A rotation isomorphic feature modeling and target detection method and device for remote sensing images and a storage medium

Abstract

The application is suitable for the technical field of remote sensing image target detection, and provides a rotation isometry feature modeling and target detection method and device for remote sensing images and a storage medium, which comprises: acquiring a first remote sensing image to be detected; generating, according to the first remote sensing image, a plurality of first target objects each corresponding to a first direction feature under a preset different rotation angle; and performing target detection on the first remote sensing image according to the plurality of first direction features, to obtain a first target category of all first target objects in the first remote sensing image and a first target pose of each first target object. The above method can improve the target detection accuracy of remote sensing images.

Description

Technical Field

[0001] This application belongs to the field of remote sensing image target detection technology, and in particular relates to a method, device and storage medium for rotating isotropic feature modeling and target detection of remote sensing images. Background Technology

[0002] Remote sensing technology is widely used in fields such as urban planning and maritime monitoring. However, targets in remote sensing images have problems such as arbitrary rotation at angles, significant intra-class differences, cluttered backgrounds, and a small proportion of some target pixels, which pose a huge challenge to accurate detection.

[0003] Related technologies employ a reconstruction method based on rotating bounding boxes for target detection. However, this method does not embed rotation as a core prior into the network structure and optimization target. Instead, it relies heavily on data augmentation or heuristic architectural design, lacks a rigorous theoretical foundation in geometric modeling, and cannot adapt to the complex situations in remote sensing scenarios where targets can rotate arbitrarily, backgrounds are cluttered, and small and dense targets coexist. This makes it difficult to accurately detect targets. Summary of the Invention

[0004] This application provides a method, apparatus, and storage medium for rotational isotropic feature modeling and target detection of remote sensing images, which can improve the target detection accuracy of remote sensing images.

[0005] In a first aspect, embodiments of this application provide a method for rotation-equal feature modeling and target detection of remote sensing images, including:

[0006] Acquire a first remote sensing image to be detected; the first remote sensing image contains multiple first target objects; Based on the first remote sensing image, generate the first orientation features of multiple first target objects at different preset rotation angles; Target detection is performed on the first remote sensing image based on multiple first directional features to obtain the first target category and the first target pose of each first target object in the first remote sensing image.

[0007] In this embodiment, the original remote sensing image to be detected (i.e., the first remote sensing image) is first acquired. Then, specific directional features (i.e., multiple first directional features) of the image under different rotation angles are extracted. Finally, detection is completed based on these features covering multiple rotational attitudes, which not only identifies multiple target categories (first target categories) in the image, but also clarifies the specific rotational attitude (first target attitude) corresponding to each target. By extracting the directional features corresponding to different rotation angles of the remote sensing image, the model can fully capture the feature information of the target under various attitudes. It can learn the model without relying on data augmentation to expand the samples, providing geometric modeling theoretical support. It can avoid feature omission or distortion caused by target rotation, thereby accurately matching the actual attitude and category of the target, effectively improving the detection accuracy of remote sensing targets with diverse rotational attitudes, and reducing missed detections and false detections.

[0008] In one possible implementation of the first aspect, generating first orientation features corresponding to multiple first target objects at preset different rotation angles based on the first remote sensing image includes: Extract initial features corresponding to the first remote sensing image; wherein, the initial features include texture, edge and spatial location information of multiple first target objects in the first remote sensing image; The initial features are reduced in dimensionality to obtain the second features; Based on the second feature, generate the first direction features corresponding to each of the first target objects at different preset rotation angles.

[0009] In this embodiment, by first extracting initial features containing target texture, edges and spatial location, and then generating exclusive first direction features at a preset angle after dimensionality reduction and simplification, the core geometric and semantic information of the target is preserved, the computational complexity is reduced, and the direction-sensitive information of different rotational postures is explicitly encoded, providing a precise foundation for subsequent feature fusion and isovariance constraints, and effectively improving the detection robustness and posture estimation accuracy of arbitrarily rotating targets in remote sensing images.

[0010] In one possible implementation of the first aspect, multiple first orientation features corresponding to different preset rotation angles of the first target objects are generated based on the second feature, including: Obtain multiple predefined raw convolution kernels; Each original convolutional kernel is transformed based on multiple preset rotation angles to obtain multiple sub-convolutional kernels corresponding to each original convolutional kernel; The second feature is convolved with multiple sub-convolutional kernels corresponding to each original convolutional kernel to obtain multiple first-direction features.

[0011] In this embodiment, a sub-convolution kernel is generated by transforming a predefined original convolution kernel at a preset angle, and then convolved with the second feature after dimensionality reduction to generate a first directional feature. This not only explicitly encodes the rotation structure by using the parameter-shared sub-convolution kernel without increasing the model complexity, but also accurately captures the directional sensitive information of the target under different rotation postures, laying a solid foundation for subsequent isovariant constraints and feature fusion, and effectively improving the detection accuracy and robustness of targets with arbitrary rotation in remote sensing images.

[0012] In one possible implementation of the first aspect, target detection is performed on the first remote sensing image based on multiple first orientation features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object, including: A comprehensive directional feature is obtained based on multiple first-directional features; Core integrated features are obtained based on directional integrated features; wherein, the core integrated features are used to represent the feature information of each first target object in the first remote sensing image that does not change under different preset rotation angles; Target detection is performed on the first remote sensing image based on directional integrated features and core integrated features to obtain the first target category and the first target pose of all first target objects in the first remote sensing image.

[0013] In this embodiment, multiple first-direction features are first aggregated to obtain a comprehensive directional feature. Then, the core comprehensive feature that shields rotation interference is extracted through group pooling. Finally, the two types of features are used for collaborative detection. The comprehensive directional feature accurately encodes the target rotation attitude and ensures the accuracy of attitude estimation. The core comprehensive feature stably captures the essential information of the target category, effectively improving the robustness of detection and the accuracy of classification and attitude inference of any rotating target in remote sensing images.

[0014] In one possible implementation of the first aspect, a directional comprehensive feature is obtained based on multiple first directional features, including: Each first-directional feature is subjected to denoising and directional feature enhancement processing to obtain multiple second-directional features; The second-direction features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel are summed to obtain the first comprehensive features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel. The directional comprehensive feature is obtained by splicing together multiple first comprehensive features.

[0015] In this embodiment, the first directional features are first purified by denoising and directional enhancement, then the sub-core features under the same mother kernel are summed and aggregated, and finally the multi-mother kernel comprehensive features are spliced ​​to obtain the directional comprehensive features. This not only effectively filters noise and enhances the target's directional sensitive information, but also integrates multi-mother kernel-multi-angle features by summing and splicing, thus fully preserving rotational and other variable properties. This provides comprehensive and high-quality feature support for subsequent accurate attitude estimation and significantly improves the robustness of remote sensing detection of targets with arbitrary rotation.

[0016] In one possible implementation of the first aspect, the core synthetic features are obtained based on the directional synthetic features, including: The directional comprehensive features are decomposed to obtain multiple third-direction features; each third-direction feature corresponds to a second-direction feature. Perform directional pooling on each third-direction feature to obtain multiple fourth-direction features after pooling. Multiple fourth-direction features are concatenated to obtain the core comprehensive features.

[0017] In this embodiment, core comprehensive features are obtained by associating second-direction features through feature decomposition, extracting rotation-invariant information through directional pooling, and splicing and integrating multi-dimensional features. This not only accurately preserves the essential information of the target category and shields against rotation interference, but also enhances the robustness of features through pooling and splicing. This provides high-quality invariant feature support for accurate identification of target categories and effectively improves the classification stability and detection reliability of remotely sensed targets with arbitrary rotation.

