A method and system for rotation and scale-invariant feature extraction based on dual coordinate system collaboration

Abstract

This invention discloses a rotation- and scale-invariant feature extraction method and system based on dual-coordinate system collaboration, belonging to the field of image processing technology. Addressing the poor matching performance of existing image feature extraction methods under rotation and scale changes, this invention employs the following scheme: The input image undergoes a logarithmic polar coordinate transformation to generate a polar coordinate image; a dual-branch network is constructed, where the feature extraction branch extracts keypoint location information in a Cartesian coordinate system, and the feature description branch extracts a polar coordinate feature map in a logarithmic polar coordinate system; the keypoint locations in the Cartesian coordinate system are mapped to their corresponding positions in the polar coordinate feature map using a coordinate mapping function, and interpolation sampling is performed to generate feature descriptors that integrate precise location information and rotation / scale invariance information; based on the feature descriptors, matching point pairs are calculated, and the spatial transformation relationship between images is determined. This invention achieves highly robust feature extraction under rotation and scale changes while maintaining high real-time processing efficiency.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a method and system for extracting rotational and scale-invariant features based on dual-coordinate system collaboration. Background Technology

[0002] In the field of UAV navigation and positioning, cross-modal image registration is crucial for achieving autonomous positioning in GNSS-rejected environments. Matching UAV imagery with satellite base maps faces the challenge of spatial rotation inconsistencies: UAV heading angles are random and dynamic, while satellite maps strictly adhere to the geographic north datum. This angular deviation causes traditional matching algorithms to fail under large angle changes.

[0003] Existing image matching algorithms, represented by SIFT, utilize the difference of Gaussians operator to construct a scale space and establish the principal direction based on the gradient histogram of the feature point neighborhood, achieving local invariance to translation, rotation, and scale. Subsequent research has proposed computationally more efficient algorithms such as ORB, which simplify the rotation description through the centroid rotation method. These traditional algorithms model in a Cartesian coordinate system and exhibit good stability when handling small to medium angle rotations.

[0004] In recent years, deep learning has been introduced into image matching. For example, the SuperPoint algorithm enables the simultaneous extraction of feature points and descriptors, while the XFeat algorithm improves real-time performance through a lightweight convolutional architecture. To address the lack of rotational equivariance in deep learning models, some studies have introduced rotational data augmentation or group convolution mechanisms (such as the GIFT algorithm) to enhance resistance to rotational interference.

[0005] However, the descriptor construction of traditional hand-crafted feature operators heavily relies on local gradient information statistics. In UAV-satellite image matching, illumination differences, ground object occlusion, and large-scale spatial distortion lead to unreliable gradient information, and the matching success rate drops sharply under large-angle rotation. Mainstream lightweight deep learning matching networks (such as XFeat and SuperPoint) utilize spatially fixed convolutional kernels. CNNs only possess translational equivariance, not rotational equivariance. When the heading angle changes drastically, the feature descriptors undergo nonlinear shifts, and the model needs to rely on massive rotational data augmentation or prior pose information, limiting its generalization ability. Although group convolutional neural network (G-CNNs)-based methods can guarantee rotational equivariance, the computational cost increases linearly with the group order. The Steerers framework achieves rotation invariance by mapping existing descriptors to an equivariant representation space. Affine-Steerers further extends this to affine transformations, but still suffers from high computational complexity or insufficient real-time performance. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a rotation and scale invariant feature extraction method and system based on dual coordinate system collaboration. This method uses a dual-branch network to extract key points in a Cartesian coordinate system and feature maps in a log-polar coordinate system. Descriptors are generated through coordinate mapping, interpolation, sampling and fusion, which solves the problem of poor matching performance caused by rotation and scale changes in image matching.

[0007] To achieve the above objectives, the present invention provides the following technical solution: The rotation and scale-invariant feature extraction method based on dual coordinate system cooperation provided by this invention includes the following steps: Logarithmic polar coordinate transformation is performed on the acquired first image and second image respectively to generate corresponding first polar coordinate image and second polar coordinate image; The first image and the second image are input into the feature extraction branch of the dual-branch network, and the key point location information of the first image and the second image is output. The first polar coordinate image and the second polar coordinate image are input into the feature description branch of the dual-branch network, and the corresponding first polar coordinate feature map and second polar coordinate feature map are output. Based on the key point location information, interpolation sampling is performed at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map using a coordinate mapping function to generate feature descriptors for the first image and the second image. Based on the feature descriptor, matching point pairs between the first image and the second image are calculated, and the spatial transformation relationship between the two images is determined according to the matching point pairs.

