A registration-free medical image fusion method based on state selection feature aggregation

Abstract

This invention relates to a registration-free medical image fusion method based on state selection feature aggregation, belonging to the field of medical image fusion. The invention includes: inputting unregistered multimodal medical images to be fused into a block feature encoding module to obtain block-encoded features; aggregating global offset information into state features using a Mamba model; selecting an information aggregation path for each block using the state features as a benchmark; aggregating offset features in adjacent blocks according to the predicted aggregation path; constraining the output of the registration-free offset aggregation network using strictly aligned features extracted by a feature encoder with fixed parameters to obtain offset-eliminating features; inputting the offset-eliminating features into a feature fusion module, and reconstructing the final fused image through feature fusion in both spatial and channel dimensions. This invention solves the problems of artifacts, modality loss, and offset caused by spatial misalignment of the source images in the fusion result, improving the quality and usability of the fusion result.

Description

Technical Field

[0001] This invention relates to a registration-free medical image fusion method based on state selection feature aggregation, belonging to the field of medical image fusion technology. Background Technology

[0002] Existing multimodal medical image fusion techniques primarily generate images containing more comprehensive lesion information by integrating data from different imaging modalities. These methods largely rely on image registration to ensure strict pixel-level alignment of images across modalities, thereby enabling subsequent fusion processes to achieve better results. However, this two-stage processing approach has many limitations in real-world applications, especially cross-modal image registration, which often faces challenges due to inconsistencies in features between modalities. Furthermore, while some existing methods attempt to integrate registration and fusion into a unified framework to improve their synergistic effect, these methods typically require multiple independent feature encoders in their model design, leading to high model complexity, a large number of parameters, and difficulty in coordinating the performance requirements of fusion and registration. In particular, the performance of these methods is often unsatisfactory when dealing with elastic transformations or preserving complementary information in multimodal images. Moreover, some single-stage unregistered fusion methods only address feature alignment under rigid transformations and cannot effectively solve the alignment requirements under elastic deformation, which is particularly insufficient in the complex scenarios of multimodal medical images. Therefore, this invention proposes a registration-free medical image fusion method based on state-selective feature aggregation. Summary of the Invention

[0003] The technical problem solved by this invention is that it provides a registration-free medical image fusion method based on state selection feature aggregation to solve the problem of spatial misalignment of multimodal medical image pairs, which leads to artifacts, modality loss and offset in the fusion result. This invention improves the accuracy and efficiency of registration and fusion of multimodal medical image pairs, and significantly improves the accuracy and robustness of multimodal medical image fusion.

[0004] The technical solution of this invention is: a registration-free medical image fusion method based on state selection feature aggregation, the method comprising:

[0005] Step 1: Obtain the training dataset for fusion of unregistered multimodal medical images;

[0006] Step 2: Input the unregistered multimodal medical images to be fused into the block feature encoding module to obtain block encoded features;

[0007] Step 3: Use the Mamba model to aggregate global offset information into state features;

[0008] Step 4: Using the state features as a benchmark, select the information aggregation path for each block;

[0009] Step 5: Based on the predicted aggregation path, aggregate the offset features in adjacent blocks;

[0010] Step 6: Use the strictly aligned features extracted by the feature encoder with fixed parameters to constrain the output of the registration-free offset aggregation network in order to obtain features that eliminate offset.

[0011] Step 7: Input the offset-eliminating features into the feature fusion module, and reconstruct the final fused image by fusing features in the spatial and channel dimensions.

[0012] Furthermore, in Step 1, each pair of multimodal medical images in the training dataset for unregistered multimodal medical image fusion consists of a set of complementary medical images, including MRI, CT; MRI, PET; MRI, SPECT; and each image has a resolution of 256×256.

[0013] The dataset of multimodal medical images is preprocessed by randomly reversing the data and normalizing the processed data to the range [0, 1].

[0014] Further, Step 2 includes:

[0015] For each pair of multimodal medical images, one of them is designated as the reference image. Another image is used as the moving image and aligned with the reference image, denoted as... Reference image and moving images The encoded features are obtained by inputting them into the encoder, and are denoted as the reference image features. and moving image features ; in features , Add learnable positional encoding And use bilinear interpolation to resample the position encoding; to obtain features Specifically, it is expressed as:

[0016] ;

[0017] in, Indicates bilinear interpolation;

[0018] Following this, the encoded features infused with location information were... Block coding is performed to obtain block-coded features that can adapt to the input of the Mamba model. and ,in and This represents the block features obtained from the encoding.