[0018] In one possible implementation of the first aspect, before performing target detection on the first remote sensing image to be detected, the method further includes: Obtain a training set; wherein the training set includes multiple second remote sensing images to be trained; wherein each second remote sensing image includes multiple second target objects; For each second remote sensing image in the training set, generate the fifth direction features corresponding to multiple second target objects in each second remote sensing image under different preset rotation angles; Target detection is performed on the second remote sensing image based on multiple fifth-direction features to obtain the second target category of all second target objects in the second remote sensing image and the second target pose of each second target object; A first loss is calculated based on the second target category of all second target objects and the second target pose of each second target object; wherein, the first loss includes the loss between the second target category and the preset category and the loss between the second target pose and the preset pose; Calculate the second loss between the first rotation feature and the second rotation feature; wherein, the first rotation feature is the feature data after synchronously moving the direction channel of the second direction comprehensive feature corresponding to the second remote sensing image by a rotation angle; the second rotation feature is the feature data after rotating the third direction comprehensive feature extracted after rotating the second remote sensing image by an angle in the opposite direction; wherein, the direction channel is used to generate the fifth direction feature corresponding to the second remote sensing image; Calculate a third loss between the first prediction result and the second prediction result; wherein the first prediction result includes the second target category and the second target pose; the second prediction result is the third target category and the third target pose corresponding to the second remote sensing image obtained by rotating the second remote sensing image by an angle and then performing target detection. Calculate the total loss based on the first loss, the second loss, and the third loss; If the total loss does not converge, the parameters are adjusted until the total loss converges, at which point the training ends. After training, the first remote sensing image to be detected is acquired for target detection.

[0019] In this embodiment, by constructing a training set containing multiple rotating targets, generating angle-specific fifth-direction features, and collaboratively calculating the detection loss and a two-level equal-variable regularization loss optimization model, and adjusting the parameters until the total loss converges, the model can fully learn the essence of the target category and the rotation posture rules. Furthermore, by strengthening geometric consistency through feature-level and prediction-level constraints, the trained model can accurately and robustly meet the detection requirements of any rotating target in the first remote sensing image.

[0020] Secondly, embodiments of this application provide a target detection device, comprising: An image acquisition module is used to detect a first remote sensing image; the first remote sensing image contains multiple first target objects; The orientation feature generation module is used to generate first orientation features corresponding to multiple first target objects at different preset rotation angles based on the first remote sensing image. The target detection module is used to perform target detection on the first remote sensing image based on multiple first directional features, and to obtain the first target category and the first target pose of all first target objects in the first remote sensing image.

[0021] Thirdly, embodiments of this application provide a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the target detection method as described in any of the first aspects above.

[0022] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the target detection method as described in any of the first aspects above.

[0023] Fifthly, embodiments of this application provide a computer program product that, when run on a terminal device, causes the terminal device to execute any of the target detection methods described in the first aspect above.

[0024] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the target detection method provided in an embodiment of this application; Figure 2 This is a flowchart illustrating the acquisition of directional features provided in an embodiment of this application. Figure 1 ; Figure 3 This is a flowchart illustrating the acquisition of directional features provided in an embodiment of this application. Figure 2 ; Figure 4 This is a schematic diagram of the process for obtaining target detection results provided in an embodiment of this application; Figure 5 This is a flowchart illustrating the computational direction synthesis features provided in an embodiment of this application; Figure 6 This is a flowchart illustrating the calculation of core comprehensive features provided in an embodiment of this application; Figure 7 This is a schematic diagram of the model training process provided in the embodiments of this application; Figure 8 This is a structural block diagram of the target detection device provided in the embodiments of this application; Figure 9 This is a schematic diagram of the structure of the terminal device provided in the embodiments of this application. Detailed Implementation

[0027] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0028] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0029] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0030] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0031] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0032] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0033] Remote sensing technology has become indispensable in applications such as urban planning, maritime monitoring, and disaster management. However, accurate target detection remains a significant challenge due to arbitrary target rotation and substantial intra-class differences. Recent research indicates that combining deep learning with rigorous mathematical principles is key to achieving model robustness and interpretability. While some related technologies employ target detection based on rotating bounding boxes, they do not embed rotation as a core prior into the network structure and target optimization. They rely heavily on data augmentation or heuristic architectural design, lacking a rigorous theoretical foundation in geometric modeling. This makes them unsuitable for the complexities of remote sensing scenarios, such as arbitrarily rotating targets, cluttered backgrounds, and the coexistence of small and dense targets, ultimately hindering accurate target detection.

[0034] To address the aforementioned technical challenges, this paper designs a lightweight and flexible adapter that can be seamlessly applied to multiple detector types without increasing network complexity. Specifically, we propose a Rotation-Aware Multi-MotherConvolution (RAMMC) module and a consistency regularization module based on the theory of rotation equivariance and invariance. We mathematically prove that RAMMC satisfies the Reynolds operator property and establish an explicit upper bound on the error to characterize the nonlinear effects in the network structure. This theory guarantees the stability of feature transformations and guides the design of the loss function from both feature-level and prediction-level consistency perspectives. Extensive experiments on various detectors, including Faster R-CNN, RoITransformer, and Oriented R-CNN, within the MMRote framework, and on YOLO series models within the Ultralytics framework, demonstrate that our adapter consistently delivers performance improvements. Notably, RAMMC achieved 84.32 mAP on DOTA-v1.0, 47.31 mAP on FAIR1M-v1, and 52.28 mAP on FAIR1M-v2.0, comprehensively outperforming strong baseline models. These results demonstrate that embedding mathematically grounded constraints into a lightweight adapter provides an efficient and universal solution for modeling rotationally equivariant features and object detection in remote sensing images. Object detection in remote sensing images has long been a core but highly challenging problem, underpinned by critical applications such as maritime monitoring, aircraft identification, urban planning, and disaster emergency response. Unlike natural images, aerial and satellite imagery are acquired in more complex environments: scenes are typically ultra-high resolution, many targets occupy only a few pixels, and they exhibit arbitrary rotational postures against cluttered backgrounds. Furthermore, these images are often affected by sensor-specific degradations (such as SAR speckle noise and haze), which collectively limit the performance of standard detection models initially designed for natural images.

[0035] RAMMC mainly consists of two parts. The first part involves rotating a learnable master kernel to generate multiple orientation-specific sub-kernels, forming a compact convolutional kernel group that explicitly encodes rotation patterns. Input features are projected 1×1 and then convolved with the rotated kernel group to reduce computation and separate orientation-sensitive channels. The second part, orientation-aware aggregation, modulates the orientation response through spatial attention and orientation weighting, and then fuses them into a single function. It also includes explicit orientation and invariant features. We further incorporate feature-level and prediction-level regularization to enhance geometric stability.

[0036] RAMMC is embedded in the block-level structure of the backbone network in parallel and fused with the original block output through an attention mechanism. This design injects rotation-aware representations while preserving the original feature extraction capabilities. Specifically, RAMMC uses a set of mother kernels, each of which generates multiple child kernels through parameter sharing, thereby explicitly encoding the rotation structure without increasing parameter complexity. Furthermore, we add two regularization terms to the loss function: a feature-level isovariability constraint and a prediction-level consistency constraint, to control geometric errors and stabilize the detection framework.

[0037] Before introducing this method, the relevant preliminary knowledge and related compliance notes involved in this application will be introduced first, as follows: Notation. Scalars are denoted by lowercase letters (x, α, λ), vectors by bold lowercase letters (x), and matrices by uppercase letters (F, K, Z). Feature maps such as F ∈ RC × H × W are considered matrices indexed by channels and spatial coordinates. The symbol " " " represents convolution, "⊙" represents Hadamard (element-wise) product, and "·" represents scalar multiplication or weighted operation. Global average pooling is denoted as GAP(·), and MLP(·) represents a two-layer perceptron. Group action uses... (Rotation α over the input) and The induced rotation of features is represented. The mapping Φ represents the universal feature extractor. Operator This indicates a cyclic translation of the direction channel. "Grouppooling" Poolr(·) indicates averaging over the direction channel to achieve invariance.

[0038] RotationGroupandEquivariance. Let Discrete rotation group of order t:

[0039] in, and They represent Group action on the input and feature space.

[0040] If the mapping Φ satisfies:

[0041] It is then called rotationally equivariant. If the classifier c satisfies:

[0042] It is then called rotationally invariant.

[0043] Quarter-TurnGroup. This article uses the quarter-turn group. As a fundamental rotation group, it is consistent with common discrete rotational isovariant networks.

[0044] GroupActiononOrientationChannels. For channels with explicit orientation (by...) The characteristic tensor F of the index has the following group action:

[0045] in Represents the group operation reindexing of the direction channel.

[0046] "Group pooling" achieves average induced invariance along the directional channels:

[0047] in, This represents the cyclic displacement by angle α.

