient operators in the x, y, and z directions, and * is the convolution operation.

[0105] The present invention constructs the target edge registration error through the coincidence rate of the image edges:

[0106]

[0107] Among them, E f is the fixed image edge information, E m ′ is the deformed moving image edge information, ∩ is the AND operation, and ∪ is the OR operation. In addition, combined with the normalized cross-correlation:

[0108]

[0109] Among them, is the mean value of the image, and v i is the value of the pixel point. Construct the final loss function:

[0110]

[0111] Among them, is the regularization penalty term for the deformation field to guide the calculation of the smooth deformation field, and λ i (i = 1, 2, 3) are the weighting coefficients.

[0112] S8. Use the Adam optimizer to optimize the parameter θ to obtain the optimal model ε θ ;

[0113] S9. According to the processing of S8 on the optimal model ε θ , obtain the deformation field ψ and the deformed moving image

[0114] S10. According to the processing of the fixed image and the moving image in S9, compare with other existing advanced methods to verify the advancement of the method proposed in the present invention.

[0115] It should be noted that by integrating multi - field - of - view correlation dependence and cross - level deformation field correlation dependence into the brain MRI image registration process, the obtained deformation field and the deformed moving image better meet the requirements. Among them, the S2 - S8 step model is Figure 2 , and the S9 - S10 steps obtain Figure 3 , and the proposed method is analyzed to obtain Figure 4 . The present invention realizes non - iterative coarse - to - fine image registration at full resolution, enabling the generated intermediate deformation field to effectively transfer to higher - resolution features. At the same time, in order to reduce the difficulty of image similarity measurement, the present invention makes full use of image edge information to construct a target edge registration error loss function. This function suppresses noise and extracts edges through implicit weighting, and then evaluates the spatial alignment degree of image pixels through the overlap rate, improving the learning speed of the model. This achievement provides a more efficient and accurate solution for brain MRI image registration, reducing the difficulty of medical image analysis.

[0116] Embodiment 2

[0117] In this embodiment, the full process of brain MRI image registration is as follows:

[0118] 1. Data pre - processing:

[0119] 1.1 Dataset: 100 brain MRI - T1 images in LPBA40, with a resolution of 160×192×144;

[0120] 1.2 Pre - processing: Skull stripping (FreeSurfer tool), intensity normalization (Z - score), resampling to 1mm 3 voxel.

[0121] 2. Model configuration:

[0122] 2.1 Redundancy - reducing encoder: 4 - layer downsampling, number of channels [8, 16, 32, 64], group convolution number of groups gr = 4, channel reduction rate r = 2;

[0123] 2.2 Multi - field - of - view KAN module: Window size [3, 5, 7], number of groups dg = 8, spatial gating unit weight

[0124] 2.3 Loss function weights: λ1 = 0.3 (similarity), λ2 = 0.4 (TERE), λ3 = 0.3 (regularization).

[0125] 3. Registration effect:

[0126] 3.1 Quantitative results: The average Dice coefficient was 73.9% (LPBA40) and 64.1% (Mindboggle), an improvement of 8.4% (LPBA40) and 9.2% (Mindboggle) compared to VoxelMorph; the 95% Hausdorff distance (HD95) was 5.43 (LPBA40) and 4.98 (Mindboggle), an improvement of 1.05 (LPBA40) and 0.68 (Mindboggle) compared to VoxelMorph;

[0127] 3.2 Qualitative results: As Figure 3 shown, the alignment effect in complex folded regions such as the precentral gyrus and cingulate gyrus is significant.

[0128] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A brain MRI image registration method for multi-field-of-view KAN guided by edge information, characterized in that, Including the following steps: S1. Preprocess the brain MRI image dataset to generate a fixed image I fixed and a moving image I moving ; S2. Extract multi-level features of the fixed image and the moving image respectively through the redundancy reduction encoder and The redundancy reduction encoder extracts low-redundancy features through convolution-normalization-channel redundancy reduction operations; S3. Based on the multi-field-of-view KAN module, starting from the low-resolution feature map and calculate the cross-field-of-view correlation dependencies at distances of 3, 5, and 7 pixels to generate the initial deformation field correlation map S4, through the non-iterative coarse-to-fine strategy, the deformation field is generated layer by layer from the 4th layer to the 1st layer The deformation field of layer i The registration head maps the deformation field according to the correlation Generate After upsampling, the features of the previous layer of moving images are Perform spatial transformation to obtain deformed features based on With fixed image features Generate new correlation maps through the multi-view KAN module And pass it to the upper layer for processing; S5. Fuse the deformation field correlation mapping between levels, and calculate the cross-level correlation dependence through the multi-field-of-view KAN module Enhance the consistency of the deformation field; S6. Integrate multi-level deformation fields to generate the final deformation field ψ; S7. Extract the edge information E of the fixed image and the deformed moving image based on the Grünwald-Letnikov fractional differential theorem f and E m ′, and construct the target edge registration error (TERE) loss function: Combined with the normalized cross - correlation loss and the deformation field regularization loss Construct the total loss function: S8. Use the Adam optimizer to optimize the model parameters and output the optimal deformation field ψ and the registered image 2. The method according to claim 1, characterized in that, The channel redundancy reduction operation of the redundancy reduction encoder includes: splitting the input feature V along the channel dimension into V up and V low , where the V up is subjected to grouped convolution and point convolution and then added to obtain F1, and the V low is subjected to point convolution and concatenated with the original data to obtain F2. After global pooling, the saliency weights S1 and S2 are obtained, and finally weighted fusion is performed as follows:

3. The method according to claim 1, wherein The multi-view KAN module is implemented based on piecewise rational functions, and its expression is: where Ω is a linear coefficient matrix, is a grouped rational function, and a spatial gating unit s(F) = F1 ⊙ (WF2 + b) is introduced to optimize the feature representation, where W is a learnable weight matrix and b is a bias term.

4. The method according to claim 1, wherein The non-iterative coarse-to-fine strategy is achieved through the transfer of the deformation field between levels, specifically: the deformation field of the i-th level After upsampling, Perform a spatial transformation. where i = 4, 3, 2, 1, and the final output is the full-resolution deformation field 5. The method according to claim 1, wherein The extraction of edge information in the TERE loss function is based on the Grünwald–Letnikov (GL) fractional differential operator: Among them, O x , O y and O z are gradient operators, ω i is the GL fractional-order coefficient, and * is the convolution operation.

6. The method according to claim 1, wherein The deformation field Convert the multi-channel feature map into a three-channel displacement field through the registration head: Among them, the initial weights Ensure smooth deformation.

7. The method according to any one of claims 1-6, characterized in that, Verify the registration accuracy through comparative experiments. The method compares with four advanced methods in 2024. The Dice coefficient is increased by 2.875% (LPBA40) and 3.775% (Mindboggle) on average, the HD95 is decreased by 0.440 (LPBA) and 0.308 (Mindboggle) on average, and the number of model parameters is reduced by 28.475M on average.

Images