A Visible Light-SAR Image Registration Algorithm Based on OS-SIFT

Abstract

A visible-light SAR image registration algorithm based on OS-SIFT computes the consistent gradient of the SAR image, the gradient magnitude image of the visible image, and the consistent gradient for each visible-light SAR image pair. Two Harris scale spaces are then constructed, and local maxima are searched in each Harris scale space to detect repeatable keypoints. Gradient position and orientation histogram descriptors are extracted from multiple image blocks to improve image saliency. Keypoint pairs are obtained using the NNDR method and further filtered using FSC. More accurate keypoint pairs are then filtered using translation, scale, and orientation constraints. FSC is then used again to remove outliers and identify the correct matching pairs. Finally, the transformation parameters between the SAR and visible images are calculated to register the visible-light SAR image pairs.

Description

Technical Field

[0001] The present invention belongs to the technical field of visible light image and synthetic aperture radar (SAR) image registration, and in particular relates to a visible light-SAR image registration algorithm based on optical-to-SAR-scale-invariant feature transform (OS-SIFT). Background Art

[0002] Remote sensing imagery, due to its convenience and intuitive nature, has gradually become an effective means of observing, describing, and analyzing Earth's surface features. Furthermore, as sensor imaging technology matures, the quality of remote sensing images continues to improve, and their variety is expanding, gradually moving towards multimodal, multispectral, multiresolution, and multitemporal characteristics. Because different image types contain different information, the combined use of multi-source remote sensing imagery to achieve information complementarity has gained increasing attention in recent years.

[0003] SAR is an active microwave imaging system for Earth observation. It uses radar motion to synthesize a small-aperture antenna into an equivalent large-aperture antenna. Similar to visible light images, synthetic aperture radar can achieve high-resolution, two-dimensional images of targets within the detection scene. SAR is an active microwave imaging system for Earth observation. It is capable of all-day, multi-weather imaging, can penetrate the Earth's surface, and is sensitive to man-made targets, especially metal targets, effectively compensating for the vulnerability of visible light images to weather.

[0004] In recent years, registration technology has been widely used in medical imaging, robotic vision, and remote sensing image applications due to its very important application value. There are two types of remote sensing image registration methods, namely grayscale (region)-based methods and feature-based methods. Grayscale-based registration methods refer to directly using the grayscale values ​​of the image and matching them using template matching. Feature-based registration methods do not directly operate on the grayscale information of the image, but rely on the similarity of significant features between images to achieve matching. Among them, in the feature-based registration process, feature extraction and feature matching need to be focused on. In this type of registration algorithm, selecting appropriate features is the key factor in determining whether the algorithm can be successful. Common features include points, lines, and surfaces.

[0005] Extracting image feature points primarily involves using the wavelet transform to perform multi-scale decomposition of the image. The modulus of the wavelet decomposition is then used to calculate the local maximum. The resulting extreme points are considered edge points in the image. After obtaining the feature points in the image, descriptors are typically constructed based on their locally invariant characteristics. Feature matching involves querying and establishing relationships between descriptors. The nearest neighbor distance ratio (NNDR) is the ratio of the nearest neighbor distance to the next nearest neighbor distance. This method first sets a threshold; a pair of points is considered a match when the ratio is smaller than the threshold. However, radiometric and geometric distortions may exist between images, necessitating the removal of false matches. A commonly used method for removing false matches is the Random Sample Consensus (RANSAC) method proposed by Fischler and Bolles. However, the RANSAC method also has limitations. It may contain outliers, is prone to non-optimal parameters, and its algorithm speed is significantly affected by the threshold parameter. Summary of the Invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a visible light-SAR image registration algorithm based on OS-SIFT, in order to solve the problems of insufficient robustness and low key point detection accuracy of the current registration algorithm.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is:

[0008] A visible light-SAR image registration algorithm based on OS-SIFT includes the following steps:

[0009] Step 1: Input the visible light-SAR image pair and calculate the consistent gradient of the SAR image;

[0010] Step 2: Calculate the gradient magnitude image of the visible light image, and calculate the consistent gradient of the visible light image based on this;

[0011] Step 3: construct two Harris scale spaces and search for local maxima in the two Harris scale spaces to detect repeatable key points;

[0012] Step 4: First, the Euclidean distance of the nearest neighbor and the ratio of the Euclidean distance of the second nearest neighbor (NNDR) of the key point corresponding descriptor are used to constrain the key point pair PP set, and the fast sample consensus (FSC) algorithm is used to further filter the key point pairs. Then, the translation, scale and direction constraints of the key points are added for screening, and finally the FSC is used to filter the correct matching point pairs;

[0013] Step 5: Calculate the transformation parameters between the SAR image and the visible light image based on the correct matching point pairs, and register the visible light-SAR image pair.