[0048] The detection model provided in this application is an instantiation of the proposed RAMMC adapter into a YOLO-style detector. (See [link to relevant documentation]). Figure 1 This is a flowchart illustrating the target detection method provided in an embodiment of this application. It is intended as an example and not a limitation. The method may include the following steps: S101, acquire the first remote sensing image to be detected; the first remote sensing image contains multiple first target objects.

[0049] In this embodiment, a remote sensing image (i.e., the "first remote sensing image") to be detected is first acquired. This image originates from remote sensing scenes such as satellite and aerial photography and has typical characteristics such as ultra-high resolution and cluttered background. This image contains multiple target instances (i.e., the "first target objects") that need to be identified and located. These targets may be common objects in the remote sensing scene, such as aircraft, ships, vehicles, and bridges, and have characteristics such as arbitrary rotation attitude, some being small targets, and possibly densely distributed.

[0050] S102, Generate first directional features of multiple first target objects at different preset rotation angles based on the first remote sensing image.

[0051] In this embodiment of the application, based on the input first remote sensing image, the RAMMC module generates a unique first direction feature for each first target object (such as a ship or vehicle) in the image for a preset discrete rotation angle (such as 0°, 90°, 180°, 270°), so that each target's different rotational posture has a corresponding explicit feature encoding, providing support for subsequent accurate detection and attitude estimation.

[0052] In one embodiment, see Figure 2 This is a flowchart illustrating the process of obtaining directional features provided in an embodiment of this application. Figure 1 ,like Figure 2 As shown, step S102 includes: S201, Extract initial features corresponding to the first remote sensing image; wherein, the initial features include texture, edge and spatial location information corresponding to multiple first target objects in the first remote sensing image.

[0053] In this embodiment, the input first remote sensing image is processed by a backbone network (such as ResNet) to extract the "initial features" of the image. These features are abstract expressions of the original image information, including the basic structural information of the background in the image, as well as key information of multiple first target objects (such as ships, aircraft, and vehicles), such as texture (such as the deck texture of ships and the outline details of vehicles), edges (such as the outline boundaries of buildings and the structural edges of bridges), and spatial location (such as the coordinate range of the target in the image and the relative distribution between targets). This lays the foundation for the subsequent RAMMC module to generate directional features and achieve accurate detection.

[0054] Specifically, the backbone network can be a common deep learning architecture such as ResNet, adapted to the MMRote and Ultralytics (YOLO series) frameworks for initial feature extraction. First, the first remote sensing image is standardized by normalizing the pixel values ​​(e.g., mapping them to the 0-1 range) and adjusting them to the preset input size of the backbone network (e.g., the uniform scale during training / inference in the document) to ensure that the network input format is consistent.

[0055] Then, the image is scanned by sliding multiple layers of convolutional kernels (such as 3×3 convolutions) to capture low-level features (edges, textures). For example, the first convolutional layer identifies the light and dark boundaries (edges) of the image. Subsequent convolutional layers aggregate these low-level features to form more complex texture features (such as the texture and structural details of the target surface). Finally, the backbone network outputs feature maps at different levels (such as feature maps F(s) with stride=8 and 16, i.e., the initial feature maps). Shallow feature maps (high resolution) retain more edge and texture details, while deep feature maps (low resolution) contain more abstract target structure and spatial distribution information, adapting to the detection needs of targets at different scales (especially small targets).

[0056] S202, dimensionality reduction is performed on the initial features to obtain the second features.

[0057] In this embodiment, dimensionality reduction of the initial features is a feature preprocessing step in the RAMMC module. The core is to perform linear transformation on the input feature map through a 1×1 convolution kernel to achieve the three major goals of "dimensionality reduction, channel fusion, and reduced computation", laying the foundation for subsequent convolution with rotational sub-kernels and generation of directional features.

[0058] In simple terms, it involves "simplifying or reorganizing" the initial features (including target texture, edges, and spatial location information) output by the backbone network—without changing the spatial dimensions (height H, width W) of the feature map, only adjusting the number of channels (C) of the features to make the features more suitable for the computational needs of subsequent rotational convolutions, while avoiding parameter redundancy.

[0059] Specifically, the multi-scale feature map output by the backbone network, i.e. the initial feature map (such as feature map F(s) with stride=8 or 16), has the shape "C_in×H×W" (C_in is the number of input channels, H is the height, and W is the width). The input features are convolved channel by channel using 1×1 convolution kernels (the number of kernels is C_out). Essentially, this is a linear projection transformation to obtain Xrot, i.e., the second feature.

[0060] S203, Generate first direction features corresponding to multiple first target objects at different preset rotation angles based on the second feature.

[0061] In this embodiment of the application, based on the second feature (including the basic abstract information of the first target object), for each first target object in the image, a corresponding exclusive first direction feature is generated for each preset different rotation angle, so that each target's different rotation posture has an explicit feature code, which provides support for subsequent accurate identification of target category, location and determination of rotation posture.

[0062] In the above method, by first extracting initial features containing target texture, edges and spatial location, and then generating exclusive first-direction features at a preset angle after dimensionality reduction and simplification, the core geometric and semantic information of the target is preserved, the computational complexity is reduced, and the direction-sensitive information of different rotational postures is explicitly encoded, providing a precise foundation for subsequent feature fusion and isovariance constraints, and effectively improving the detection robustness and posture estimation accuracy of arbitrarily rotating targets in remote sensing images.

[0063] In the above method, by first extracting initial features containing target texture, edges and spatial location, and then generating exclusive first direction features at a preset angle after dimensionality reduction and simplification, the core geometric and semantic information of the target is preserved, the computational complexity is reduced, and the direction-sensitive information of different rotational postures is explicitly encoded, providing an accurate foundation for subsequent feature fusion and isovariance constraints, and effectively improving the detection robustness and posture estimation accuracy of arbitrarily rotating targets in remote sensing images.

[0064] In one embodiment, see Figure 3 This is a flowchart illustrating the process of obtaining directional features provided in an embodiment of this application. Figure 2 ,like Figure 3 As shown, step S203 includes: S301, obtain multiple predefined raw convolution kernels.

[0065] In the embodiments of this application, before module training, a set of learnable basic convolutional kernels (i.e. "mother kernels") are predefined and initialized. These mother kernels are the "basic templates" for generating subsequent directional sub-kernels. They do not directly participate in feature extraction, but generate multiple directional specific sub-kernels by rotation to achieve feature capture of targets with different rotation angles.

[0066] For example, M=4 learnable mother kernels are set. (The number can be adjusted according to the scene), the shape of each mother core is as follows: .

[0067] S302, transform each original convolution kernel based on multiple preset rotation angles to obtain multiple sub-convolution kernels corresponding to each original convolution kernel.

[0068] In this embodiment, based on preset discrete rotation angles (such as 0°, 90°, 180°, 270°), each predefined original convolution kernel (mother kernel) is rotated and transformed. Finally, a set of sub-convolution kernels (sub-kernels) with the same number of preset angles are generated for each mother kernel, forming a correspondence of "1 mother kernel → t (preset number of angles) sub-kernels". All sub-kernels share the basic parameters of the mother kernel, and only the spatial structure is adjusted with the rotation angle.

[0069] Specifically, this paper uses the quarter-rotation group. As a basic rotation group, corresponding to four discrete angles of 0°, 90°, 180°, and 270°, it ensures coverage of the most common rotational attitudes of remote sensing targets. For each parent kernel... The daughter nucleus is generated by rotating the mother nucleus, as shown in the formula:

[0070] This results in M×t directional convolution kernels (sub-convolution kernels).

[0071] S303, the second feature is convolved with multiple sub-convolution kernels corresponding to each original convolution kernel to obtain multiple first-direction features.

[0072] In this embodiment, the second feature (including target texture, edge, and spatial location information) after 1×1 projection is used as input, and discrete convolution operations are performed one by one with all the sub-convolution kernels (M×t, such as 4×4=16 in the document) generated by rotating the parent kernel. The final output is multiple first-direction features corresponding to each sub-kernel. Each first-direction feature is bound to a preset rotation angle to specifically capture the target's direction-sensitive information at the corresponding angle. The calculation formula is as follows:

[0073] in, For the m-th mother nucleus, the α-th angle daughter nucleus This refers to the first directional feature obtained by convolving a single sub-kernel with the second feature.