[0008] Furthermore, the logarithmic polar coordinate transformation is implemented based on the following formula: ; ; ; in, This represents the radial distance from the point to the origin. Indicates azimuth. Represents the original input image The x and y coordinates of any point; This represents the x and y coordinates of the center point of the original image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

[0009] Furthermore, the coordinate mapping function is used to establish the correspondence between the key point positions in the rectangular coordinate system and the sampling points on the logarithmic polar coordinate feature map. Its mathematical principle is based on the inverse transformation of the logarithmic polar coordinate transformation.

[0010] Furthermore, calculating the matching point pairs between the first image and the second image based on the feature descriptor specifically includes: The nearest neighbor algorithm is used to calculate matching point pairs based on the similarity between the feature descriptors of the first image and the second image.

[0011] Furthermore, determining the spatial transformation relationship between the two images based on the matching point pairs specifically includes: Using the Random Sample Consensus (RANSAC) algorithm, a homography matrix is ​​calculated based on the matching point pairs to determine the affine relationship between the first image and the second image.

[0012] Furthermore, the first image is a drone image, and the second image is a satellite map image.

[0013] The present invention provides a rotation and scale-invariant feature extraction system based on dual-coordinate system cooperation, comprising: Coordinate transformation module: used to perform logarithmic polar coordinate transformation on the acquired first image and second image respectively, to generate the corresponding first polar coordinate image and second polar coordinate image; A two-branch network, the two-branch network comprising: Feature extraction branch: used to extract features from the input first and second images, and output the key point location information of the first and second images; Feature description branch: used to extract features from the input first polar coordinate image and second polar coordinate image, and output the corresponding first polar coordinate feature map and second polar coordinate feature map; Descriptor generation module: used to generate feature descriptors for the first image and the second image by interpolating and sampling at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map respectively through a coordinate mapping function based on the key point location information. Matching and localization module: used to calculate matching point pairs between the first image and the second image based on the feature descriptor, and determine the spatial transformation relationship between the two images based on the matching point pairs.

[0014] Furthermore, the coordinate transformation module implements the logarithmic polar coordinate transformation based on the following formula: ; ; ; in, This represents the radial distance from the point to the origin. Indicates azimuth. Represents the original input image The x and y coordinates of any point; This represents the x and y coordinates of the center point of the original image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

[0015] Furthermore, the descriptor generation module is specifically used to: establish the correspondence between the key point positions in the Cartesian coordinate system and the sampling points on the log-polar coordinate feature map through the coordinate mapping function, and perform bitrilinear interpolation sampling based on the correspondence.

[0016] Furthermore, the matching and localization module is specifically used to: calculate matching point pairs using the nearest neighbor algorithm and calculate the homography matrix using the Random Sample Consensus (RANSAC) algorithm to determine the affine relationship between the first image and the second image.

[0017] The beneficial effects of this invention are as follows: This invention provides a rotation and scale-invariant feature extraction method and system based on dual-coordinate system collaboration, belonging to the field of image processing technology. Addressing the poor matching performance of existing image feature extraction methods under rotation and scale changes, this invention employs the following scheme: The input image undergoes a logarithmic polar coordinate transformation to generate a polar coordinate image; a dual-branch network is constructed, where the feature extraction branch extracts key point location information in a Cartesian coordinate system, and the feature description branch extracts a polar coordinate feature map in a logarithmic polar coordinate system; the key point locations in the Cartesian coordinate system are mapped to their corresponding positions in the polar coordinate feature map using a coordinate mapping function, and interpolation sampling is performed to generate feature descriptors that integrate precise location information and rotation / scale invariance information; based on the feature descriptors, matching point pairs are calculated, and the spatial transformation relationship between images is determined. This invention achieves highly robust feature extraction under rotation and scale changes while maintaining high real-time processing efficiency. Compared with existing technologies, this application has the following beneficial effects: 1. Achieved full-angle rotation invariance without additional rotation training. This method transforms rotation in Cartesian coordinates into linear translation in log-polar coordinates, leveraging the inherent translational equivariance of convolutional neural networks to achieve rotation invariance. This overcomes the limitations of traditional descriptors that overly rely on large-scale rotation data augmentation or prior matching information. The proposed Cartesian and log-polar coordinate dual-branch collaborative network effectively addresses the challenge of full-angle rotation variations in UAV-satellite image matching without requiring additional rotation training.

[0018] 2. Balancing feature extraction capability and rotation invariance In the dual-branch framework of this application, the feature extraction branch operates in a Cartesian coordinate system, preserving the original network's accurate extraction capability for high-frequency pixel features such as edges and corners; the feature description branch operates in a logarithmic polar coordinate system, extracting descriptors with rotation invariance. The two branches work together, enabling this application to retain the feature extraction capability of the original network while improving the matching reliability under full-angle rotation changes.