[0014] Experimental results on measured images show that the present invention improves the accuracy of key point detection and the robustness of image registration. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the flow of the visible light-SAR image registration algorithm based on OS-SIFT in the present invention.

[0016] Figure 2 The first pair of images in this embodiment of the present invention is registered using the improved OS-SIFT algorithm. (a) is the SAR image; (b) is the visible light image; (c) is the corresponding key points; (d) is the fused image; and (e) is the checkerboard image.

[0017] Figure 3 The first pair of images in the embodiment of the present invention is registered using the OS-SIFT algorithm, where (a) is the corresponding key points, (b) is the fused image, and (c) is the chessboard image.

[0018] Figure 4 The second pair of images in this embodiment of the present invention is registered using the improved OS-SIFT algorithm. (a) is the SAR image; (b) is the visible light image; (c) is the corresponding key points; (d) is the fused image; and (e) is the checkerboard image.

[0019] Figure 5 The second pair of images is registered using the OS-SIFT algorithm in the present invention, where (a) represents the corresponding key points, (b) represents the fused image, and (c) represents the checkerboard image. DETAILED DESCRIPTION

[0020] The embodiments of the present invention are described in detail below with reference to the accompanying drawings and examples.

[0021] Visible light images have the characteristics of good imaging effect and good readability; SAR has the characteristics of all-day and all-weather coverage and strong penetration ability. Existing visible light-SAR image registration methods often have problems such as insufficient robustness and inaccurate detection. To achieve more accurate visible light-SAR image registration, this paper improves the visible light image feature point extraction algorithm based on OS-SIFT and improves the key point matching strategy.

[0022] The present invention comprises three main components: keypoint detection, direction assignment and descriptor extraction in two Harris scale spaces, and keypoint matching. Taking into account the inherent characteristics of SAR and optical images, the consistent gradients of the SAR and optical images are calculated using the multi-scale ratio of the exponentially weighted average and the isotropic Sobel operator. Two Harris scale spaces are then constructed based on this. Keypoints are detected by searching for local maxima in the scale space, and then localization is refined based on the spatial relationships of the keypoints. Furthermore, descriptors such as gradient position and direction histograms are extracted from multiple image patches to enhance recognition.

[0023] For visible light-SAR image pairs, refer to Figure 1 The process includes multi-scale ROEWA operator calculation, direction assignment, gradient calculation, key point detection, main direction assignment, and construction of multi-scale descriptors for SAR images; multi-scale Isotropic Sobel calculation for visible light images to obtain gradient amplitude images, multi-scale Isotropic Sobel operator calculation, direction assignment, gradient calculation, key point detection, main direction assignment, and construction of multi-scale descriptors for the gradient amplitude images; then NNDR constrained key point matching is performed on the processed SAR image and visible light image; FSC further constrains key point matching; translation, scaling, and rotation constrain key point matching; FSC constrains key point matching again; and finally obtains the transformation matrix.

[0024] Specifically, the present invention is based on the OS-SIFT visible light-SAR image registration algorithm, which includes the following specific steps:

[0025] Step 1: Calculate the consistent gradient of the SAR image.

[0026] Considering the inherent characteristics of SAR images and visible light images, and the reliability of the ROEWA operator for SAR images has been verified in multiple literatures, in this step, the multi-scale ROEWA operator with exponential weighted average is used to calculate the consistent gradient of the SAR image.