[0074] In the above method, a sub-convolution kernel is generated by transforming the predefined original convolution kernel at a preset angle, and then convolved with the dimension-reduced second feature to generate the first directional feature. This method not only explicitly encodes the rotation structure by using the parameter-shared sub-convolution kernel without increasing the model complexity, but also accurately captures the directional sensitive information of the target under different rotation postures. This lays a solid foundation for subsequent isovariant constraints and feature fusion, and effectively improves the detection accuracy and robustness of targets with arbitrary rotation in remote sensing images.

[0075] S103, target detection is performed on the first remote sensing image based on multiple first directional features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object.

[0076] In this embodiment, multiple first directional features (each bound to a preset rotation angle) generated by the RAMMC module are used, combined with the classification and regression branches of the network, to perform target detection on the first remote sensing image and identify the first target category (such as ships, aircraft, vehicles, etc.) of each first target object; on the other hand, the first target pose (i.e., the actual rotation angle) corresponding to each target is accurately inferred, and finally the complete detection result of "category + pose" of all targets in the whole image is output.

[0077] In the above method, the original remote sensing image to be detected (i.e., the first remote sensing image) is first acquired, and then the specific directional features of the image under different rotation angles (i.e., multiple first directional features) are extracted. Finally, the detection is completed based on these features covering multiple rotational attitudes, which not only identifies multiple target categories (first target categories) in the image, but also clarifies the specific rotational attitude (first target attitude) corresponding to each target. Since the directional features corresponding to different rotation angles of the remote sensing image are extracted, the model can fully capture the feature information of the target under various attitudes. It can learn the model without relying on data augmentation to expand the samples, and provides geometric modeling theoretical support. It can avoid feature omission or distortion caused by target rotation, thereby accurately matching the actual attitude and category of the target, effectively improving the detection accuracy of remote sensing targets with diverse rotational attitudes, and reducing missed detections and false detections.

[0078] In one embodiment, see Figure 4 This is a schematic diagram of the process for obtaining target detection results provided in an embodiment of this application, such as... Figure 4 As shown, step S103 includes: S401, directional comprehensive features are obtained based on multiple first directional features.

[0079] In this embodiment, each first directional feature is bound to a preset rotation angle, specifically capturing the target's directional sensitive information at the corresponding angle. By fusing these scattered angle-specific features, a single comprehensive directional feature is formed. This feature integrates the directional information of all preset rotation angles, fully covering the possible rotational attitudes of the target, while maintaining equivariance (when the input feature rotates, it will synchronously present predictable rotational changes), accurately encoding the target's rotational attitude information and providing core support for subsequent target attitude regression.

[0080] In one embodiment, see Figure 5 This is a flowchart illustrating the computational direction synthesis features provided in an embodiment of this application, such as... Figure 5 As shown, step S401 includes: S501, each first directional feature is subjected to denoising and directional feature enhancement processing to obtain multiple second directional features.

[0081] In this embodiment, for the multiple first directional features (each bound to a preset rotation angle) previously generated by sub-kernel convolution, denoising (suppressing background noise and redundant information) and directional feature enhancement (strengthening key information matching the target with the corresponding rotation angle) are performed respectively. Finally, a purer second directional feature with higher directional recognition is output for each first directional feature, laying the foundation for subsequent fusion to generate comprehensive directional features.

[0082] In simple terms, it involves "refining and strengthening" each "angle-specific first direction feature"—removing irrelevant interference, highlighting the target's direction-sensitive information, making each feature more accurately correspond to its bound rotation angle, and improving the accuracy of subsequent attitude estimation.

[0083] S502, sum the second-direction features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel to obtain the first comprehensive features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel.

[0084] In this embodiment, for each original convolutional kernel (parent kernel), the second-direction features (already denoised and direction-enhanced) corresponding to the multiple sub-convolutional kernels generated by its rotation are integrated through summation. Finally, a set of first comprehensive features, consistent with the number of sub-convolutional kernels, is output for each parent kernel. Each first comprehensive feature retains the direction-sensitive information of the corresponding sub-kernel binding angle and, through summation, fuses the associated features of other sub-kernels under the same parent kernel, improving the completeness and robustness of the features. The calculation formula is as follows:

[0085] in, For spatial attention, This represents the directional weight.

[0086] S503, directional comprehensive features are obtained by splicing together multiple first comprehensive features.

[0087] In this embodiment, multiple first comprehensive features (each corresponding to an angle-related feature under a single parent kernel) previously obtained through summation are integrated into a single comprehensive directional feature through a channel concat operation. This feature, as a typical isovariant feature, fully preserves the directional sensitive information of all parent kernels and all preset rotation angles, providing comprehensive and accurate feature support for subsequent target attitude regression.

[0088] In simple terms, it involves concatenating a set of first comprehensive features corresponding to each mother core along the channel dimension to form a "total feature" that contains information from all mother cores and all angles. This maintains equivariance while achieving comprehensive information aggregation, enabling the network to accurately capture the target's rotational attitude. The formula is as follows:

[0089] in, It is an isovariant feature, namely a directional comprehensive feature.

[0090] In the above method, the first directional features are purified by denoising and directional enhancement, then the sub-kernel features under the same mother kernel are summed and aggregated, and finally the multi-mother kernel comprehensive features are spliced ​​to obtain the directional comprehensive features. This not only effectively filters noise and enhances the target's directional sensitive information, but also integrates multi-mother kernel-multi-angle features by summing and splicing, and fully preserves rotational and other variable properties, providing comprehensive and high-quality feature support for subsequent accurate attitude estimation, and significantly improving the robustness of remote sensing detection of arbitrarily rotating targets.

[0091] S402, obtain core integrated features based on directional integrated features; wherein, the core integrated features are used to represent the feature information of each first target object in the first remote sensing image that has not changed under preset different rotation angles.

[0092] In this embodiment, core integrated features are obtained by further extracting, filtering, or fusing the directional integrated features of the target object in the first remote sensing image (i.e., integrating the feature information of the object in different directional dimensions). The key value of this feature is that it can accurately capture the "rotation invariance" of each first target object in the first remote sensing image. That is, no matter what posture the target object presents at multiple preset different rotation angles (such as 0°, 90°, 180°, 270°, etc.), the core integrated features can retain the most essential inherent information of the object that does not change with the rotation angle (such as the shape outline, key structural proportions, core texture patterns, etc. of the object), thereby achieving stable identification, matching, or analysis of the target object and avoiding feature misjudgment caused by differences in rotation posture.

[0093] In one embodiment, see Figure 6 This is a flowchart illustrating the calculation of core comprehensive features provided in an embodiment of this application, such as... Figure 6 As shown, step S503 includes: S601, perform feature decomposition on the directional comprehensive features to obtain multiple third-direction features; among them, one third-direction feature corresponds to one second-direction feature.

[0094] In this embodiment of the application, the integrated directional features are "splitting". Each third directional feature obtained after splitting will correspond one-to-one with a certain second directional feature before splitting (one to one, without repetition or omission).

[0095] S602, perform directional pooling on each third-direction feature to obtain multiple fourth-direction features after pooling.

[0096] In this embodiment, after obtaining multiple third-direction features that correspond one-to-one with the original second-direction features through feature decomposition, directional pooling operation is performed on each third-direction feature separately (essentially extracting key information of the feature and reducing dimensionality), and finally outputting multiple fourth-direction features with more concise dimensions and more focused information.

[0097] The core of directional pooling is to aggregate statistics according to the directional dimension. Common operations include "maximum pooling, average pooling, global pooling", etc. The appropriate method should be selected according to the feature type (such as vector type, matrix type). After performing directional pooling on each third directional feature, its corresponding fourth directional feature is obtained.

[0098] S603 concatenates multiple fourth-direction features to obtain the core comprehensive feature.

[0099] In this embodiment, after obtaining multiple simplified fourth-direction features (each corresponding to core information of an angle) through directional pooling, these features are concatenated into a complete high-dimensional feature vector according to preset rules (such as angle order), which is the core comprehensive feature. This feature integrates key information about the target object under all preset rotation angles, ultimately achieving rotation invariance (no matter which preset angle the target rotates to, the core feature can stably represent the essence of the target).

