A multi-source remote sensing image registration method based on decoupled feature mutual information

Abstract

The present invention discloses a multi-source remote sensing image registration method based on decoupled feature mutual information, normalizes optical images and SAR images in terms of scale and dimension, performs speckle denoising on SAR images, and constructs network training data sets and test sets; builds a feature decoupling network and a registration field estimation network based on a convolutional neural network; trains the built network, sends the optical image and the SAR image into the built feature decoupling network, extracts shared features and unique features based on a mutual information maximization strategy, sends the shared features into the built registration field estimation network, and estimates the registration field; registers the images using the trained model to obtain a registration result. The present invention proposes a feature decoupled optical-SAR image registration method based on mutual information, extracts shared features of optical and SAR images using a neural network, and estimates the registration field based on the shared features, thereby improving the accuracy of optical-SAR image registration.

Description

Technical Field

[0001] The invention relates to the field of remote sensing image registration, and in particular to a multi-source remote sensing image registration method based on decoupled feature mutual information optical-SAR images. Background Art

[0002] Synthetic Aperture Radar (SAR) is an active sensor with a satellite-borne microwave energy source. Microwave radiation has a long wavelength, is not affected by weather conditions, can provide images continuously, and excels in characterizing the structural properties of surface objects. However, backscatter from the sensor tends to produce speckle noise, reducing clarity and detail. Although SAR images have high-quality surface details and robustness, they are still limited in practical applications. Currently, many Earth observation applications rely mainly on spectral data.

[0003] Optical satellites rely on solar illumination as an energy source, capturing reflected sunlight from objects, and are more susceptible to weather conditions and time. In rainy or humid areas, optical images are not always available due to cloud cover. In addition, in emergency situations such as natural disasters (such as earthquakes, tsunamis, etc.), rapid data acquisition is an extremely critical issue. In this case, additional information from optical data can greatly advance SAR data processing.

[0004] SAR and optical images provide complementary information about the imaged area, and the fusion of these images helps to generate an image rich in spatial and spectral information. Analysis of the fused images helps to better understand and interpret the imaged area.

[0005] Mutual information is a measure used in information theory to evaluate the degree of dependence between two random variables. Mutual information estimation and maximization is a means of representation learning, but the mutual information of high-dimensional variables is difficult to calculate. Estimating the mutual information between high-dimensional continuous random variables through gradient descent on neural networks, or learning unsupervised representation by maximizing mutual information, cannot solve these problems well, and the accuracy of registration cannot be improved. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to provide a multi-source remote sensing image registration method based on decoupled feature mutual information optical-SAR images.

[0007] Technical solution: The present invention comprises the following steps:

[0008] (1) Normalize the scale and dimension of optical images and SAR images, perform speckle denoising on SAR images, and construct network training and test data sets;

[0009] (2) Building feature decoupling network and registration field estimation network based on convolutional neural network;

[0010] (3) training the network constructed in step (2), sending the optical image and the SAR image to the feature decoupling network constructed in step (2), extracting shared features and unique features based on the strategy of maximizing mutual information, and sending the shared features to the constructed registration field estimation network to estimate the registration field;

[0011] (4) Use the trained model obtained in step (3) to align the images and obtain the alignment result.

[0012] Further, step (1) comprises:

[0013] (1.1) Lee filtering is performed on SAR images to suppress speckle noise;

[0014] (1.2) Normalize the scale and dimension of the optical image and the SAR image;

[0015] (1.3) Perform random projection transformation on the SAR image, record the displacement of the four corner points before and after the transformation, and use the matching points and their displacements before and after the transformation to find the unique solution of the homography matrix;

[0016] (1.4) The images are divided into training set and test set in a ratio of 8:2 for subsequent network training and registration effect testing.

[0017] Furthermore, the step (2) comprises:

[0018] (2.1) Construct a feature decoupling network based on mutual information;

[0019] (2.2) Construct a registration field estimation network.