[0027] According to the coherent imaging mechanism, SAR images are often interfered by multiplicative speckle noise. The traditional differential gradient operator is greatly affected by the random high-frequency components caused by speckle, especially in high reflectivity uniform areas. After setting the threshold, some erroneous key points may be found in these areas. Therefore, using the traditional differential gradient operator to detect feature points will lead to an increase in the false detection rate. The gradient ratio (GR) used in the SAR-SIFT algorithm is specifically used for SAR images. The ROEWA operator is a ratio detector that calculates the exponentially weighted local mean. Utilizing the constant false alarm rate characteristic of the ROEWA detector, the gradient obtained by the GR method is highly robust to speckle noise. Therefore, this step uses the ROEWA operator to calculate the gradient amplitude and direction in the SAR image. The specific principle can be described as follows:

[0028] The ratio of exponentially weighted averages (ROEWA) is an improvement to the ratio of averages ROA, and is obtained by calculating the exponentially weighted local averages. For example, given a point (a, b), the direction is divided into four directions, namely 0, π / 4, π / 2, and 3π / 4. The average value of direction i = 3 (π / 2) is defined as:

[0029]

[0030] Where I represents the image pixel, M 1,α It represents the exponential weighted average of the upper half of the image along the π / 2 direction (a, b), M 2,α It represents the exponentially weighted average of the lower half of the image along the π / 2 direction (a, b), where α is the exponential weighting parameter.

[0031] As in ROA, the ratio in one direction and its normalization are defined as:

[0032]

[0033] T i,α Calculated along the horizontal (i=3) and vertical (i=1) directions. Similar to the gradient-based optical image edge detector, the edge image is obtained by the following method:

[0034]

[0035] Because the weighting parameter α allows adaptive smoothing of the image, ROEWA is more accurate in multi-scale edge images and more robust to noise than ROA, and can well estimate the gradient magnitude.

[0036] Step 2: Calculate the gradient magnitude image of the visible light image, and based on this, calculate the consistent gradient of the visible light image.

[0037] In this step, the exponentially weighted average multi-scale isotropic Sobel operator is used to calculate the gradient magnitude image of the visible light image. On this basis, the isotropic Sobel operator is used to calculate the consistent gradient, thereby obtaining the gradient magnitude gradient and direction of the visible light image. The isotropic Sobel operator template is as follows:

[0038]

[0039] Among them, f H is the horizontal gradient, f V is a vertical gradient.

[0040] The gradient calculated using the Isotropic Sobel operator is greatly affected by the size of the rectangular processing window. Therefore, by setting different values ​​for the template size, a multi-scale Isotropic Sobel operator can be obtained, as follows:

[0041]

[0042] In the formula and Respectively expressed in β j Horizontal and vertical gradients at different scales, The standard deviation used as the weight is β j Gaussian kernel, and Indicates size β j Horizontal and vertical rectangular windows, β j Equal to scale α j ,× represents matrix multiplication;

[0043]

[0044] The proposed gradient magnitude and gradient direction Defined as:

[0045]

[0046] In the formula and Represents the gradient amplitude The horizontal and vertical derivatives of the image are calculated using the Isotropic Sobel operator, that is, the β of the visible light image j Horizontal and vertical gradients at scale.

[0047] Step 3: Construct two Harris scale spaces and extract repeatable key points by finding local maxima in the two Harris scale spaces.

[0048] Corner points have higher stability and repeatability in both visible light and SAR images. Therefore, this step constructs two Harris scale spaces. By replacing the first-order derivative with a multi-scale gradient calculation, a multi-scale Harris function can be obtained:

[0049]

[0050]

[0051] In the formula and Represents the SAR image at α i The horizontal and vertical gradients under scale, d is an arbitrary parameter, Represents Gaussian kernel, * represents convolution, det represents the value of matrix determinant, tr represents matrix trajectory; finally, the SAR-Harris scale space R is established. S and the visible light Harris scale space R O .

[0052] The key points are extracted by finding the local maximum in the Gaussian scale space of three dimensions (x, y, α), and then performing sub-pixel positioning and unstable key point elimination through the Hessian matrix.

[0053] In step 4, the ratio of the Euclidean distance of the nearest neighbor to the second nearest neighbor (NNDR) of the key point corresponding descriptor is first used to constrain the key point pair PP set, and the fast sampling consensus (FSC) algorithm is used to further screen the key point pairs (i.e., the initial matching stage). Then, the translation, scale, and direction constraints of the key points are added for screening, and finally, the FSC is used to screen out the correct matching point pairs (i.e., the secondary matching stage).

[0054] Similarity transformations involve three parameters: translation, scale, and rotation. Under the similarity transformation model, correctly matched pairs have the same rotation angle, the same scale, the same horizontal displacement, and the same vertical displacement in space. Therefore, this step uses the inherent information of each keypoint (i.e., position, scale, and main orientation) to increase the number of correct correspondences.