[0019] 3. Significantly improves cross-modal image matching performance Compared with traditional image matching algorithms (such as SIFT and ORB), this application can extract more feature points; compared with existing deep learning algorithms that extract descriptors based on Cartesian coordinates (such as XFeat and SuperPoint), the descriptors extracted by this application have rotation invariance and show good performance advantages in UAV image and satellite image matching tasks.

[0020] 4. Maintain stable matching accuracy across the entire rotation range. This method exhibits stable matching performance across the entire rotation range and has low positioning error, thus meeting the needs of autonomous navigation and positioning for UAVs in complex environments.

[0021] 5. Maintain high real-time processing efficiency This method achieves rotation invariance without significantly increasing computational overhead, and its runtime is basically the same as that of the basic feature extraction network, meeting the real-time requirements of UAV platforms.

[0022] The above and other objects, advantages, and features of the present invention will be more fully set forth and demonstrated through the following detailed description of specific embodiments in conjunction with the accompanying drawings. Those skilled in the art, upon referring to the following detailed description and the accompanying drawings, will be able to better understand and realize the above advantages of the present invention. Other objects, features, and advantages of the present invention will become clearer after being described in detail in the detailed description section in conjunction with the accompanying drawings. Attached Figure Description

[0023] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0024] Figure 1 The flowchart shows a rotation and scale-invariant feature extraction method based on dual coordinate system collaboration. Figure 2 A schematic diagram of image rotation and its corresponding polar coordinate image; Figure 3 A schematic diagram of image scaling and its corresponding polar coordinate image; Figure 4 This is a diagram of the network architecture for feature extraction and description based on logarithmic polar coordinates. Figure 5 This is a schematic diagram showing the matching results between the UAV and satellite images at different rotation angles; Figure 6 A statistical chart showing the number of correctly matched points and root mean square error results under different rotation angles; Figure 7 Schematic diagrams of matching results without rotation and at different scales; Figure 8 Statistical chart of the number of correctly matched points and root mean square error under no rotation and different scales; Figure 9 This is a schematic diagram showing the positioning results of different algorithms under rotational differences. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention. Example 1

[0026] like Figure 1 As shown, the rotation and scale-invariant feature extraction method based on dual coordinate system cooperation provided in this embodiment is characterized by the following steps: Logarithmic polar coordinate transformation is performed on the acquired first image and second image respectively to generate corresponding first polar coordinate image and second polar coordinate image; The first image and the second image are input into the feature extraction branch of the dual-branch network, and the key point location information of the first image and the second image is output. The first polar coordinate image and the second polar coordinate image are input into the feature description branch of the dual-branch network, and the corresponding first polar coordinate feature map and second polar coordinate feature map are output. Based on the key point location information, interpolation sampling is performed at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map using a coordinate mapping function to generate feature descriptors for the first image and the second image. Based on the feature descriptor, matching point pairs between the first image and the second image are calculated, and the spatial transformation relationship between the two images is determined according to the matching point pairs.

[0027] The logarithmic polar coordinate transformation described in this embodiment is based on the following formula: ; ; ; in, This represents the radial distance from the point to the origin. Indicates azimuth. Represents the original input image The x and y coordinates of any point; This represents the x and y coordinates of the center point of the original image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

[0028] The coordinate mapping function described in this embodiment is used to establish the correspondence between the key point positions in the rectangular coordinate system and the sampling points on the logarithmic polar coordinate feature map. Its mathematical principle is based on the inverse transformation of the logarithmic polar coordinate transformation.

[0029] The interpolation sampling described in this embodiment is bilinear interpolation.

[0030] In this embodiment, calculating the matching point pair between the first image and the second image based on the feature descriptor specifically includes: The nearest neighbor algorithm is used to calculate matching point pairs based on the similarity between the feature descriptors of the first image and the second image.

[0031] In this embodiment, determining the spatial transformation relationship between two images based on the matching point pairs specifically includes: Using the Random Sample Consensus (RANSAC) algorithm, a homography matrix is ​​calculated based on the matching point pairs to determine the affine relationship between the first image and the second image.

[0032] In this embodiment, the first image is a drone image, and the second image is a satellite map image.