[0019] Furthermore, Step 3 includes:

[0020] Extracted block-encoded features and The features are concatenated into a sequence consisting of block-coded features, with a learnable class token feature introduced at the beginning of the sequence. and The sequence is fed into the Mamba model, where features are aggregated from three different directions to obtain a final state representation that incorporates information from these different directions. , and The gradient is propagated using class token features introduced into the sequence. Specifically, the class token features are... and After linear layer mapping, and , and Addition to pass gradients:

[0021] ;

[0022] in, Indicates a linear layer. This indicates a cascaded operation; in this case, the state characteristics are... It contains global offset information.

[0023] Furthermore, Step 4 includes:

[0024] State characteristics As an initial state, the block-encoded features and In the same position and The output is obtained by performing state selection calculation. Specifically:

[0025] ;

[0026] ;

[0027] in, , , It is the state selection matrix used for feature mapping. These are implicit features generated during the feature mapping process;

[0028] Will Vector mapping to the current number Each block feature is labeled with adjacent block labels; the selected adjacent blocks are used as blocks containing offset features, providing a reference for the next offset feature aggregation operation; by performing the above operation on all block features in the sequence, the information aggregation path is obtained. .

[0029] Furthermore, Step 5 includes:

[0030] For block coding features For each token in the process, the path is aggregated based on the predicted information. Filter out offset feature sequences containing offset information Then use the Mamba model to... As the initial input, the offset feature sequence is then traversed. Each time, a block from the offset feature sequence is used as input to the Mamba model, ultimately resulting in a token feature that aggregates all offset features. In practice, a scan-select algorithm is used to perform parallel processing on the GPU. The above operations are performed to obtain the motion image features after offset removal. .

[0031] Furthermore, Step 6 includes:

[0032] When training the registration-free offset aggregation network, the image will be moved. Corresponding reference image Registration Labels Input to a feature encoder with fixed parameters In this process, the feature registration labels of the moving image were obtained. Registering labels using moving image features To constrain the output of the registration-free offset aggregation network;

[0033] Calculate the registration label features of moving images Compared with the moving image features after offset removal Feature alignment loss :

[0034] .

[0035] Furthermore, Step 7 includes:

[0036] (1) In the channel feature fusion module Next, the block-coded features to be merged will be... Compared with the moving image features after offset removal Mapping to the feature space corresponding to the channel dimension, calculating the channel feature similarity between them, and using the obtained channel similarity matrix to enhance their respective features, resulting in channel fusion features. Channel feature fusion module The calculation process is shown below:

[0037] ;

[0038] in, Represents convolution. This represents the feature shape transformation of the channel dimension. Indicates a feature cascade operation;

[0039] (2) A spatial feature fusion module was designed. ;exist In this process, the features to be fused are expanded in a spatial dimension, and the fused features are enhanced by calculating a spatial attention matrix, resulting in more detailed spatial fused features. Spatial Feature Fusion Module The operation process is as follows:

[0040] ;

[0041] in Represents shape transformations in spatial dimensions;

[0042] After obtaining channel fusion characteristics and spatial integration features Then, they are cascaded and fed into the final output layer to obtain the final fused image. .

[0043] Furthermore, Step 7 also includes:

[0044] Using structural loss To optimize network parameters and ensure structural consistency between the fused image and the source image:

[0045] ;

[0046] in, Represents moving images Corresponding reference image The registration label, SSIM() represents structural similarity calculation;

[0047] Pixel intensity loss was also introduced. This is used to ensure good contrast in the fusion results.

[0048] ;

[0049] in, This indicates the operation of retrieving the maximum value;

[0050] Gradient loss was introduced. To prevent the loss of edge details in the source image:

[0051] ;

[0052] in, This represents the gradient operator.

[0053] The beneficial effects of this invention are:

[0054] 1. This invention satisfies the dual requirements of feature alignment and feature fusion by employing a single image feature encoding module; it provides spatially consistent features for subsequent feature fusion, and solves the artifacts and misalignment problems caused by spatial mismatch of the source images in the practical application of medical image fusion.