[0100] In the above method, core comprehensive features are obtained by associating second-direction features through feature decomposition, extracting rotation-invariant information through directional pooling, and splicing and integrating multi-dimensional features. This not only accurately preserves the essential information of the target category and shields rotation interference, but also enhances the robustness of features through pooling and splicing. This provides high-quality invariant feature support for accurate identification of target categories and effectively improves the classification stability and detection reliability of remotely sensed targets with arbitrary rotation.

[0101] S403, target detection is performed on the first remote sensing image based on the directional integrated features and the core integrated features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object.

[0102] In this embodiment of the application, the two types of features output by the RAMMC module are the core—the equivariant directional synthesis feature ( ) and the core integrated feature of rotation invariance ( The core integrated features are adapted to the regression and classification branches of the detection network respectively, and work together to complete the target detection: the core integrated features are responsible for shielding the rotation interference and accurately identifying the first target category of each first target object (such as ships, aircraft, vehicles, etc.); the orientation integrated features are responsible for encoding the rotation attitude information and accurately inferring the first target attitude (actual rotation angle) of each target, and finally outputting the complete detection result of "category + attitude" of all targets in the whole image.

[0103] Before acquiring the first remote sensing image to be trained, the detection model needs to be trained. The following is the specific content of training the detection model, in which the proposed RAMMC adapter is instantiated into the YOLO style detector, and the YOLO style detector containing the RAMMC adapter is trained.

[0104] In the above method, multiple first-direction features are first aggregated to obtain directional comprehensive features, and then core comprehensive features that shield rotation interference are extracted through group pooling. Finally, relying on the collaborative detection of the two types of features, the directional comprehensive features are used to accurately encode the target rotation attitude and ensure the accuracy of attitude estimation, while the core comprehensive features are used to stably capture the essential information of the target category, effectively improving the robustness of detection of arbitrary rotating targets in remote sensing images and the accuracy of classification and attitude inference.

[0105] In one embodiment, see Figure 7 This is a schematic diagram of the model training process provided in the embodiments of this application, such as... Figure 7 As shown, including S701, Obtain the training set; wherein the training set includes multiple second remote sensing images to be trained; wherein each second remote sensing image includes multiple second target objects.

[0106] In this embodiment of the application, a “training set” for model training is obtained. This dataset consists of multiple second remote sensing images to be trained (“second” is only a descriptive term and has no special technical meaning; it corresponds to the input data in the training phase). Each second remote sensing image contains multiple second target objects that the model needs to learn to recognize (i.e., target instances in the training samples, such as ships, aircraft, vehicles, etc.).

[0107] In simple terms, it involves collecting a batch of labeled remote sensing images as training data—each image contains multiple targets. The model learns from the labeled information (category, pose, location, etc.) of these images and the corresponding targets, thereby mastering the characteristic patterns of remote sensing targets and gaining the ability to detect new images.

[0108] For example, training subsets of three benchmark datasets for rotational equivariant feature modeling and object detection of remote sensing images—DOTA-v1.0, FAIR1M-v1, and FAIR1M-v2.0—can be used. These datasets are characterized by high annotation quality, comprehensive object types, and wide scene coverage. The DOTA-v1.0 training set contains 1,411 images, covering 15 types of objects (aircraft, ships, etc.), and annotates more than 188,000 oriented bounding boxes. The FAIR1M-v1 / v2.0 training sets contain 15,000 / more high-resolution images, covering 37 types of fine-grained objects, and have more than 1 million / 2 million annotated instances, respectively, which are suitable for fine-grained classification and training requirements for complex scenes.

[0109] S702, for each second remote sensing image in the training set, generate the fifth direction features corresponding to each of the multiple second target objects in each second remote sensing image at different preset rotation angles.

[0110] In this embodiment, for each second remote sensing image in the training set, using the same feature extraction logic as in the inference stage, a unique fifth-direction feature is generated for each second target object (target instance in the training sample) in the image at multiple preset discrete rotation angles (such as 0°, 90°, 180°, and 270° in the document). These features are the core basis for the "isovariability constraint" and "classification / regression loss calculation" during training; essentially, they are "angle-specific feature labels" for the targets in the training samples, used to allow the model to learn the correspondence between "target rotation and feature response".

[0111] In simple terms, it involves generating a set of "angle-specific features" for each target in each image in the training set, based on a preset angle. This allows the model to clearly learn "what features should a target at a certain angle correspond to" during training, laying the foundation for subsequent isovariance regularization and accurate detection.

[0112] The core process of generating the fifth-direction feature during the training phase is completely synchronized with the logic of generating the first-direction feature during the inference phase (only the term "fifth" is used to distinguish the training phase feature), ensuring consistency between training and inference. This process relies on the core design of the RAMMC module, which will be elaborated here. For details, please refer to the generation process of the first direction mentioned above.

[0113] S703, target detection is performed on the second remote sensing image based on multiple fifth-direction features to obtain the second target category of all second target objects in the second remote sensing image and the second target pose of each second target object.

[0114] In this embodiment, multiple fifth-direction features (each bound to a preset rotation angle and denoised and enhanced angle-specific features) generated based on the second remote sensing image of the training set are used to perform "simulated detection" of the second target object in the training sample through a detection branch (classification + pose regression) consistent with the inference stage. This outputs the prediction result (second target category + second target pose) of each second target object. This result is not the final application output, but is used as a "predicted label" to compare with the real annotation, and is used to calculate the training loss (detection loss + isovariance regularization term) and update the model parameters in reverse.

[0115] The detection logic and network structure during the training phase are completely consistent with those during the inference phase (only the "second" designation is used to distinguish the prediction results of training samples), ensuring consistency between training and inference and avoiding "detection during training, failure during inference." Specifically, the network structure (e.g., MLP, convolutional layers) and parameters of the classification and pose regression branches are exactly the same as those in the inference phase, and are updated synchronously during training. The aggregation method of the fifth-direction features (summation and concatenation to generate comprehensive directional features) and the extraction of core comprehensive features (group pooling) are completely consistent with the first-direction feature processing logic during the inference phase. For details, refer to the detection process for the first target category and the first target pose described above. Further details will not be elaborated here.

[0116] S704, calculate a first loss based on the second target category of all second target objects and the second target pose of each second target object; wherein, the first loss includes the loss between the second target category and the preset category and the loss between the second target pose and the preset pose.

[0117] In this embodiment, based on the prediction results (second target category + second target pose) of all second target objects obtained during the "simulated detection" phase of training, two types of losses are calculated and integrated into a first loss. The first loss is the classification loss between the "second target category" (model-predicted category) and the "preset category" (human-labeled true category), measuring the bias in category prediction. The second loss is the regression loss between the "second target pose" (model-predicted rotation angle) and the "preset pose" (human-labeled true rotation angle), measuring the bias in pose inference. The first loss is the core supervision signal driving model parameter updates and directly determines the accuracy of model classification and pose estimation.

[0118] Specifically, the classification loss, i.e., the loss between the second target class (the class predicted by the model) and the preset class (the real class labeled by humans), can use cross-entropy loss, which is suitable for multi-class classification scenarios (such as 15 classes in DOTA and 37 classes in FAIR1M). The core formula is:

[0119] Where N is the total number of second target objects, ycls,i is the one-hot encoding of the true category of the i-th target (e.g., if the true category is "ship", the corresponding index position is 1, and the rest are 0), and y^cls,i is the confidence score of the category predicted by the model. The true category of the i-th target is encoded using a one-hot encoding (e.g., if the true category is "ship", the corresponding index position is 1, and the rest are 0). This represents the confidence level of the class predicted by the model.

[0120] The pose regression loss, i.e., the loss between the second target pose (model-predicted rotation angle) and the preset pose (human-annotated true rotation angle), can use CIoU loss (CompleteIntersectionoverUnion Loss) instead of the traditional L1 / L2 loss. The core reason is that CIoU simultaneously considers the overlap of the bounding boxes, center distance, aspect ratio, and rotation angle, solving the problem of zero gradient when the bounding boxes do not overlap, making it more suitable for pose regression of remotely sensed rotating targets. Its calculation formula is:

[0121] Where IoU represents the overlap between the two frames. Let c be the squared center distance, c be the diagonal length of the minimum bounding rectangle enclosing the two boxes, α be the weighting coefficient, and v be the consistency measure of aspect ratio and rotation angle; the pose regression loss is:

[0122] The smaller the loss value, the closer the predicted pose is to the actual pose.