[0033] The rotation and scale invariance feature extraction device based on polar coordinate transformation provided in this embodiment is characterized by comprising: Coordinate transformation module: used to perform logarithmic polar coordinate transformation on the acquired first image and second image respectively, to generate the corresponding first polar coordinate image and second polar coordinate image; A two-branch network, the two-branch network comprising: Feature extraction branch: used to extract features from the input first and second images, and output the key point location information of the first and second images; Feature description branch: used to extract features from the input first polar coordinate image and second polar coordinate image, and output the corresponding first polar coordinate feature map and second polar coordinate feature map; Descriptor generation module: used to generate feature descriptors for the first image and the second image by interpolating and sampling at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map respectively through a coordinate mapping function based on the key point location information. Matching and localization module: used to calculate matching point pairs between the first image and the second image based on the feature descriptor, and determine the spatial transformation relationship between the two images based on the matching point pairs.

[0034] In this embodiment, the coordinate transformation module implements the logarithmic polar coordinate transformation based on the following formula: ; ; ; in, This represents the radial distance from the point to the origin. Indicates azimuth. This represents the original input image. Indicates the center of the image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

[0035] In this embodiment, the descriptor generation module is specifically used to: establish the correspondence between the key point positions in the Cartesian coordinate system and the sampling points on the log-polar coordinate feature map through the coordinate mapping function, and perform bitrilinear interpolation sampling based on the correspondence.

[0036] In this embodiment, the matching and localization module is specifically used to: calculate matching point pairs using the nearest neighbor algorithm and calculate the homography matrix using the Random Sample Consensus (RANSAC) algorithm to determine the affine relationship between the first image and the second image.

[0037] In this embodiment, the first image is a drone image, and the second image is a satellite map image. Example 2

[0038] This embodiment details the implementation process of the rotation and scale-invariant feature extraction method based on dual coordinate system collaboration, as follows: 1. Perform polar coordinate transformation on the input UAV images and satellite images to generate corresponding polar coordinate images, and then input them into the network. 2. Extract feature points from the input UAV and satellite images in a Cartesian coordinate system.

[0039] 3. Calculate the transformation relationship between the extracted image feature points and their polar coordinates.

[0040] 4. Extract the corresponding multidimensional descriptors from the feature map in polar coordinates based on the transformation relationship.

[0041] 5. Use the nearest neighbor algorithm to calculate the similarity of feature points and obtain the matching feature points.

[0042] 6. Based on the matched feature points, use RANSAC to calculate the homography matrix to obtain the affine relationship between the UAV image and the satellite image.

[0043] 7. Calculate the specific location information of the target point on the UAV image on the satellite image based on the affine relationship.

[0044] The logarithmic polar coordinate transformation in this embodiment is a non-uniform sampling mechanism that simulates the biological visual system. Its core advantage lies in its ability to decouple rotation and scaling transformations in Cartesian coordinates into translation transformations in polar coordinates.

[0045] Assume the original input image is With the image center Let the origin be the point whose rectangular coordinates are... polar coordinates The mapping relationship is defined as follows: (1) in, This represents the radial distance from the point to the origin. Indicates the azimuth angle.

[0046] To further handle scale transformation, the radial distance Take the logarithm and introduce logarithmic polar coordinate variables. .

[0047] At this point, the original image is resampled to logarithmic polar coordinate space. .

[0048] Under alteration, the geometric deformation of the original image exhibits the following characteristics.

[0049] 1. Rotational isomorphism: When the original image is rotated by an angle Let the coordinates of the original image in the rectangular coordinate system be... The coordinates of the rotated image are The original image's coordinates on polar coordinates are The coordinates of the rotated image are Representing along in a logarithmic polar coordinate graph Cyclic translation of the axis: (2) 2. Scale isovariability: When the original image is scaled When the image is large, let the coordinates of the original image in the rectangular coordinate system be... The coordinates of the rotated image are The original image's coordinates on polar coordinates are The coordinates of the rotated image are In a logarithmic polar plot, it is represented as along Translation of the axis: (3) Represents the x and y coordinates of any point in the original image; express The horizontal and vertical coordinate values ​​after scaling; Represents the coordinate values ​​after polar coordinate transformation; express Coordinate values ​​after scaling; Represents the polar radius before scaling in logarithmic polar coordinates; Represents the polar radius after scaling in logarithmic polar coordinates; This indicates the polar radius of the polar coordinates without logarithmic transformation. Represents the polar angle in polar coordinates; Represents a logarithmic polar coordinate transformation; Indicates the scaling factor; The mathematical properties of the transformation provided in this embodiment greatly facilitate CNNs. Since CNNs are inherently equivariant in translation, performing convolution operations in the logarithmic polar coordinate domain is equivalent to achieving continuous equivariant feature extraction in rotation and scaling in a Cartesian coordinate system.