[0020] Furthermore, the step (3) comprises:

[0021] (3.1) Input the optical and SAR image training datasets into the optical and SAR image decoupling network branches respectively to extract shared features and unique features;

[0022] (3.2) Input the unique features obtained in step (3.1) into the unique feature discrimination network to classify the source of the features;

[0023] (3.3) Calculate the loss function based on the output of the model obtained in step (3.1) and step (3.2), use the back propagation algorithm to calculate the gradient of the loss function of the feature decoupling network based on mutual information to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient;

[0024] (3.4) splicing the optical image shared features and the SAR image shared features obtained in step (3.1) and inputting them into the registration field estimation network;

[0025] (3.5) Calculate the loss function based on the output of the model obtained in step (3.4) and the true value of the displacement vector of the matching point obtained in step (3.1), use the back propagation algorithm to calculate the gradient of the loss function of the registration field estimation network to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient;

[0026] (3.6) Repeat steps (3.1) to (3.5) until the maximum number of iterations is reached and save the model.

[0027] Furthermore, the shared feature extraction network structure in step (3.1) includes:

[0028] The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed;

[0029] After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed;

[0030] After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a shared feature map M^s with a size of (128, 30, 30), and performs a ReLU operation;

[0031] The output of the third convolutional layer is flattened and input into the first fully connected layer to output the shared feature S with a dimension of (1,32).

[0032] Furthermore, the unique feature extraction network structure of step (3.1) includes:

[0033] The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed;

[0034] After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed;

[0035] After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a unique feature map Me with a size of (128, 30, 30), and performs a ReLU operation;

[0036] The output of the third convolutional layer is flattened and input into the first fully connected layer to output the unique feature E with a size of (1, 32).

[0037] Furthermore, the unique feature discrimination network structure of step (3.2) includes:

[0038] After the first fully connected layer, the output size is (1, 200) and the ReLU operation is performed;

[0039] After the second fully connected layer, the output size is (1, 1).

[0040] Furthermore, the loss function of the feature decoupling network based on mutual information in step (3.3) is as follows:

[0041] Loss D =L MI +L sh +L c

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] L sh =||S o -S s ||1

[0048] L c =-(1-y)log(1-y′)-ylog(y′)

[0049] Among them, L MI , L sh , L cThey are mutual information loss, shared feature loss and classification loss respectively; They are the optical image feature map and SAR image feature map when extracting shared features; S o , S s They are the shared features of optical images and the shared features of SAR images respectively; is the mutual information estimator based on Jensen-Shannon divergence; C(·) is the local feature representation of the feature map; They are the optical image feature map and SAR image feature map when extracting unique features; E o , E s are the unique features of optical images and SAR images respectively; ||·||1 is the 1-norm operation; y is the true value of the unique feature source, and y′ is the output of the unique feature discrimination network.

[0050] Furthermore, the loss function of the registration field estimation network in step (3.5) is as follows:

[0051]

[0052] Where n is the number of training sample pairs, D is the true value of the matching point displacement vector, and D′ is the predicted value of the matching point displacement vector output by the registration field estimation network.

[0053] Furthermore, the step (4) includes: using the trained model to register the images, inputting the optical-SAR image pair to be registered into the model obtained in step (3.6), and decoupling the features; inputting the obtained shared features into the registration field estimation network to obtain the displacement vector of the matching point; calculating the homography transformation matrix according to the displacement vector of the matching point, transforming the SAR image, and obtaining the registration result.

[0054] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0055] The neural network is used to extract the shared features of optical and SAR images, which effectively captures the similarities and correlations between the two different modal images. By extracting the shared features, the dimension and redundancy of the features can be reduced, and the efficiency and accuracy of the registration can be improved.