[0055] In this step, the visible light image is defined as the reference image, and the SAR image is defined as the sensed image. Two key point sets P = p1, p2, ..., p are extracted from the reference image and the sensed image. i ,…,p M and P′=p′1,p′2,…,p′ i ,…,p′ M , reference image key point p i The position, scale and main direction are (xi ,y i ),s i ,θ i , the position, scale and main direction of the key point p′ of the sensed image are (x′ i ,y′ i ), s′ i ,θ′ i , corresponding to point p i and p′ position transformation error e p (i) is expressed as:

[0056] e p (i)=||(x i ,y i )-T((x i ',y i '),μ)|| (10)

[0057] Where T((x i ',y i '), μ) is the similarity transformation model, μ is the similarity transformation model parameter. At the same time, p i The scale error e s (i) and the main direction error e o (i) is expressed as:

[0058]

[0059] Where r * and Δθ * Denote the scale ratio and main direction difference between the reference image and the sensed image, Δθ i =θ i -θ′ i , indicating p i and p′ i The main direction difference.

[0060] As mentioned above, in the present invention, the matching stage can be divided into an initial matching stage and a secondary matching stage.

[0061] ① Initial matching stage

[0062] Keypoints are matched by the ratio of the Euclidean distance of the nearest neighbor to the second nearest neighbor of the corresponding descriptor (NNDR), and the threshold of the ratio is set to d ratio . We get the point pair set PP and establish the scale ratio r * , main bearing difference Δθ * , horizontal displacement Δx * and vertical displacement Δy * The histogram of r is obtained from the histogram * , Δθ * , Δx* and Δy * The FSC algorithm is used to further filter key point pairs from the point pair set PP.

[0063] ② Secondary matching stage

[0064] In the point pair set obtained by the first step, the r * , Δθ * , Δx * and Δy * The point pair set obtained in the first step is screened again to filter out the mismatched points, thereby obtaining more accurate similarity transformation model parameters on more accurate correct matching point pairs. * , Δθ * , Δx * and Δy * When performing false match filtering, define

[0065] PSO(i)=(1+e p (i))(1+e s (i))(1+e o (i)) (12)

[0066] During the second matching, only the point with the smallest PSO among the points selected in the first step is considered a candidate correct matching point. Point pairs with non-minimum PSO are then eliminated, resulting in more robust candidate matching points. FSC is then used to further select key point pairs and calculate the initial transformation parameter μ.

[0067] Step 5: Calculate the transformation parameters between the SAR image and the visible light image based on the correct matching point pairs selected in step 4. Based on the transformation parameters, the corresponding transformation matrix can be obtained, and then the visible light-SAR image pair can be registered.

[0068] The effects of the present invention are further illustrated by the following processing of measured data:

[0069] (1) Visual inspection of the chessboard mosaic image and the magnified sub-image

[0070] The SAR-Harris method sets the first scale to α1=2 and the constant between two adjacent scales to k=2. 1 / 2.5 The number of scales is 8, and the parameter d is set to 0.04. The parameters of the Optical-Harris method are the same as those of the SAR-Harris method. The threshold used in keypoint detection has a significant impact on detection performance and requires fine-tuning to obtain a reasonable number of keypoints for different data. The thresholds used here are 0.003 and 1 for SAR and visible light images, respectively.

[0071] In terms of descriptor extraction and keypoint matching, the gradient direction is quantized into 8 bins, and three GLOH-like circular neighborhoods of size {8α, 12α, 16α} are used to construct the descriptor. The ratio threshold used in the NNDR method is set to 0.9.

[0072] In the registration performance experiment, two pairs of measured images were used. The first and second pairs consisted of TerraSAR images and Google Earth images. The sampling resolution of these images was 1m / pixel. The TerraSAR image was set as the reference image, as shown in Figure 2. Figure 2 、 3 (a). The Google Earth image is set as the perception image, as shown in Figure 2 、 3 (b) The first pair of images used in the experiment depicts an airport in Tucson, Arizona, USA. It can be observed that there are rotational and translational differences between the SAR image and the visible light image in the first and second pairs of images.

[0073] The parameter settings in this measurement are the same as those in Measurement 1.