[0050] Based on the characteristics of polar coordinates, we designed a polar coordinate descriptor (Log-Polar, LP) extraction method, specifically a feature extraction network consisting of a feature extraction branch and a feature description branch. Since this chapter uses XFeat as the basic feature extraction backbone, it is denoted as XFeat-LP, and its network structure diagram is shown below. Figure 4 As shown, Figure 4 This is a network architecture for feature extraction and description based on LP; by Figure 4 It can be known that: 1. Cartesian Coordinate Branch: The main task of the Cartesian coordinate branch is to directly utilize the original pixel information in the Cartesian coordinate system to extract feature heatmaps, thereby achieving accurate localization of key points. The specific steps are as follows: the network directly receives the image in the original Cartesian coordinate system as input, extracts local texture features through shallow convolutional modules, and outputs an image with a spatial resolution equal to the original image. A dense feature map with 64 channels; subsequently, using The convolutional layer expands the number of feature channels to 65 dimensions; through the "folding back image" operation, it reconstructs the low-resolution channel information to the same physical resolution as the original image, generating a size of... The key points are then analyzed using a heatmap. Finally, the non-maximum suppression (NMS) algorithm is applied to this heatmap to remove redundant local responses, thereby extracting the final discrete key points that are evenly distributed and have accurate coordinates.

[0051] 2. Logarithmic Polar Coordinate Branch: The core purpose of the logarithmic polar coordinate branch is to utilize the translational invariance of logarithmic polar coordinates to extract descriptors with rotation and scale invariance, while simultaneously evaluating the reliability of the features. This branch first performs a logarithmic polar coordinate transformation on the input image, converting rotation and scaling in Cartesian space into linear translation in the logarithmic polar coordinate system. Then, the logarithmic polar coordinate image is fed into a deep convolutional network, where a multi-scale feature pyramid is constructed through layer-by-layer downsampling, extracting features of different sizes. , as well as The network utilizes multi-level features; to integrate semantic information from different receptive fields, it employs upsampling and The convolution operation aligns the spatial resolution and number of channels of the features in each layer to a uniform value. The feature maps are then aggregated across scales, with element-wise addition performed. Finally, the aggregated feature maps are processed by the fusion module and fed into two task heads: one directly outputs the feature maps that inherently possess rotation and scale invariance. The other is the output through an additional convolutional layer, which is a dense descriptor tensor. A single-channel reliability mask is used to filter out low-confidence feature descriptors in subsequent processes.

[0052] The feature extraction branch aims to ensure accurate detection of feature points. This branch performs convolution operations in standard Cartesian coordinates, avoiding geometric distortion caused by coordinate transformations. This is crucial for capturing high-frequency pixel features such as edges and corners. Through the feature map extracted by this branch, the network can identify salient key points in the image and output a probability map. Because no logarithmic polar coordinate transformation is performed, this branch maintains the accuracy of feature extraction, providing accurate feature point locations for subsequent descriptor extraction. information.

[0053] The feature description branch aims to generate rotation-invariant descriptors using logarithmic polar coordinates. This branch also utilizes the keypoint locations determined by the feature extraction branch as a geometric reference. A Cartesian coordinate system is established. With logarithmic coordinate system A mapping function between the two is used to project the feature point locations onto the polar coordinate sampling network. On the reconstructed polar coordinate feature space, we directly extract descriptors using interpolation sampling techniques. Specifically, we extract descriptors from the polar coordinate feature map... The descriptor of the feature point is obtained by performing bitrilinear interpolation sampling at the corresponding feature point location. Due to the rotation transformation... The space has been transformed into a lateral translation. This interpolation sampling method can ensure that rotation-invariant feature descriptors are obtained under full-angle rotation.

[0054] To verify the effectiveness of the LP descriptor framework proposed in this patent for UAV and satellite imagery tasks, a performance evaluation was conducted under a unified hardware platform and software framework. The GPU used in the experiment was an NVIDIA GeForce RTX 4060. We used the Number of Correct Matches (NCM) as an indicator of the algorithm's matching capability and the Root Mean Square Error (RMSE) as an indicator of positioning accuracy.

[0055] We evaluated our model on the ALTO dataset. The dataset consists of 1683 pairs of corresponding drone and satellite images. For each drone image, we rotated it 8 times around the image center, with each rotation being 40°, resulting in a dataset with full angular variation.

[0056] 1. Rotation-invariant evaluation like Figure 2 As shown, Figure 2 The images shown are the UAV image, the rotated image, and the corresponding polar coordinate system image; where (b), (c), and (d) are the rotated image of (a), and (e), (f), (g), and (h) are the images of (a), (b), (c), and (d) after being transformed into polar coordinates, respectively. Figure 2The image displayed shows the drone image and its rotated form, along with the corresponding logarithmic polar coordinate image. In the logarithmic polar coordinate image, the horizontal axis is... The axis, the vertical axis is The axis. As can be seen from the figure, when the rectangular coordinate system image is rotated, the corresponding logarithmic polar coordinate image appears as follows. Translation of the axis. In a polar coordinate system image, the horizontal coordinate is... The axis, the vertical axis is The axis. As can be seen from the figure, when the rectangular coordinate system image is rotated, the corresponding polar coordinate image is represented by a translation of the axis.