[0123] In summary, the first loss can be determined as:

[0124] Through weighting coefficients Balancing the importance of classification loss and pose regression loss (default) Set to 1 (the weights can be adjusted according to the characteristics of the dataset, such as increasing the weights for fine-grained pose tasks), and finally obtain the first loss. .

[0125] S705, calculate the second loss between the first rotation feature and the second rotation feature; wherein, the first rotation feature is the feature data after synchronously moving the direction channel of the second direction comprehensive feature corresponding to the second remote sensing image by a preset rotation angle; the second rotation feature is the feature data of the third direction comprehensive feature extracted after rotating the second remote sensing image by an angle and then rotating it in the opposite direction by an angle; wherein, the direction channel is used to generate the fifth direction feature corresponding to the second remote sensing image.

[0126] In this embodiment, two sets of "rotation-related features" (first rotation feature and second rotation feature) are constructed, and the difference between them is calculated as a second loss, forcing the model to satisfy rotation equivariance—that is, the geometric consistency of "input image rotation → feature synchronous rotation". Essentially, through loss constraints, the model learns that "after the target rotates, the change in the direction channel of the feature strictly matches the image rotation angle", ensuring the purity of the equivariance of the comprehensive direction features and providing theoretical support for accurate pose estimation.

[0127] In simple terms, it compares rotated features generated in two different ways, penalizing the difference between the two to ensure that the model obtains consistent results regardless of whether it rotates the image first and then extracts features or extracts features first and then rotates the channels, thereby solidifying the equivariant properties of the features. The formula for calculating the second loss (with related proof and explanation below) is as follows:

[0128] S706, calculate the third loss between the first prediction result and the second prediction result; wherein, the first prediction result includes the second target category and the second target pose; the second prediction result is the third target category and the third target pose corresponding to the second remote sensing image obtained by rotating the second remote sensing image by an angle and then performing target detection.

[0129] In this embodiment, the difference between the "prediction result of the original second remote sensing image (first prediction result)" and the "prediction result after image rotation correction (second prediction result)" is calculated to constrain the predictive consistency of the model—ensuring that after target rotation, the class and pose predictions output by the model still conform to geometric logic, avoiding prediction distortion caused by rotation, and providing supervision for the geometric stability of the detection results. The formula (related proof and explanation are given below) is as follows:

[0130] in, d( represents the detection prediction result (including category and pose) for input x. , () is a difference measure based on IoU.

[0131] S707, calculate the total loss based on the first loss, the second loss, and the third loss.

[0132] In this embodiment, the total loss is calculated by weighted fusion of the first loss (basic detection loss). Second loss (feature-level regularization term) ) and the third loss (predictive regularization term) The formula, strictly following the document definition, is based on the core logic of balancing "detection accuracy optimization" and "geometric consistency constraints," ensuring that the model possesses stable rotational equivariance while accurately identifying target categories and poses. The specific formula (with related proofs and explanations below) is as follows:

[0133] S708: If the total loss does not converge, the parameters are adjusted until the total loss converges, at which point the training ends.

[0134] In this embodiment, when the total loss has not converged, it is necessary to continuously iterate and train by selectively adjusting the model parameters (including hyperparameters and structural parameters) until the loss value stabilizes at a low level without significant fluctuations. At this point, the model training is complete and can be used for rotation-sensitive feature modeling and target detection inference for remote sensing images. The core logic is to eliminate loss fluctuations or stagnation problems through parameter optimization, ensuring that the model fully learns rotation-aware features and geometric consistency constraints.

[0135] It should be noted that during the training process or parameter adjustment, a channel gating mechanism is used to separate the original feature stream (the basic features F(s) output by the backbone) from the rotated feature stream (the invariant features generated by the RAMMC module). Weighted fusion is performed to inject rotation-aware invariant information while preserving the original feature extraction capabilities, achieving a complementary advantage of "basic features + rotation-robust features". The formula is:

[0136] Fusion features Multi-scale feature fusion is performed on the neck of the input detector (such as FPN), followed by branching. and regression branch Make predictions.

[0137] S709, after training, acquires the first remote sensing image to be detected for target detection.

[0138] In this embodiment, after training, target detection is performed on the first remote sensing image according to the process of "image preprocessing → feature extraction → RAMMC module enhancement → dual feature fusion → classification and pose regression → post-processing". The final output is "first target category + first target pose" of all first target objects. The core is to reuse the trained model parameters (especially the rotation perception capability of the RAMMC module) to ensure that the detection accuracy matches the geometric consistency constraints of the training stage.

[0139] In the above method, by constructing a training set containing multiple rotating targets, generating angle-specific fifth-direction features, and co-calculating the detection loss and the two-level equal-variable regularization loss optimization model, and adjusting the parameters until the total loss converges, the model can fully learn the essence of the target category and the rotation posture rules. At the same time, the geometric consistency is strengthened through feature-level and prediction-level constraints, ensuring that the trained model can accurately and robustly meet the detection requirements of arbitrary rotating targets in the first remote sensing image.

[0140] This application includes comprehensive experiments to validate the effectiveness and generality of the proposed framework. Based on the YOLO series of rotating target detection tasks, our method achieves significant accuracy improvements; furthermore, we integrate it into other detection backbones to further verify its adaptability. This section details the benchmark dataset, implementation details, comparisons with state-of-the-art methods, and ablation experiments. Specifically: data: (a) DOTAv1.0: This is one of the largest and most challenging remote sensing detection datasets to date, containing 2,806 aerial images (resolutions from 800×800 to 4000×4000) and providing over 188,000 directional bounding boxes covering 15 categories (such as aircraft, ships, tanks, bridges, large vehicles, small vehicles, ports, helicopters, etc.). The dataset is divided into a training set of 1,411 images, a validation set of 937 images, and a test set of 458 images. The evaluation metric is mAP at IoU 0.5.

[0141] (b) FAIR1Mv1: This dataset contains 15,000 high-resolution images (maximum 8000×8000), with over 1 million annotated instances across 37 fine-grained categories. It primarily covers aircraft, ships, and vehicles, with a 6:2:2 split for training / validation / testing. Compared to DOTA, FAIR1Mv1 places greater emphasis on fine-grained category differentiation, such as the distinction between Boeing and Airbus aircraft models.

[0142] (c)FAIR1Mv2: This version expands to over 2 million target instances, while still maintaining 37 categories. Compared to v1, it features greater diversity, a more balanced category distribution, and higher-quality annotations, making it a benchmark closer to real-world applications in complex and dense scenarios.

[0143] Experimental details We implement the RAMMC module based on UltralyticsYOLO and MMRotate, covering both anchor-free and anchor-based detectors. In YYOLO, we follow the default enhancement strategies, including random scaling, HSV / color perturbation, Mosaic, and MixUp. In MMRotate, training is directly based on the entire image (without cropping or piecing) and includes multi-scale scaling, random rotation, flipping, and photometric enhancement.

[0144] Module instantiation.

[0145] Within each backbone block, we first generate rotational branch input features using 1×1 convolutions (dimensionality reduction ratio β=0.5). RAMMC employs M=4 parent kernels, each expanded into K=4 rotational copies (uniformly sampled angles). We use lightweight gating and attention modules, including SE-like selective-kernel gating, cross-directional orientation attention, and channel gates for fusing the rotational and original streams. The default weight for the orientation consistency regularization term is λ=0.1.

[0146] Differentiable approximation.

[0147] In the prediction layer regularization term, we use CIoU as an alternative to standard IoU because it still provides stable gradients when the predicted boxes do not overlap. In the matching step, we employ Sinkhorn optimal transport with entropy regularization (5 iterations). =0.05), to obtain a differentiable double random matrix as an approximation of the Hungarian matching. The above settings were kept constant in all experiments.

[0148] Optimize strategies.

[0149] All models were trained on 8 NVIDIA RTX 3090 GPUs with a batch size of 16 per GPU. The optimizer was SGD with momentum of 0.9 and weight decay set to 10. 4. Use cosine learning rate scheduling. Enable automatic mixed precision (AMP) during training.

[0150] Inference Strategies. We evaluate model performance in two scenarios: (1) whole-graph inference (non-slicing); and (2) slicing inference, using overlapping windows of size 1024×1024 and aggregating results by merging NMS. Both approaches ensure a fair comparison with existing methods and reflect real-world deployment requirements.

