Polarimetric sar bridge detection method based on fusion of cross-section probability modeling and graph topology analysis

Abstract

The application provides a polarimetric SAR bridge detection method fusing section probability modeling and graph topology analysis, first, water and land segmentation is performed on the polarimetric SAR image, and independent water area branches are extracted; for the end of each water area branch, a particle filtering algorithm is used for probability modeling, and a rectangular section representing a potential bridge connection point is robustly extracted; a water area network graph is constructed with the water area branches as nodes and matched section pairs as edges, the sections are accurately connected through a two-stage matching strategy combining bidirectional propagation verification and geometric constraint, and non-river water bodies are filtered out based on geometric features; edges in the network graph are traversed, and the bridge region is accurately positioned according to the geometric relationship between the matched sections. The application utilizes the stable topological characteristics that bridges cause water area rupture and form symmetrical sections, overcomes the problems that traditional methods are unstable, easy to miss detection and misjudgment under complex water area networks, narrow tributaries and strong noise interference, and realizes high-precision and high-robustness detection of multi-scale bridges.

Description

Technical Field

[0001] This invention relates to a method for detecting bridge targets in remote sensing images, and in particular to a polarimetric SAR bridge detection method that integrates cross-sectional probability modeling and graph topology analysis. Background Technology

[0002] Bridges play a crucial role as a key component of transportation infrastructure. Accurate and efficient bridge inspection is of great significance for transportation network planning, facility management, and post-disaster emergency response. With the rapid development of remote sensing technology, synthetic aperture radar (SAR), especially polarimetric SAR (PolSAR), has become an important data source for bridge inspection due to its all-weather, all-day imaging capabilities. However, due to the speckle noise inherent in SAR images, interference from complex scenes, and the structural diversity and scale variations of bridge targets themselves, achieving robust and accurate bridge inspection still faces many challenges.

[0003] Currently, bridge detection methods based on SAR images mainly include the following categories:

[0004] 1. Geometric Feature-Based Methods: These methods identify bridge structures by extracting geometric features such as edges and parallel line pairs from images. For example, bridge detection algorithms based on fuzzy theory utilize the linear and parallel features of bridges in SAR images for discrimination. However, these methods are sensitive to image quality and are prone to false positives or false negatives in situations with strong noise, strong scattering interference from riverbanks, or unclear bridge geometric features, resulting in poor stability.

[0005] 2. Spatial Relationship-Based Methods: These methods utilize the spatial distribution relationship between bridges and water bodies for detection, such as by detecting linear structures spanning water bodies. However, in complex water network scenarios (such as multi-branched rivers or densely networked river areas) or narrow river scenarios, the water structure is fragmented and the boundaries are blurred, which can easily lead to the failure of spatial relationship criteria, resulting in false positives or false negatives.

[0006] 3. Scattering Feature-Based Methods: These methods rely on the polarization scattering characteristics of the target, achieving detection by modeling the differences in scattering mechanisms between bridges and water / land. Although polarization information can provide richer target features, in real-world scenarios, bridges are diverse in type and complex in structure, and are affected by factors such as imaging angle and terrain undulations, making scattering characteristic modeling difficult. Especially under strong scattering background interference, the model's generalization ability is limited, and detection performance is prone to degradation.

[0007] 4. Deep Learning Methods: In recent years, deep learning has made significant progress in SAR target detection and has been introduced into bridge detection tasks. For example, some solutions propose a deep learning network based on balance and attention mechanisms, which improves the model's ability to identify bridges through feature fusion. These methods overcome the shortcomings of traditional methods in feature design to some extent and improve anti-interference capabilities. However, facing real-world challenges such as large bridge scale variations, complex backgrounds, significant scattering interference along the riverbank, and large differences in imaging parameters between data sources, existing deep learning models still struggle to completely avoid missed detections and false detections. Furthermore, their generalization ability is limited, and their performance on small bridges on narrow tributaries remains unsatisfactory.

[0008] Furthermore, bridge inspection often relies on the accurate extraction and modeling of water network. Existing water network modeling methods mainly include:

[0009] 1. Topographic-based methods: For example, some methods use digital elevation models (DEMs) to extract water flow direction and confluence networks. This method works well in areas with significant topographic relief, but in plains, urban areas, and other regions, it is difficult to construct a complete water network structure due to the lack of continuous topographic gradient information.

[0010] 2. Linear structure-based methods: These methods extract linear features (such as water body centerlines) from SAR images and connect them using graphical models or energy constraints. These methods are sensitive to noise in the image; under speckle noise and strong scattering interference, centerline extraction is prone to breakage, leading to network connection errors.