[0055] 2. This invention utilizes a registration-free feature correction module; by predicting the overall offset features, the offset path of the features is obtained based on this; by aggregating the features offset to adjacent blocks, the offset of the moving features relative to the reference features is corrected.

[0056] 3. The offset correction mechanism of this invention not only avoids explicit registration and reduces the computational overhead during registration resampling; compared with traditional registration methods, it also inherits feature encoding and feature correction in the same encoding framework, eliminating the need to design a separate computational network for the deformation field, greatly simplifying the network framework and improving the algorithm execution efficiency.

[0057] 4. This invention addresses the problem of multimodal medical image fusion by constructing a dual-branch feature fusion network that enhances the fusion features in both the channel and spatial dimensions. Combined with a registration-free feature correction module, registration and fusion are integrated into a unified framework, solving the current difficulty of achieving fusion of unregistered multimodal medical images within the same framework.

[0058] 5. Based on the sample metrics collected from experiments on publicly available datasets, the method proposed in this invention can effectively fuse unregistered medical images, outperforming existing methods and improving the accuracy and efficiency of registration and fusion, thereby significantly enhancing the accuracy and robustness of multimodal medical image fusion. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the process structure of the present invention;

[0060] Figure 2 This is a schematic diagram of the block feature encoding module of the present invention;

[0061] Figure 3 This is a schematic diagram of the global offset aggregation module of the present invention;

[0062] Figure 4 This is a schematic diagram of the offset feature aggregation and correction module of the present invention;

[0063] Figure 5 This is a schematic diagram of the feature fusion module of the present invention;

[0064] Figure 6 This is a comparison chart of the experimental results of the method of the present invention and existing methods. Detailed Implementation

[0065] Example 1: As Figures 1-6 As shown, a registration-free medical image fusion method based on state selection feature aggregation is described, the method comprising:

[0066] Step 1: Obtain the training dataset for unregistered multimodal medical image fusion; each multimodal medical image pair in the training dataset for unregistered multimodal medical image fusion consists of a set of complementary medical images, including MRI, CT; MRI, PET; MRI, SPECT; each image has a resolution of 256×256;

[0067] The dataset of multimodal medical images is preprocessed by randomly reversing the data and normalizing the processed data to the range [0, 1].

[0068] Step 2: Input the unregistered multimodal medical images to be fused into the block feature encoding module to obtain block encoded features; the encoded features can well preserve the complementary information of the multimodal medical images; specific operations are as follows: Figure 2 As shown;

[0069] Further, Step 2 includes:

[0070] For each pair of multimodal medical images, one of them is designated as the reference image. Another image is used as the moving image and aligned with the reference image, denoted as... Reference image and moving images The encoded features are obtained by inputting them into the encoder, and are denoted as the reference image features. and moving image features To ensure that the location information of each feature block can be perceived by subsequent networks after feature segmentation, in the feature... , Add learnable positional encoding And bilinear interpolation is used to resample the positional encoding, allowing it to adapt to the feature scale; thus obtaining the features. Specifically, it is expressed as:

[0071] ;

[0072] in, Indicates bilinear interpolation;

[0073] Following this, the encoded features infused with location information were... Perform patch encoding (i.e., patch embedding encoding) to obtain patch encoded features that can adapt to the input of the Mamba model. and ,in and This represents the block features obtained through encoding. Among them, the positional encoding features use learnable parameters in squares with a side length of 256 pixels. Unlike traditional 1D positional encoding, 2D positional encoding can adapt to sequence data of different lengths and is superior in terms of spatial position preservation.

[0074] Step 3: Utilize the global offset aggregation module in the Mamba model to aggregate global offset information into the state features. The Mamba model will aggregate global offset features comprehensively from different scan directions. The parameter updates of the Mamba model will combine category token features with state features. Specific operations are as follows: Figure 3 ;

[0075] Furthermore, Step 3 includes:

[0076] Extracted block-encoded features and The features are concatenated into a sequence consisting of block-coded features, with a learnable class token feature introduced at the beginning of the sequence. and The sequence is fed into the Mamba model, where features are aggregated from three different directions to obtain a final state representation that incorporates information from these different directions. , and By feature aggregation, global modal information is gathered into these state features. To address the issue of non-transferable gradients from state features, class token features introduced into the sequence are used to facilitate gradient transfer. Specifically, the class token features... and After linear layer mapping, and , and Addition to pass gradients:

[0077] ;

[0078] in, Indicates a linear layer. This indicates a cascaded operation; in this case, the state characteristics are... It includes global offset information; it should be noted that the scanning direction of features in Mamba is divided into three types: forward scanning from the beginning to the end of the sequence, reverse scanning from the end to the beginning of the sequence, and bidirectional scanning from both ends of the sequence towards the middle.