[0151] Quantitative assessment: We employ standard metrics widely used in rotating target detection and model efficiency analysis, AP50. Following the VOC evaluation protocol, we calculate AP at IoU 0.5. For class c, let the precision-recall function be:

[0152] in, These represent true positives, false positives, and false negatives, respectively. Category AP is defined as the area under the precision-recall curve:

[0153] The final result is the category average:

[0154] Intersection over Union (IoU). For the predicted oriented bounding box Bp and the ground truth bounding box Bgt:

[0155] ConfusionMatrix. Defined as:

[0156] diagonal The diagonal indicates a correct classification, while off-diagonal items indicate a misclassification.

[0157] ModelSize (number of parameters). The total number of model parameters is:

[0158] Inference Time. The average single-graph inference latency is:

[0159] These metrics collectively measure detection accuracy (AP50, IoU, confusion matrix) and efficiency (parameter count, inference latency). These results demonstrate that our design not only improves overall detection accuracy but also maintains stable robustness under challenging conditions such as fine-grained categories, complex scenarios, and no data augmentation.

[0160] This paper proposes RAMMC—a theoretically grounded rotating target detection adapter. Unlike previous heuristic plugins, RAMMC explicitly encodes rotating geometry through a rotation kernel library and orientation-aware aggregation, and establishes a provable upper bound for rotationally equivariant errors by combining a mathematically derived two-level consistency regularization term. This ensures stable feature transformations while maintaining a unified expression of invariant and equivariant features.

[0161] Our theoretical analysis covers the invariance brought by pooling, the strict equivariance guaranteed by the group loop design, and the upper bound of error under discretization conditions, providing sufficient theoretical support for the experimental results. Extensive experiments on multiple benchmarks show that our method achieves significant and consistent performance improvements (e.g., 84.32 mAP on DOTA-v1.0, 47.31 mAP on FAIR1M-v1, and 52.28 mAP on FAIR1M-v2.0), validating the framework's generality.

[0162] Overall, this study demonstrates that embedding mathematically rigorous geometric priors into the detection network structure is feasible and effective. RAMMC not only delivers performance improvements but also showcases the potential for combining theory and practice in high-resolution remote sensing scenarios. Future work will explore its real-time deployment, multimodal expansion, and broader applications of isovariant structures in vision tasks.

[0163] The proof of the relevant formulas provided in this application is as follows: This application establishes the theoretical properties of RAMMC and its regularization strategy. We first give the definition of equivariance defect and explain how group-based structural design and regularization terms jointly mitigate its influence throughout the detection pipeline. Definition 1 (Equivariance defect). Let Φ be the detection network and x be the input image. In the group action... Below (for example) The variable error is defined as: (1) This quantity measures the degree to which the network as a whole deviates from perfect isovariability.

[0164] Lemma1(Group pooling induces invariance). Let... ×H×W is a feature tensor with directional channels, which in the group According to a certain unit Transformation. Define the Reynolds operator (group average): (2) but right Unchanged: For all ,have .

[0165] Proof. Using the associative law of groups : (3) Proposition 1 (RAMMC isovariability based on group cycle structure). The effect on the image / feature is spatial rotation. and set Indicates direction index Cyclic translation, i.e. Consider a RAMMCblock containing M mother cores. and the sub-nuclei generated by rotating according to the direction index Defined as: (4) set up Let P be the feature of input X after a 1×1 projection (where P is a fixed linear mapping). Define the directional response (directional feature). (Discrete convolution).

[0166] Assuming gating mapping The spatial graph and the directional weights Am,r(X) (scalar or vector) satisfy the following group-circulanttying: (5) That is, when the input rotation is applied, the direction index is translated. And simultaneously rotate S uniformly.

[0167] RAMMC aggregation is defined as: (6) Then the block satisfies equivariance: (7) in right Its function is spatial rotation (if the direction axis is preserved, it is spatial rotation and channel circulation). combination).

[0168] Proof is performed in three steps.

[0169] Step 1 (Linear Projection and Convolution). P is a channel-wise 1×1 linear mapping, therefore it is commutative with spatial rotation: (8) The directional convolution part is defined by the rotational convolution kernel and the convolution with 90°. Mesh rotation interchangeability, has (9) Step 2 (Group Loop Binding). When inputting rotation, the following applies: (10) (11) Combine (10) and (11) above:

[0170] It utilizes spatial rotation and commutative element-wise multiplication: (12) Step 3 (Index Transformation and Concatenation). Utilizing the invariance of circular indices: (13) All m satisfy isovariability. Concatenating them, we get: (14) If the direction axis is retained, the overall effect is If the direction is pooled, then it is Therefore: (15) Theorem 1 (Isovariant Error Propagation under RAMMC Integration). Based on existing Lipschitz continuity analysis of neural networks, SKgating and the attention module each possess a Lipschitz constant. and Therefore, its deviation propagates additively between layers: (16) Where h is the grid size, p is the kernel radius, and t is the number of directional channels. This indicates the contextual bias caused by input rotation; This indicates a cyclic misalignment on the direction axis.

[0171] Proposition2 (Consistency Regularization Constraint: Upper Bound of Isovariant Error). If the network contains two auxiliary regularization terms. and Then we have: (17) in ¯Includes the approximate residuals generated by kernel rotation and attention projection.

[0172] Conclusion: This upper bound indicates that the group structure of RAMMC, together with the two regularization terms, restricts the equivariance error; the larger t is, the smaller the discretization error; t=1 degenerates into a regular CNN. The classification head uses invariant features. The regression head uses equivariant features This achieves a balance between robustness and expressiveness.

[0173] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0174] Corresponding to the target detection method in the above embodiments, Figure 8 This is a structural block diagram of the rotational isotropic feature modeling and target detection device for remote sensing images provided in the embodiments of this application. For ease of explanation, only the parts related to the embodiments of this application are shown.

[0175] Reference Figure 8 The device includes: Training module 81 is used for: Obtain a training set; wherein the training set includes multiple second remote sensing images to be trained; wherein each second remote sensing image includes multiple second target objects; For each second remote sensing image in the training set, generate the fifth direction features corresponding to multiple second target objects in each second remote sensing image under different preset rotation angles; Target detection is performed on the second remote sensing image based on multiple fifth-direction features to obtain the second target category of all second target objects in the second remote sensing image and the second target pose of each second target object; A first loss is calculated based on the second target category of all second target objects and the second target pose of each second target object; wherein, the first loss includes the loss between the second target category and the preset category and the loss between the second target pose and the preset pose; Calculate the second loss between the first rotation feature and the second rotation feature; wherein, the first rotation feature is the feature data after synchronously moving the direction channel of the second direction comprehensive feature corresponding to the second remote sensing image by a preset rotation angle; the second rotation feature is the feature data after rotating the second remote sensing image by a certain angle and then rotating the extracted third direction comprehensive feature by the opposite angle; wherein, the direction channel is used to generate the fifth direction feature corresponding to the second remote sensing image; Calculate a third loss between the first prediction result and the second prediction result; wherein the first prediction result includes the second target category and the second target pose; the second prediction result is the third target category and the third target pose corresponding to the second remote sensing image obtained by rotating the second remote sensing image by an angle and then performing target detection. Calculate the total loss based on the first loss, the second loss, and the third loss; If the total loss does not converge, the parameters are adjusted until the total loss converges, at which point the training ends. After training, the first remote sensing image to be detected is acquired for target detection.

[0176] Image acquisition module 82 is used to detect a first remote sensing image; the first remote sensing image contains multiple first target objects; The orientation feature generation module 83 is used to generate first orientation features corresponding to multiple first target objects at different preset rotation angles based on the first remote sensing image. The target detection module 84 is used to perform target detection on the first remote sensing image based on multiple first direction features, and to obtain the first target category and the first target pose of all first target objects in the first remote sensing image.

[0177] Optionally, the orientation feature generation module 83 is also used for: Extract initial features corresponding to the first remote sensing image; wherein, the initial features include texture, edge and spatial location information of multiple first target objects in the first remote sensing image; The initial features are reduced in dimensionality to obtain the second features; Based on the second feature, generate the first direction features corresponding to each of the first target objects at different preset rotation angles.