[0057] This experiment selected XFeat and Affine-Steerers as the main comparison algorithms to evaluate the matching performance of the LP descriptor frame when there is viewpoint rotation between UAV and satellite imagery. Experimental results are as follows: Figure 5 As described above, the NCM, RMSE, and average running time of each algorithm are as follows: Figure 6 As described in Table 1.

[0058] Figure 5 The matching results between the UAV and satellite images under different rotations; Figure 5 The images show the matching results of three algorithms—XFeat, Affine-Steerers, and XFeat-LP (our)—at rotation angles from 0° to 320°. In each matching result image, the left side is the drone image, and the right side is the satellite image. The lines connecting the images represent the feature points matched by the algorithm. It can be seen that XFeat can extract sufficient correct matching points in small-angle scenes, but when the rotation angle reaches 80° or more, the number of matching points decreases significantly, accompanied by obvious mismatches. This reflects the inherent limitations of standard convolutional networks in handling large-angle rotations. While Affine-Steerers retains a certain number of matching points at all angles, their number fluctuates significantly with the angle, and the feature point distribution shows obvious regional limitations. In contrast, XFeat-LP maintains a stable number of matching points across the entire rotation range from 0° to 320°, with feature points evenly covering the entire image area and a low mismatch rate, directly verifying the algorithm's robustness to large-angle rotations.

[0059] Figure 6 Statistical charts of NCM and RMSE results for XFeat, Affine-Steerers, and XFeat-LP at different angles; Figure 6The charts show the NCM and RMSE results of three algorithms—XFeat, Affine-Steerers, and XFeat-LP (our)—at rotation angles from 0° to 320°. It can be seen that XFeat only outperforms XFeat-LP in NCM at the 0° reference position. Once the rotation angle exceeds 80°, its correct match count drops sharply, and the RMSE rises rapidly, indicating that it struggles to achieve effective feature matching under extreme rotation conditions. Affine-Steerers exhibits high NCM around 0°, 40°, and 320°. Although the match count drops at other angles, its RMSE remains consistently low, demonstrating a degree of rotation invariance. XFeat-LP's NCM curve fluctuates smoothly across the entire range, consistently remaining in the high range of 330 to 490, while its RMSE remains consistently low. This indicates that the feature representation after introducing the LP descriptor framework exhibits stable rotation invariance and can effectively handle the challenges of large-angle rotations between images.

[0060] Table 1. Average runtime of XFeat, Affine-Steerers, and XFeat-LP As can be seen from the charts, the original XFeat can extract a sufficient number of correct matches. However, when the rotation angle reaches 80° or higher, its number of NCMs drops rapidly to around 50 and remains at a low level for subsequent large angles, reflecting the limitations of conventional convolutional networks in handling large-angle rotations. On the other hand, while the Affine-Steerers algorithm retains a certain number of matches at all angles, the number fluctuates significantly with the angle. Furthermore, the average runtime of Affine-Steerers is 0.446 seconds, making it unsuitable for real-time applications like UAVs. In contrast, the XFeat-LP algorithm, with the LP framework, consistently maintains a number of correct matches between 330 and 490 across the entire angle range from 0° to 320°, demonstrating stable rotation invariance. Moreover, the average runtime of XFeat-LP is 0.026 seconds, very similar to that of the original XFeat.

[0061] 2. Scale Invariance Assessment like Figure 3 As shown, Figure 3 The images provided are a UAV image, a scaled image, and the corresponding polar coordinate system image. (b), (c), and (d) are scaled versions of (a), and (e), (f), (g), and (h) are the images of (a), (b), (c), and (d) after being converted to polar coordinates, respectively. Figure 3The image shows a drone image and its scaled-down counterpart, along with the corresponding logarithmic polar coordinate image. As can be seen from the image, when the Cartesian coordinate image is scaled, the corresponding logarithmic polar coordinate image appears as follows: Translation of the axis. Furthermore, benefiting from the logarithmic mapping properties of the logarithmic polar coordinate transformation, the scaling in the original rectangular coordinate system is transformed into a linear translation in the logarithmic polar coordinate domain, thereby effectively compressing scale differences and making the image features exhibit scale consistency in representation.