[0079] Step 4: Using the state features as a benchmark, select the information aggregation path for each block. The selection of the aggregation path will take global offset information as a reference and combine the actual situation of each block to predict their respective feature offsets to adjacent blocks, thereby constructing the feature aggregation path.

[0080] Furthermore, Step 4 includes:

[0081] In order to eliminate the spatial offset between the two features, the state features As an initial state, the block-encoded features and In the same position and The output is obtained by performing state selection calculation. Specifically:

[0082] ;

[0083] ;

[0084] in, , , It is the state selection matrix used for feature mapping. These are implicit features generated during the feature mapping process;

[0085] Will Vector mapping to the current number Each block feature is labeled with adjacent block labels; the selected adjacent blocks are used as blocks containing offset features, providing a reference for the next offset feature aggregation operation; by performing the above operation on all block features in the sequence, the information aggregation path is obtained. The data structure of the aggregation path is a vector of length n, where n represents the number of neighbors of the corresponding block. When the value in the vector is greater than a set threshold, it means that the neighbors of the block at that position contain offset features.

[0086] Step 5: Based on the predicted aggregation path, aggregate the offset features in adjacent blocks, including designs such as... Figure 4The offset feature aggregation and correction module shown realizes motion image feature correction through feature aggregation operations in adjacent blocks. In particular, the feature aggregation uses the aggregation path predicted in step 4 to construct an offset feature sequence containing offset information. The feature selection capability of the Mamba model is used to aggregate these offset features into the corresponding blocks, thereby realizing the spatial position offset of the motion feature relative to the reference feature.

[0087] Furthermore, Step 5 includes:

[0088] For block coding features For each token in the process, the path is aggregated based on the predicted information. Filter out offset feature sequences containing offset information Then use the Mamba model to... As the initial input, the offset feature sequence is then traversed. Each time, a block from the offset feature sequence is used as input to the Mamba model, ultimately resulting in a token feature that aggregates all offset features. In actual operation, a scanning selection algorithm is used, such as... Figure 4 As shown, parallel processing in the GPU The above operations are performed to obtain the motion image features after offset removal. .

[0089] Step 6: Constrain the output of the registration-free offset aggregation network using the strictly aligned features extracted by the feature encoder with fixed parameters, so as to obtain the features that eliminate the offset; wherein, the registration-free offset aggregation network is pre-trained using the MAE training paradigm.

[0090] Furthermore, Step 6 includes:

[0091] In order to ensure In this process, the spatial offset of features relative to the reference image can be effectively eliminated, and a feature encoder with the same architecture as the coding network used in the aforementioned feature encoding, namely the block feature encoding module, is constructed. The MAE training paradigm is used for pre-training. And fix its parameters; when training the registration-free offset aggregation network, move the image Corresponding reference image Registration Labels Input to a feature encoder with fixed parameters In this process, the feature registration labels of the moving image were obtained. Registering labels using moving image features To constrain the output of the registration-free offset aggregation network;

[0092] Calculate the registration label features of moving images Compared with the moving image features after offset removal Feature alignment loss :

[0093] .