[0056] The mutual information-based loss function is used for training, which can maximize the mutual information between images, thereby better retaining the relevant information of the images and improving the accuracy and robustness of the registration;

[0057] The entire registration process is uniformly optimized using end-to-end neural network learning, avoiding the complex process of manually designing feature extractors and aligners in traditional methods and simplifying the registration process. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a flow chart of the present invention;

[0059] Figure 2 It is a framework diagram of the present invention;

[0060] Figure 3 The structural diagram of the feature decoupling network and the registration field estimation network;

[0061] Figure 4 To decouple the distribution of shared and unique features;

[0062] Figure 5 This is a diagram showing the registration effect of the present invention. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0064] like Figure 1 , Figure 2 As shown, the present invention comprises the following steps:

[0065] (1) Normalize the scale and dimension of optical images and SAR images, perform speckle denoising on SAR images, and construct network training and test data sets;

[0066] (1.1) Lee filtering is performed on SAR images to suppress speckle noise;

[0067] (1.2) Normalize the scale and dimension of the optical image and the SAR image; make the image size 64*64 and the image format grayscale.

[0068] (1.3) Perform random projection transformation on the SAR image, record the displacement of the four corner points before and after the transformation, and use the matching points and their displacements before and after the transformation to find the unique solution of the homography matrix;

[0069]

[0070] It is impossible to use a deep neural network to directly estimate the value of each element of the homography transformation matrix. The unique solution of the homography matrix can be obtained using the matching points before and after the four transformations. Similarly, the unique solution of the homography matrix can also be obtained using the displacement of the matching points before and after the four transformations.

[0071] (1.4) The images are divided into training set and test set in a ratio of 8:2 for subsequent network training and registration effect testing.

[0072] (2) Building feature decoupling network and registration field estimation network based on convolutional neural network;

[0073] (2.1) Construct a feature decoupling network based on mutual information; Figure 3 As shown in the figure, for optical images and SAR images, there are two network branches: shared feature extraction and unique feature extraction and discrimination. The feature extraction network has the same architecture but does not share parameters. It contains 3 convolutional layers and 1 fully connected layer. ReLU operation and batch normalization operation are performed after each convolution. The unique feature discrimination network contains 2 fully connected layers. ReLU operation is performed after the first fully connected layer, and Sigmoid operation is performed after the second fully connected layer to classify the unique feature category.

[0074] (2.2) Construct the registration field estimation network. The registration field estimation network consists of three fully connected layers. The first and second fully connected layers are followed by ReLU operations, and the third fully connected layer directly outputs the predicted point displacement vector D′=[Δx1, Δy1, Δx2, Δy2, Ax3, Δy3, Δx4, Δy4].

[0075] (3) training the network constructed in step (2), sending the optical image and the SAR image to the feature decoupling network constructed in step (2), extracting shared features and unique features based on the strategy of maximizing mutual information, and sending the shared features to the constructed registration field estimation network to estimate the registration field;

[0076] (3.1) Input the optical and SAR image training datasets into the optical and SAR image decoupling network branches respectively to extract shared features and unique features;

[0077] The shared feature extraction network structure includes:

[0078] The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed;

[0079] After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed;

[0080] After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a shared feature map M^s with a size of (128, 30, 30), and performs a ReLU operation;

[0081] The output of the third convolutional layer is flattened and input into the first fully connected layer to output the shared feature S with a dimension of (1, 32).

[0082] The unique feature extraction network structure includes:

[0083] The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed;

[0084] After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed;

[0085] After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a unique feature map M e , size is (128, 30, 30), and ReLU operation is performed;

[0086] The output of the third convolutional layer is flattened and input into the first fully connected layer to output the unique feature E with a size of (1, 32).

[0087] (3.2) Input the unique features obtained in step (3.1) into the unique feature discrimination network to classify the source of the features;

[0088] The unique feature discrimination network structure includes:

[0089] After the first fully connected layer, the output size is (1, 200) and the ReLU operation is performed;

[0090] After the second fully connected layer, the output size is (1, 1).

[0091] (3.3) Calculate the loss function based on the output of the model obtained in step (3.1) and step (3.2), use the back propagation algorithm to calculate the gradient of the loss function of the feature decoupling network based on mutual information to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient;

[0092] The loss function of the feature decoupling network based on mutual information is as follows:

[0093] Loss D =L MI +L sh +Lc

[0094]

[0095]

[0096]

[0097]

[0098] L sh =||S o -S s ||1

[0099] L c =-(1-y)log(1-y′)-ylog(y′)

[0100] Among them, L MI , L sh , L c They are mutual information loss, shared feature loss and classification loss respectively; They are the optical image feature map and SAR image feature map when extracting shared features; S o , S s They are the shared features of optical images and the shared features of SAR images respectively; is the mutual information estimator based on Jensen-Shannon divergence; C(·) is the local feature representation of the feature map; They are the optical image feature map and SAR image feature map when extracting unique features; E o , E s are the unique features of optical images and SAR images respectively; ||·||1 is the 1-norm operation; y is the true value of the unique feature source, and y′ is the output of the unique feature discrimination network.