[0062] As can be seen from the figure, when the Cartesian coordinate image is scaled, the corresponding polar coordinate image appears as follows: Translation of the axis. Furthermore, benefiting from the logarithmic mapping properties of the logarithmic polar coordinate transformation, the scaling in the original rectangular coordinate system is transformed into a linear translation in the polar coordinate domain, thereby effectively compressing scale differences and making the image features exhibit scale consistency in representation.

[0063] This experiment selected XFeat and Affine-Steerers as comparison algorithms to evaluate the matching performance of the LP framework when there are scale differences between UAV and satellite images. Figure 7 , Figure 8 It can be seen from this that Figure 7 Matching results for XFeat, Affine-Steerers, and XFeat-LP at no rotation and different scales; Figure 7 The image shows the matching results of three algorithms—XFeat, Affine-Steerers, and XFeat-LP(our)—at scales ranging from 0.2 to 2.0. In each matching result image, the left side is a drone image, and the right side is a satellite image. The lines connecting the images represent the feature points matched by the algorithm. The images show that at a baseline scale of 1.0 and close to it, XFeat can extract a stable number of matching points. However, as the scale difference between the two images gradually increases, the number of matches for XFeat decreases rapidly. The Affine-Steerers algorithm shows some adaptability within a specific scale range, but the overall number of extracted matching points is relatively small, and the matching points are concentrated in specific areas. In contrast, the XFeat-LP algorithm, which incorporates the LP descriptor framework, shows a stable trend in the number of matching points throughout the entire test range, and the feature points can evenly cover the entire image area.

[0064] Figure 8 Statistical plots of NCM and RMSE for XFeat, Affine-Steerers, and XFeat-LP under conditions of no rotation and different scales. Figure 8The paper presents statistical graphs of NCM and RMSE results for three algorithms—XFeat, Affine-Steerers, and XFeat-LP(our)—at scales ranging from 0.2 to 2.0. XFeat's correct match count drops sharply after the scale factor exceeds 1.8, with only a very small number of correct matches remaining at the end of the curve. The RMSE curves further illustrate that when the scale ratio shrinks to 0.2, XFeat's RMSE error rises significantly to the set upper limit, leading to match failures. Affine-Steerers shows a rapid decrease in the number of matches even at scale ratios below 0.6. In contrast, the XFeat-LP algorithm exhibits a relatively gentle decay curve in the number of correct matches, maintaining a certain scale of correct matches. Simultaneously, its RMSE remains consistently low and stable across the entire scale range, without error fluctuations or failures. Considering both metrics, the proposed method improves the robustness of the feature network to drastic scale changes by sacrificing a small number of baseline scale matches, thus ensuring the overall stability of localization.

[0065] 3. UAV and satellite imagery positioning assessment The comparison algorithms used in this experiment include SIFT, ORB, XFeat, SuperPoint, Aliked, LiftFeat, and Steerers. We used each algorithm to perform image matching and localization on an image rotated 80°. The experimental results are as follows: Figure 9 As shown, Figure 9 The figure shows the localization results of each algorithm under 80° rotation differences, and illustrates the image matching results; Figure 9 The image displays the matching and localization results for eight algorithms—SIFT, ORB, XFeat, SuperPoint, ALIKED, LiftFeat, Affine-Steerers, and XFeat-LP(our)—under different rotation angles. In each matching result image, the left side shows the drone image, and the right side shows the satellite image. The lines connecting the images represent the feature points matched by the algorithm. In the left image, red dots represent the target localization point, and in the right image, red dots represent the ground truth localization point. Green asterisks represent the localization points predicted by the algorithm.

[0066] The NCM, RMSE, and runtime of the experiment are shown in Table 2.

[0067] Table 2. NCM, RMSE, and running time results for each algorithm under 80° rotation differences. When faced with a large 80° rotation, traditional handcrafted features like SIFT and ORB, as well as conventional deep learning models such as SuperPoint, Aliked, and LiftFeat, all exhibited a low number of correct matching points. Their predicted localization points significantly deviated from the true coordinates, resulting in generally high RMSE (Real-Time Sequence) errors. While the original XFeat algorithm maintained extremely fast processing speed, it also exhibited reduced matching points, localization point deviations from true coordinates, and increased localization errors under large rotations. On the other hand, the Affine-Steerers algorithm extracted a relatively large number of matching points in the first set of test images, with relatively low error and localization points closely matching the ground truth. However, in the second set of test images, its matching points decreased, and the predicted positions also shifted somewhat.

[0068] In contrast, the XFeat-LP algorithm, which incorporates the LP framework in this embodiment, maintained good matching scale in the tests, with the localization error remaining at a low level of 1.16, and the predicted coordinates closely matching the ground truth. Furthermore, considering the runtime, XFeat-LP's average execution time is approximately 0.025 seconds, roughly equivalent to the original feature network. Overall, this method improves the model's robustness to large-angle rotations and its actual localization accuracy without significantly increasing time overhead.