[0094] Step 7: Input the offset-reduced features into the feature fusion module. By fusing features in both spatial and channel dimensions, the final fused image is reconstructed. Specific operations are as follows: Figure 5 As shown;

[0095] Furthermore, Step 7 includes:

[0096] (1) In order to maintain good visual consistency in the final fusion result, a channel feature fusion module was designed. By enhancing the fusion features in a high-dimensional feature space, a better fusion result can be obtained. Next, the block-coded features to be merged will be... Compared with the moving image features after offset removal Mapping to the feature space corresponding to the channel dimension, calculating the channel feature similarity between them, and using the obtained channel similarity matrix to enhance their respective features, resulting in channel fusion features. To achieve feature fusion along the channel dimension; Channel Feature Fusion Module The calculation process is shown below:

[0097] ;

[0098] in, Represents convolution. This represents the feature shape transformation of the channel dimension. Indicates a feature cascade operation;

[0099] (2) In order to ensure that the final fusion result retains the detailed information of the source image, a spatial feature fusion module was designed. ;exist In this process, the features to be fused are expanded in a spatial dimension, and the fused features are enhanced by calculating a spatial attention matrix, resulting in more detailed spatial fused features. Spatial Feature Fusion Module The operation process is as follows:

[0100] ;

[0101] in Represents shape transformations in spatial dimensions;

[0102] After obtaining channel fusion characteristics and spatial integration features Then, they are cascaded and fed into the final output layer to obtain the final fused image. .

[0103] Furthermore, Step 7 also includes:

[0104] Using structural loss To optimize network parameters and ensure structural consistency between the fused image and the source image:

[0105] ;

[0106] in, Represents moving images Corresponding reference image The registration label, SSIM() represents structural similarity calculation;

[0107] Pixel intensity loss was also introduced. This is used to ensure good contrast in the fusion results.

[0108] ;

[0109] in, This indicates the operation of retrieving the maximum value;

[0110] Gradient loss was introduced. To prevent the loss of edge details in the source image:

[0111] ;

[0112] in, This represents the gradient operator.

[0113] To verify the effectiveness of the method, the performance was evaluated on the CT-MRI, PET-MRI, and SPECT-MRI datasets downloaded from the Harvard public database. These three datasets contain 144, 194, and 261 images, respectively, all of 256×256 size. The present invention selected 2055 and 77 images for testing, respectively, and the remainder for model training. The proposed model was trained on a server platform equipped with an RTX4090 and a PyTorch environment. During training, the number of epochs was set to 3000, the learning rate to 2e-5, the batch size to 32, and the AdamW optimizer was used to update the network parameters.

[0114] Furthermore, the visual effects of this invention were compared with existing unregistered multimodal image fusion methods UMF-CMGR, SuperFusion, MURF, IMF, and the unregistered multimodal medical image fusion method PAMRFusion. The comparison results of the fusion results of this method with UMF-CMGR, SuperFusion, MURF, IMF, and PAMRFusion are as follows: Figure 6 As shown, the method proposed in this invention can better address the negative impact of spatial misregistration of source images on the final fusion result during medical image fusion, thereby obtaining a fused image with highly consistent spatial positions.

[0115] This invention effectively reduces model complexity by seamlessly embedding the registration process into the fusion process, avoiding the use of multiple independent feature encoders, thereby reducing the computational overhead and number of parameters in the model. On this basis, this method also effectively addresses the spatial offset problem between modal features through an innovative feature aggregation strategy, achieving improved accuracy and efficiency of registration and fusion while maintaining the integrity of complementary information, thus significantly improving the accuracy and robustness of multimodal medical image fusion.

[0116] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A registration-free medical image fusion method based on state selection feature aggregation, characterized in that: The method includes: Step 1: Obtain the training dataset for fusion of unregistered multimodal medical images; Step 2: Input the unregistered multimodal medical images to be fused into the block feature encoding module to obtain block encoded features; Step 3: Use the Mamba model to aggregate global offset information into state features; Step 4: Using the state features as a benchmark, select the information aggregation path for each block; Step 5: Based on the predicted aggregation path, aggregate the offset features in adjacent blocks; Step 6: Use the strictly aligned features extracted by the feature encoder with fixed parameters to constrain the output of the registration-free offset aggregation network in order to obtain features that eliminate offset. Step 7: Input the offset-eliminating features into the feature fusion module, and reconstruct the final fused image by fusing features in the spatial and channel dimensions. Step 2 includes: For each pair of multimodal medical images, one of them is designated as the reference image. Another image is used as the moving image and aligned with the reference image, denoted as... Reference image and moving images The encoded features are obtained by inputting them into the encoder, and are denoted as the reference image features. and moving image features ; in features , Add learnable positional encoding And use bilinear interpolation to resample the position encoding; to obtain features Specifically, it is expressed as: ； in, Indicates bilinear interpolation; Following this, the encoded features infused with location information were... Block coding is performed to obtain block-coded features that can adapt to the input of the Mamba model. and ,in and This represents the block features obtained from the encoding; Step 3 includes: Extracted block-encoded features and The features are concatenated into a sequence consisting of block-coded features, with a learnable class token feature introduced at the beginning of the sequence. and The sequence is fed into the Mamba model, where features are aggregated from three different directions to obtain a final state representation that incorporates information from these different directions. , and The gradient is propagated using class token features introduced into the sequence. Specifically, the class token features are... and After linear layer mapping, and , and Addition to pass gradients: ； in, Indicates a linear layer. This indicates a cascaded operation; in this case, the state characteristics are... It includes global offset information; Step 4 includes: State characteristics As an initial state, the block-encoded features and In the same position and The output is obtained by performing state selection calculation. Specifically: ； ； in, , , It is the state selection matrix used for feature mapping. These are implicit features generated during the feature mapping process; Will Vector mapping to the current number Each block feature is labeled with adjacent block labels; the selected adjacent blocks are used as blocks containing offset features, providing a reference for the next offset feature aggregation operation; by performing the above operation on all block features in the sequence, the information aggregation path is obtained. .