[0074] The experimental steps of the OS-SIFT registration algorithm of the present invention are:

[0075] 1) Use SAR-Harris to detect SAR image key points;

[0076] 2) Use the Isotropic Sobel operator to calculate the gradient of the original image gradient image;

[0077] 3) Use NNDR to perform the first key point matching;

[0078] 4) Use FSC to further screen key point pairs;

[0079] 5) Using the information of translation, scaling, and rotation between the reference image and the perceived image to further eliminate outliers to ensure the accuracy of the subsequent transformation matrix;

[0080] 6) Use FSC to remove residual outliers and obtain the transformation matrix between the reference image and the perceived image;

[0081] 7) Obtain the fused image.

[0082] The experimental steps of the traditional OS-SIFT registration algorithm are:

[0083] 1) Use SAR-Harris to detect SAR image key points;

[0084] 2) Visible light images use Sobel-Harris to detect key points in visible light images;

[0085] 3) Match the established multi-scale descriptors until a transformation matrix is ​​obtained;

[0086] 4) Obtain the fused image.

[0087] The registration performance is evaluated from three aspects. The first is visual inspection of the checkerboard image. The second is quantitative criteria, RMSE and CMR. The third is computational time.

[0088] The measured data results are as follows Figure 2 , 3, 4, and 5.

[0089] The first pair of images is Figure 2 and Figure 3 The scene depicts an airport, where the runway outline and surrounding facilities are clearly visible. The OS-SIFT algorithm takes into account the inherent characteristics of SAR and visible light imagery, successfully registering the two images. The improved OS-SIFT algorithm further enhances keypoint detection in visible light images, making the detected keypoints more stable and less susceptible to noise. The consistent gradient calculation is also robust to nonlinear intensity differences. Furthermore, the improved OS-SIFT algorithm imposes additional constraints on keypoint matching, removing more outliers and selecting more accurate corresponding point pairs. This makes it more reliable than the NNDR method used in the OS-SIFT algorithm. The improved OS-SIFT algorithm produces more correct corresponding point pairs than the OS-SIFT algorithm, resulting in a higher CMR. However, the RMSE is slightly higher than that of the OS-SIFT algorithm.

[0090] The second pair of images is Figure 4 and Figure 5 The scene depicts a residential area, where the outlines of buildings and some facilities are clearly visible. It is also clear that there are strong radiometric differences between the pair of images. Due to the different imaging mechanisms of SAR and visible light sensors, the appearance of buildings differs significantly, increasing the geometric distortion between the reference image and the perceived image. Both OS-SIFT and the improved algorithm based on OS-SIFT achieve registration for this pair of images. Due to the stability of the key points obtained by the improved algorithm based on OS-SIFT and the further point pair constraints of the key point matching algorithm, a higher CMR is achieved than OS-SIFT, while also achieving a lower RMSE for this pair of images. However, the increase in correctly matched point pairs also increases the computation time.

[0091] Table 1 also shows the runtime for two image pairs using the two compared algorithms. The computational complexity of SIFT-like algorithms depends significantly on the size of the descriptor and the number of keypoints. Regarding the number of keypoints, to ensure that the two algorithms can extract a similar number of keypoints, the detection threshold was fine-tuned to ensure that both algorithms extract a similar number of keypoints. Therefore, when the number of keypoints and matching point pairs is similar, the runtime of the two algorithms is relatively similar. When the number of keypoints is similar but the number of matching point pairs differs significantly, the runtime increases. All experiments were conducted in MATLAB 2017b software. Further improvement in computational efficiency can be achieved by implementing the proposed algorithm in C / C++.

[0092] Table 1 Comparison of RMSE, CMR and running time of measured images

[0093]