[0011] 3. Improved methods based on tree-graph models: For example, Markov tree models can be used to model water network to better describe the tree-like topology of the water system. This method performs well in simple water systems, but its connection reasoning ability is still insufficient in complex environments, narrow tributaries, or networked water areas, and it is prone to producing false connections or missing connections.

[0012] In summary, existing bridge detection methods generally suffer from insufficient detection stability and weak generalization ability in complex water networks, narrow tributaries, and scenarios with strong noise interference. This is especially true for small bridges spanning narrow rivers and tributaries in polarimetric SAR images, where significant water fracturing, weak cross-sectional features, and complex background scattering often make reliable detection difficult with existing methods. Therefore, there is an urgent need for a novel bridge detection method that can integrate geometric, topological, and scattering features and possess strong robustness in complex water environments to improve the accuracy and reliability of identifying multi-scale, multi-structure bridges. Summary of the Invention

[0013] Technical problems to be solved

[0014] To address the shortcomings of existing technologies, this invention aims to solve the technical problems of poor stability and low reliability in bridge target detection in polarimetric SAR images under complex water network (such as dense river networks and intersecting tributaries) and narrow tributary environments. Specifically, existing methods struggle to effectively address the following challenges: (1) Bridges vary in scale and shape, and small bridges on narrow tributaries have weak features, making them prone to missed detection; (2) Strong speckle noise and interference from strong scatterers such as riverside buildings lead to inaccurate extraction of the land-water boundary, easily causing false detections; (3) In complex backgrounds, the water network structure is broken and the connection relationships are blurred, making it difficult for traditional geometric or spatial relationship models to robustly recover its topological connections, thus affecting the accurate location and identification of bridges. Therefore, a new method is needed that can overcome the above interferences and achieve high-precision and robust bridge detection in complex scenarios.

[0015] Technical solution

[0016] To address the aforementioned technical problems, this invention proposes a polarimetric SAR bridge detection method that integrates cross-sectional probabilistic modeling and graph topology analysis. The core idea of ​​this method is to leverage the physical and geometric characteristics of bridges crossing water bodies, which inevitably lead to "breaks" in the segmentation of continuous water areas. These breaks create a pair of "cross-sections" with spatial symmetry and directional consistency. By robustly extracting and matching these cross-sections using a probabilistic model, the topological structure of the water network can be reconstructed, and ultimately, the bridge can be accurately located based on this topological relationship.

[0017] Specifically, the following steps are included:

[0018] Step S1: Extraction of water branch:

[0019] The input polarimetric SAR image is segmented into land and water to obtain a water mask; the water mask is then subjected to connected component analysis to extract independent water branches, and the centerline of each water branch is calculated.

[0020] Step S2: Cross-sectional probability modeling and extraction:

[0021] For each water branch, a particle filter algorithm is used to perform Bayesian estimation of the cross-sectional state in its terminal region, extracting the cross-section represented by a rectangular model; specifically:

[0022] Cross-section modeling: The potential connection area formed by the bridge obstruction at the end of each water branch is abstracted into a rectangular cross-section model:

[0023]

[0024] in, Represents the coordinates of the center of the rectangle. Indicates the direction angle of the longer side of the rectangle. For length, For width.

[0025] Cross-section extraction based on particle filtering: The particle filtering algorithm is used to perform probability estimation and optimization of the cross-section state at the end of each water branch.

[0026] Step S3: Construction of water network map and cross-section matching:

[0027] Construction Graph , where each vertex Represents a branch of a water area, each edge This represents the spatial topological connection between two water branches based on matched cross sections, wherein a two-stage matching strategy is used to connect cross sections to construct graph edges; the graph is then analyzed based on geometric features. Filter the connected subgraphs in the graph and remove subgraphs that are determined to be non-river water bodies;

[0028] Step S4: Bridge Inspection and Positioning

[0029] Traverse the graph For all edges in the array, for each matching section corresponding to an edge, the boundary vertices of the bridge are determined based on the geometric relationship between the two sections, and the area enclosed by the boundary vertices is the detected bridge target.

[0030] Furthermore, in step S1, the input polarimetric SAR image is segmented into land and water using a threshold segmentation method based on likelihood ratio test, which effectively suppresses strong scattering interference such as side lobes and obtains an accurate water mask. Subsequently, connected component analysis is performed on the water mask to extract independent water branches and calculate the centerline of each water branch, providing a geometric and topological basis for subsequent processing.

[0031] Likelihood ratio is defined as:

[0032]

[0033] in, The threshold used to distinguish between water and land areas The average power of the entire region. and They represent the first Each region ( Average power and number of pixels; by searching to make Maximum threshold To determine the optimal segmentation threshold.