2. The registration-free medical image fusion method based on state selection feature aggregation according to claim 1, characterized in that: In Step 1, each pair of multimodal medical images in the training dataset for unregistered multimodal medical image fusion consists of a set of complementary medical images, including MRI and CT. MRI, PET; MRI and SPECT; each image has a resolution of 256×256; The dataset of multimodal medical images is preprocessed by randomly reversing the data and normalizing the processed data to the range [0, 1].

3. The registration-free medical image fusion method based on state selection feature aggregation according to claim 1, characterized in that: Step 5 includes: For block coding features For each token in the process, the path is aggregated based on the predicted information. Filter out offset feature sequences containing offset information Then use the Mamba model to... As the initial input, the offset feature sequence is then traversed. Each time, a block from the offset feature sequence is used as input to the Mamba model, ultimately resulting in a token feature that aggregates all offset features. In practice, a scan-select algorithm is used to perform parallel processing on the GPU. The above operations are performed to obtain the motion image features after offset removal. .

4. The registration-free medical image fusion method based on state selection feature aggregation according to claim 1, characterized in that: Step 6 includes: When training the registration-free offset aggregation network, the image will be moved. Corresponding reference image Registration Labels Input to a feature encoder with fixed parameters In this process, the feature registration labels of the moving image were obtained. Registering labels using moving image features To constrain the output of the registration-free offset aggregation network; Calculate the registration label features of moving images Compared with the moving image features after offset removal Feature alignment loss : 。 5. The registration-free medical image fusion method based on state selection feature aggregation according to claim 1, characterized in that: Step 7 includes: (1) In the channel feature fusion module Next, the block-coded features to be merged will be... Compared with the moving image features after offset removal Mapping to the feature space corresponding to the channel dimension, calculating the channel feature similarity between them, and using the obtained channel similarity matrix to enhance their respective features, resulting in channel fusion features. Channel feature fusion module The calculation process is shown below: ； in, Represents convolution. This represents the feature shape transformation of the channel dimension. Indicates a feature cascade operation; (2) A spatial feature fusion module was designed. ;exist In this process, the features to be fused are expanded in a spatial dimension, and the fused features are enhanced by calculating a spatial attention matrix, resulting in more detailed spatial fused features. Spatial Feature Fusion Module The operation process is as follows: ； in Represents shape transformations in spatial dimensions; After obtaining channel fusion characteristics and spatial integration features Next, the channel fusion features will be used. and spatial integration features The concatenated and input images are fed into the final output layer to obtain the final fused image. .

6. The registration-free medical image fusion method based on state selection feature aggregation according to claim 1, characterized in that: Step 7 also includes: Using structural loss To optimize network parameters and ensure structural consistency between the fused image and the source image: ； in, Represents moving images Corresponding reference image The registration label, SSIM() represents structural similarity calculation; Pixel intensity loss was also introduced. This is used to ensure good contrast in the fusion results. ； in, This indicates the operation of retrieving the maximum value; Gradient loss was introduced. To prevent the loss of edge details in the source image: ； in, This represents the gradient operator.

Images