[0069] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A rotation and scale-invariant feature extraction method based on dual-coordinate system collaboration, characterized in that, Includes the following steps: Logarithmic polar coordinate transformation is performed on the acquired first image and second image respectively to generate corresponding first polar coordinate image and second polar coordinate image; The first image and the second image are input into the feature extraction branch of the dual-branch network, and the key point location information of the first image and the second image is output. The first polar coordinate image and the second polar coordinate image are input into the feature description branch of the dual-branch network, and the corresponding first polar coordinate feature map and second polar coordinate feature map are output. Based on the key point location information, interpolation sampling is performed at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map using a coordinate mapping function to generate feature descriptors for the first image and the second image. Based on the feature descriptor, matching point pairs between the first image and the second image are calculated, and the spatial transformation relationship between the two images is determined according to the matching point pairs.

2. The method for rotation and scale-invariant feature extraction based on dual coordinate system collaboration according to claim 1, characterized in that, The logarithmic polar coordinate transformation is implemented based on the following formula: ； ； ； in, This represents the radial distance from the point to the origin. Indicates azimuth. Represents the original input image The x and y coordinates of any point; This represents the x and y coordinates of the center point of the original image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

3. The method for rotation and scale-invariant feature extraction based on dual coordinate system collaboration according to claim 1, characterized in that, The coordinate mapping function is used to establish the correspondence between the key point positions in the rectangular coordinate system and the sampling points on the logarithmic polar coordinate feature map. Its mathematical principle is based on the inverse transformation of the logarithmic polar coordinate transformation.

4. The rotation and scale-invariant feature extraction method based on dual coordinate system collaboration according to claim 1, characterized in that, The step of calculating the matching point pairs between the first image and the second image based on the feature descriptor specifically includes: The nearest neighbor algorithm is used to calculate matching point pairs based on the similarity between the feature descriptors of the first image and the second image.

5. The rotation and scale-invariant feature extraction method based on dual coordinate system collaboration according to claim 1, characterized in that, The step of determining the spatial transformation relationship between the two images based on the matching point pairs specifically includes: Using a random sampling consensus algorithm, a homography matrix is ​​calculated based on the matching point pairs to determine the affine relationship between the first image and the second image.

6. The method for rotation and scale-invariant feature extraction based on dual coordinate system collaboration according to any one of claims 1-5, characterized in that, The first image is a drone image, and the second image is a satellite map image.

7. A rotation and scale-invariant feature extraction system based on dual-coordinate system cooperation, characterized in that, include: Coordinate transformation module: used to perform logarithmic polar coordinate transformation on the acquired first image and second image respectively, to generate the corresponding first polar coordinate image and second polar coordinate image; A two-branch network, the two-branch network comprising: Feature extraction branch: used to extract features from the input first and second images, and output the key point location information of the first and second images; Feature description branch: used to extract features from the input first polar coordinate image and second polar coordinate image, and output the corresponding first polar coordinate feature map and second polar coordinate feature map; Descriptor generation module: used to generate feature descriptors for the first image and the second image by interpolating and sampling at corresponding positions in the first polar coordinate feature map and the second polar coordinate feature map respectively through a coordinate mapping function based on the key point location information. Matching and localization module: used to calculate matching point pairs between the first image and the second image based on the feature descriptor, and determine the spatial transformation relationship between the two images based on the matching point pairs.

8. The rotation and scale-invariant feature extraction system based on dual coordinate system cooperation according to claim 7, characterized in that, The coordinate transformation module implements the logarithmic polar coordinate transformation based on the following formula: ； ； ； in, This represents the radial distance from the point to the origin. Indicates azimuth. Represents the original input image The x and y coordinates of any point; This represents the x and y coordinates of the center point of the original image; radial distance Take the logarithm and introduce logarithmic polar coordinate variables. ; Resample the original image to logarithmic polar coordinates. .

9. The rotation and scale-invariant feature extraction system based on dual coordinate system cooperation according to claim 7, characterized in that, The descriptor generation module is specifically used to: establish the correspondence between the key point positions in the Cartesian coordinate system and the sampling points on the log-polar coordinate feature map through the coordinate mapping function, and perform bitrilinear interpolation sampling based on the correspondence.

10. The rotation and scale-invariant feature extraction system based on dual coordinate system collaboration according to claim 7, characterized in that, The matching and positioning module is specifically used to: calculate matching point pairs using the nearest neighbor algorithm and calculate the homography matrix using the random sampling consensus algorithm to determine the affine relationship between the first image and the second image.

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