[0094] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A visible light-SAR image registration algorithm based on OS-SIFT, characterized by: The steps include: Step 1: Input the visible light-SAR image pair and use the multi-scale ROEWA operator with exponential weighted average to calculate the consistent gradient of the SAR image; Step 2: Use the exponentially weighted average multi-scale Isotropic Sobel operator to calculate the gradient magnitude image and the consistent gradient of the visible light image. The Isotropic Sobel operator template is as follows: Among them, f H is the horizontal gradient, f V is the vertical gradient; By setting different values ​​for the template size, a multi-scale Isotropic Sobel operator is obtained, as follows: In the formula and Respectively expressed in β j Horizontal and vertical gradients at different scales, The standard deviation used as the weight is β j Gaussian kernel, and Indicates size β j Horizontal and vertical rectangular windows, β j Equal to scale α j ,× represents matrix multiplication; The gradient magnitude is expressed as follows: Gradient amplitude and gradient direction Defined as: In the formula and Represents the gradient amplitude The horizontal and vertical derivatives of the image are calculated using the Isotropic Sobel operator, that is, the β of the visible light image j horizontal and vertical gradients at scale; Step 3: Construct two Harris scale spaces and search for local maxima in each of them to detect repeatable key points. The method is as follows: Replacing the first-order derivative with multi-scale gradient calculations yields the multi-scale Harris function: R S (α i )=det(M S (α i ))-d·tr(M S (α i )) 2 R O (β j )=det(M O (β j ))-d·tr(M O (β j )) 2 In the formula and Represents the SAR image at α i The horizontal and vertical gradients under scale, d is an arbitrary parameter, Represents Gaussian kernel, * represents convolution, det represents the value of matrix determinant, tr represents matrix trajectory; finally, according to α i SAR-Harris scale space M under scale S (α i ) Establish the SAR-Harris scale space R S , according to α i Harris scale space R for visible light at scale O (β j ) Establish the visible light Harris scale space R O ; By finding the local maximum in the three-dimensional (x, y, α) Gaussian scale space, and then performing sub-pixel positioning and unstable key point elimination through the Hessian matrix, the key points are extracted; Step 4: First, the Euclidean distance of the nearest neighbor and the ratio of the Euclidean distance of the second nearest neighbor (NNDR) of the key point corresponding descriptor are used to constrain the key point pair PP set, and the fast sample consensus (FSC) algorithm is used to further filter the key point pairs. Then, the translation, scale and direction constraints of the key points are added for screening, and finally the FSC is used to filter the correct matching point pairs; Step 5: Calculate the transformation parameters between the SAR image and the visible light image based on the correct matching point pairs, and register the visible light-SAR image pair.

2. The OS-SIFT-based visible light-SAR image registration algorithm according to claim 1, characterized in that: In step 4, the visible light image is defined as the reference image, the SAR image is defined as the sensed image, and two key point sets P = p1, p2, ..., p are extracted from the reference image and the sensed image respectively. i ,…,p M and P′=p1′,p2′,…,p i ′,…,p′ M , reference image key point p i The position, scale and main direction are (x i ,y i ),s i ,θ i , the position, scale and main direction of the key point p′ of the sensed image are (x i ′,y i ′),s i ′、θ i ′, corresponding point p i and p′ position transformation error e p (i) is expressed as: e p (i)=||(x i ,y i )-T((x i ',y i '),μ)|| Where T((x i ',y i '), μ) is the similarity transformation model, μ is the similarity transformation model parameter; p i The scale error e s (i) and the main direction error e o (i) is expressed as: e o (i)=|Δθ i -Dth * | Where r * and Δθ * denote the scale ratio and main direction difference of the reference image and the sensed image, θ i =θ i -θ i ′ represents p i and p i The main direction difference of ′.

3. The OS-SIFT-based visible light-SAR image registration algorithm according to claim 2, characterized in that: Said step 4 includes an initial matching stage and a secondary matching stage; In the initial matching stage, key points are matched by the ratio of the Euclidean distance of the nearest neighbor to the second nearest neighbor (NNDR) of the corresponding descriptor, and the threshold of the ratio is set to d ratio , get the point pair set PP, and establish the scale ratio r * , main bearing difference Δθ * , horizontal displacement Δx * and vertical displacement Δy * The histogram of r is obtained from the histogram * , Δθ * , Δx * and Δy * , the FSC algorithm is used to further filter key point pairs from the point pair set PP; In the secondary matching stage, r * , Δθ * , x * and Δy * The point pair set obtained in the first step is filtered again to filter out the mismatched points. Definition: PSO(i)=(1+e p (i))(1+e s (i))(1+e o (i)) In the secondary matching, only when the PSO of the point pair obtained in the first step is the smallest, it is considered to be a candidate correct matching point, thereby eliminating the point pairs with non-minimum PSO. Then, FSC is used to further screen the key point pairs and calculate the initial transformation parameter μ.

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