[0101] (3.4) The optical image shared feature S obtained in step (3.1) o , SAR image shared features S s Splicing is performed and input into the registration field estimation network. The registration field estimation network structure is as follows:

[0102] The input feature size is (1, 64), after the first fully connected layer, the output size is (1, 500), and the ReLU operation is performed.

[0103] After the second fully connected layer, the output size is (1, 100) and the ReLU operation is performed.

[0104] After the third fully connected layer, the predicted value D^′ of the matching point displacement vector is output, with a size of (1, 8).

[0105] (3.5) Calculate the loss function based on the output of the model obtained in step (3.4) and the true value of the displacement vector of the matching point obtained in step (3.1), use the back propagation algorithm to calculate the gradient of the loss function of the registration field estimation network to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient;

[0106] The loss function of the registration field estimation network is shown as follows:

[0107]

[0108] Where n is the number of training sample pairs, D is the true value of the matching point displacement vector, and D′ is the predicted value of the matching point displacement vector output by the registration field estimation network.

[0109] (3.6) Repeat steps (3.1) to (3.5) until the maximum number of iterations is reached and save the model.

[0110] (4) Use the trained model obtained in step (3) to align the images and obtain the alignment result.

[0111] Use the trained model to register the images, input the optical-SAR image pair to be registered into the model obtained in step (3.6) to decouple the features; input the obtained shared features into the registration field estimation network to obtain the displacement vector of the matching point; calculate the homography transformation matrix based on the displacement vector of the matching point, transform the SAR image, and obtain the registration result.

[0112] Next, the feature decoupling optical-SAR image registration method based on mutual information proposed in this invention is verified by taking the OSDstaset dataset as an example through actual data.

[0113] like Figure 4 As shown in the figure, the optical image and the SAR image are decoupled in the image decoupling network proposed in the present invention to obtain the distribution map of shared features and unique features. Through the decoupling network, the shared features and unique features of the two images can be effectively separated, while reducing the differences in shared features between multi-source images and increasing the differences in unique features. Image decoupling can reduce the dimension and redundancy of features, providing accurate feature representation for subsequent registration tasks.

[0114] like Figure 5 As shown in FIG. 1 , the registration effect diagram of the optical image and the SAR image in the feature decoupled optical-SAR image registration method based on mutual information of the present invention is shown in FIG. The proposed method can automatically learn the relationship between image features and apply it to the registration task, thereby achieving a good registration effect.

Claims

1. A multi-source remote sensing image registration method based on decoupled feature mutual information, characterized in that: The steps include: (1) Normalize the scale and dimension of optical images and SAR images, perform speckle denoising on SAR images, and construct network training and test data sets; (2) Based on the convolutional neural network, a feature decoupling network and a registration field estimation network are built. The registration field estimation network consists of three fully connected layers. The first and second fully connected layers are followed by a ReLU operation, and the third fully connected layer directly outputs the predicted displacement vector of the matching point. (3) training the network constructed in step (2), sending the optical image and the SAR image to the feature decoupling network constructed in step (2), extracting shared features and unique features based on the strategy of maximizing mutual information, and sending the shared features to the constructed registration field estimation network to estimate the registration field; (4) Use the trained model obtained in step (3) to register the images and obtain the registration result. The step (3) comprises: (3.1) Input the optical and SAR image training datasets into the optical and SAR image decoupling network branches respectively to extract shared features and unique features; (3.2) Input the unique features obtained in step (3.1) into the unique feature discrimination network to classify the source of the features; (3.3) Calculate the loss function based on the output of the model obtained in step (3.1) and step (3.2), use the back propagation algorithm to calculate the gradient of the loss function of the feature decoupling network based on mutual information to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient; (3.4) splicing the optical image shared features and the SAR image shared features obtained in step (3.1) and inputting them into the registration field estimation network; (3.5) Calculate the loss function based on the output of the model obtained in step (3.4) and the true value of the displacement vector of the matching point obtained in step (3.1), use the back propagation algorithm to calculate the gradient of the loss function of the registration field estimation network to the model parameters, and use the Adam optimization algorithm to update the network parameters based on the calculated gradient; (3.6) Repeat steps (3.1) to (3.5) until the maximum number of iterations is reached and save the model.

2. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The step (1) comprises: (1.1) Lee filtering is performed on SAR images to suppress speckle noise; (1.2) Normalize the scale and dimension of the optical image and the SAR image; (1.3) Perform random projection transformation on the SAR image, record the displacement of the four corner points before and after the transformation, and use the matching points and their displacements before and after the transformation to find the unique solution of the homography matrix; (1.4) The images are divided into training set and test set in a ratio of 8:2 for subsequent network training and registration effect testing.

3. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The step (2) comprises: (2.1) Construct a feature decoupling network based on mutual information; (2.2) Construct the registration field estimation network.

4. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The shared feature extraction network structure of step (3.1) includes: The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed; After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed; After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a shared feature map M^s with a size of (128, 30, 30), and performs a ReLU operation; The output of the third convolutional layer is flattened and input into the first fully connected layer to output the shared feature S with a dimension of (1, 32).

5. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The unique feature extraction network structure of step (3.1) includes: The image input layer size is (1, 64, 64). After the first convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 64, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the first convolution layer is (64, 64, 64), and ReLU operation and batch normalization operation are performed; After the second convolution layer, the convolution kernel size is (5*5), the step size is 1, the number of convolution kernels is 128, and the surrounding pixels are padded with 0 to ensure that the size of the array remains unchanged after convolution. The output size of the second convolution layer is (128, 64, 64), and ReLU operation and batch normalization operation are performed; After the third convolution layer, the convolution kernel size is (5*5), the step size is 2, the number of convolution kernels is 256, and the third convolution layer outputs a unique feature map M e , size is (128, 30, 30), and ReLU operation is performed; The output of the third convolutional layer is flattened and input into the first fully connected layer to output the unique feature E with a size of (1, 32).

6. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The unique feature discrimination network structure of step (3.2) includes: After the first fully connected layer, the output size is (1, 200) and the ReLU operation is performed; After the second fully connected layer, the output size is (1, 1).

7. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The loss function of the feature decoupling network based on mutual information in step (3.3) is as follows: Loss D =L MI +L sh +L c L sh =||S o -S s ||1 L c =-(1-y)log(1-y′)-ylog(y′) Among them, L MI , L sh , L c They are mutual information loss, shared feature loss and classification loss respectively; They are the optical image feature map and SAR image feature map when extracting shared features; S o , S s They are the shared features of optical images and the shared features of SAR images respectively; is the mutual information estimator based on Jensen-Shannon divergence; C(·) is the local feature representation of the feature map; They are the optical image feature map and SAR image feature map when extracting unique features; E o , E s are the unique features of optical images and SAR images respectively; ||·||1 is the 1-norm operation; y is the true value of the unique feature source, and y′ is the output of the unique feature discrimination network.

8. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The loss function of the registration field estimation network in step (3.5) is as follows: Where n is the number of training sample pairs, D is the true value of the matching point displacement vector, and D′ is the predicted value of the matching point displacement vector output by the registration field estimation network.

9. The multi-source remote sensing image registration method based on decoupled feature mutual information according to claim 1, characterized in that: The step (4) comprises: using the trained model to register the images, inputting the optical-SAR image pair to be registered into the model obtained in step (3.6), and decoupling the features; inputting the obtained shared features into the registration field estimation network to obtain the displacement vector of the matching point; calculating the homography transformation matrix according to the displacement vector of the matching point, transforming the SAR image, and obtaining the registration result.

Images