[0178] Optionally, the orientation feature generation module 83 is also used for: Obtain multiple predefined raw convolution kernels; Each original convolutional kernel is transformed based on multiple preset rotation angles to obtain multiple sub-convolutional kernels corresponding to each original convolutional kernel; The second feature is convolved with multiple sub-convolutional kernels corresponding to each original convolutional kernel to obtain multiple first-direction features.

[0179] Optionally, the target detection module 84 is also used for: A comprehensive directional feature is obtained based on multiple first-directional features; Core integrated features are obtained based on directional integrated features; wherein, the core integrated features are used to represent the feature information of each first target object in the first remote sensing image that does not change under different preset rotation angles; Target detection is performed on the first remote sensing image based on directional integrated features and core integrated features to obtain the first target category and the first target pose of all first target objects in the first remote sensing image.

[0180] Optionally, the target detection module 84 is also used for: Each first-directional feature is subjected to denoising and directional feature enhancement processing to obtain multiple second-directional features; The second-direction features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel are summed to obtain the first comprehensive features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel. The directional comprehensive feature is obtained by splicing together multiple first comprehensive features.

[0181] Optionally, the target detection module 84 is also used for: The directional comprehensive features are decomposed to obtain multiple third-direction features; each third-direction feature corresponds to a second-direction feature. Perform directional pooling on each third-direction feature to obtain multiple fourth-direction features after pooling. Multiple fourth-direction features are concatenated to obtain the core comprehensive features.

[0182] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0183] in addition, Figure 8 The target detection device shown can be a software unit, hardware unit, or a combination of software and hardware built into existing terminal equipment, or it can be integrated into the terminal equipment as an independent component, or it can exist as an independent terminal equipment.

[0184] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0185] Figure 9 This is a schematic diagram of the structure of the terminal device provided in the embodiments of this application. For example... Figure 9 As shown, the terminal device 9 of this embodiment includes: at least one processor 90 ( Figure 9 (Only one is shown in the diagram) a processor, a memory 91, and a computer program 92 stored in the memory 91 and executable on at least one processor 90, wherein the processor 90 executes the computer program 92 to implement the steps in any of the above-described target method embodiments.

[0186] The terminal device can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. This terminal device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that... Figure 9 This is merely an example of terminal device 9 and does not constitute a limitation on terminal device 9. It may include more or fewer components than shown in the figure, or combine certain components, or different components, such as input / output devices, network access devices, etc.

[0187] The processor 90 may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0188] In some embodiments, memory 91 may be an internal storage unit of terminal device 9, such as a hard disk or memory of terminal device 9. In other embodiments, memory 91 may be an external storage device of terminal device 9, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on terminal device 9. Furthermore, memory 91 may include both internal storage units and external storage devices of terminal device 9. Memory 91 is used to store operating system, application programs, bootloader, data, and other programs, such as program code of computer programs. Memory 91 can also be used to temporarily store data that has been output or will be output.

[0189] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the steps in the above-described method embodiments.

[0190] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0191] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. A computer-readable medium can include at least: any entity or device capable of carrying computer program code to a device / terminal device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0192] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0193] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0194] In the embodiments provided in this application, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0195] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0196] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for modeling rotationally equivariant features and detecting targets in remotely sensed images, characterized in that, The method includes: Acquire a first remote sensing image to be detected; the first remote sensing image contains multiple first target objects; Based on the first remote sensing image, generate multiple first orientation features corresponding to the first target object at different preset rotation angles; Target detection is performed on the first remote sensing image based on multiple first directional features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object.

2. The method for rotation-equal feature modeling and target detection of remote sensing images as described in claim 1, characterized in that, The step of generating multiple first orientation features corresponding to the first target objects at different preset rotation angles based on the first remote sensing image includes: Extract initial features corresponding to the first remote sensing image; wherein, the initial features include texture, edge and spatial location information corresponding to multiple first target objects in the first remote sensing image; The initial features are subjected to dimensionality reduction processing to obtain the second features; Based on the second feature, multiple first orientation features corresponding to the first target object at different preset rotation angles are generated.

3. The method for rotation-equal feature modeling and target detection of remote sensing images as described in claim 2, characterized in that, The step of generating multiple first orientation features corresponding to the first target object at different preset rotation angles based on the second feature includes: Obtain multiple predefined raw convolution kernels; Each original convolutional kernel is transformed based on multiple preset rotation angles to obtain multiple sub-convolutional kernels corresponding to each original convolutional kernel; The second feature is convolved with each of the multiple sub-convolutional kernels corresponding to each of the original convolutional kernels to obtain multiple first-direction features.

4. The method for rotation-equal feature modeling and target detection of remote sensing images as described in claim 3, characterized in that, The step of performing target detection on the first remote sensing image based on multiple first directional features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object includes: A comprehensive directional feature is obtained based on multiple first directional features; The core integrated features are obtained based on the directional integrated features; wherein, the core integrated features are used to represent the feature information of each of the first target objects in the first remote sensing image that does not change under preset different rotation angles; Target detection is performed on the first remote sensing image based on the directional integrated features and the core integrated features to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object.

5. The method for rotation-equal feature modeling and target detection of remote sensing images as described in claim 4, characterized in that, The step of obtaining the directional comprehensive feature based on multiple first directional features includes: Each first directional feature is subjected to denoising and directional feature enhancement processing to obtain multiple second directional features; The second directional features corresponding to each of the multiple sub-convolutional kernels of each original convolutional kernel are summed to obtain the first comprehensive features corresponding to the multiple sub-convolutional kernels of each original convolutional kernel. The directional comprehensive feature is obtained by splicing together multiple first comprehensive features.

6. The method for rotation-equal feature modeling and target detection of remote sensing images as described in claim 5, characterized in that, The process of obtaining core comprehensive features based on the directional comprehensive features includes: The comprehensive directional features are decomposed to obtain multiple third-party directional features; wherein, one third-party directional feature corresponds to one second-directional feature; Perform directional pooling on each of the aforementioned third-direction features to obtain multiple fourth-direction features after pooling. The core integrated feature is obtained by concatenating multiple fourth-direction features.

7. The method for rotational isotropic feature modeling and target detection of remote sensing images as described in any one of claims 1-6, characterized in that, Before performing target detection on the first remote sensing image to be detected, the method further includes: Obtain a training set; wherein the training set includes multiple second remote sensing images to be trained; wherein each second remote sensing image includes multiple second target objects; For each of the second remote sensing images in the training set, generate the fifth direction features corresponding to each of the multiple second target objects in each second remote sensing image at different preset rotation angles; Target detection is performed on the second remote sensing image based on multiple fifth-direction features to obtain the second target category of all second target objects in the second remote sensing image and the second target pose of each second target object; A first loss is calculated based on the second target category of all second target objects and the second target pose of each second target object; wherein, the first loss includes the loss between the second target category and the preset category and the loss between the second target pose and the preset pose; Calculate the second loss between the first rotation feature and the second rotation feature; wherein, the first rotation feature is the feature data after synchronously moving the directional channel of the second directional comprehensive feature corresponding to the second remote sensing image by a preset rotation angle; the second rotation feature is the feature data of the third directional comprehensive feature extracted after rotating the second remote sensing image by the rotation angle and then rotating it in the opposite direction by the rotation angle; wherein, the directional channel is used to generate the fifth directional feature corresponding to the second remote sensing image; Calculate a third loss between the first prediction result and the second prediction result; wherein, the first prediction result includes the second target category and the second target pose; the second prediction result is the third target category and the third target pose corresponding to the second remote sensing image obtained by rotating the second remote sensing image by the rotation angle and then performing target detection; Calculate the total loss based on the first loss, the second loss, and the third loss; If the total loss does not converge, the parameters are adjusted until the total loss converges, at which point the training ends. After training, the first remote sensing image to be detected is acquired for target detection.

8. A device for modeling rotational isotropic features and detecting targets in remote sensing images, characterized in that, include: Image acquisition module, used for detecting the first remote sensing image; The first remote sensing image contains multiple first target objects; The orientation feature generation module is used to generate multiple first orientation features corresponding to the first target object at different preset rotation angles based on the first remote sensing image. The target detection module is used to perform target detection on the first remote sensing image based on multiple first direction features, and to obtain the first target category of all first target objects in the first remote sensing image and the first target pose of each first target object.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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