[0034] Furthermore, in step S2, the Bayesian estimation of the cross-sectional state using the particle filter algorithm includes the following sub-steps:

[0035] First, a set of particles is initialized based on the endpoints and geometric features of the water branch centerline;

[0036] Then, an observation model is defined, and the particle weights are evaluated by calculating the geometric consistency error between the rectangle represented by the particle and the boundary of the real water body.

[0037] Finally, through the iterative process of state prediction, weight update and resampling, the particle swarm converges to the optimal cross-sectional parameters, realizing robust estimation of cross-sectional shape and position, and effectively overcoming boundary irregularities and noise interference.

[0038] Furthermore, in step S2, the process of initializing the particles is as follows:

[0039] Centered on the endpoint of the centerline, a set of candidate points P is sampled from the Gaussian distribution; points falling within the water mask are retained to form an effective subset. ;calculate minimum bounding rectangle and take Geometric Center As the initial cross-section center; through Construct two mutually orthogonal lines:

[0040]

[0041]

[0042] in for The direction angle of the longer side, The average width of the water branch, Indicates relative to the direction along the straight line The signed distance;

[0043] calculate and The points of intersection with the water body boundary are respectively denoted as... and The corresponding distance is and Choose the smaller one. or The corresponding direction is taken as the initial cross-sectional direction; the selected direction is compared with... The center coordinates, length, and width are used together as the initial state estimate; this estimate is then copied to generate... There are 10 particles, and each particle is assigned an equal weight. This forms the initial distribution for particle filtering.

[0044] Furthermore, in step S2, the geometric consistency error is defined as:

[0045]

[0046] in and These are the distance observation values, which are the distances from all points on the two sides closest to the riverbank in the rectangular cross-section to the nearest water boundary. and For balancing parameters.

[0047] Furthermore, in step S3, the two-stage matching strategy is divided into coarse matching and fine matching; in the coarse matching stage, a bidirectional propagation verification mechanism is used to screen potential connection pairs as candidate pairs; in the fine matching stage, spatial geometric constraints are used to screen candidate pairs.

[0048] Furthermore, the bidirectional propagation verification mechanism is as follows:

[0049] For two candidate cross sections, probes are extended from their center points along the cross section direction to the opposite water area. If both probe points can fall into the water branch of the other's water area, they are topologically reachable and a candidate pair is formed.

[0050] Furthermore, the spatial geometric constraints are as follows:

[0051] For the two cross sections in the candidate pair and , build connections and The central axis of the centroid is used to extract the boundary line segments of the two rectangular sections that intersect this axis, denoted as... and Constraints:

[0052] The difference in line segment lengths does not exceed a preset threshold. :

[0053]

[0054] The angle between the principal directions of the two line segments is less than the angle tolerance. :

[0055]

[0056] in Represents line segment Length, Its direction angle.

[0057] Furthermore, in step S3, based on the graph The aspect ratio and compactness of the minimum bounding rectangle of the connected subgraph are used to filter the connected subgraph: if the aspect ratio is less than a first threshold and the compactness is greater than a second threshold, the subgraph is determined to be a non-river water body and is removed.

[0058] Furthermore, in step S4, the water network map is traversed. For all edges (i.e. matching cross sections), the region of interest for the bridge is extracted and located: For each matching cross section corresponding to an edge, the precise boundary line between the two sides of the bridge and the water body is determined based on the nearest boundary line segment between the two cross section rectangles; by finding the nearest point of the endpoint of the boundary line segment on the water branch contour, four precise vertices are obtained; the area enclosed by this is determined and located as the bridge target.

[0059] Beneficial effects

[0060] The polarimetric SAR bridge detection method proposed in this invention, which integrates cross-sectional probabilistic modeling and graph topology analysis, has the following advantages:

[0061] 1. A novel bridge detection framework is proposed. This method does not directly rely on the scattering intensity of the bridge or a fixed geometric template. Instead, it models the cross-sections of the water branch after separating land and water, and combines topological analysis to achieve cross-sectional matching and water network reconstruction. Bridge detection is then performed based on the constructed water network. This framework can achieve robust bridge detection in complex water networks and narrow tributary scenarios.

[0062] 2. Applying particle filtering to probabilistic modeling of cross-sections. Particle filtering possesses the ability to handle nonlinear, non-Gaussian observations and multiple hypothesis tracking, effectively addressing the uncertainty in cross-section shape and position estimation under complex backgrounds, thus ensuring reliable matching of cross-sections within the framework. This method still achieves stable convergence under nonlinear and non-Gaussian observation conditions. Compared to traditional edge- or template-based methods, it provides more accurate and stable estimation of cross-section shape and position, laying a reliable foundation for subsequent matching.

[0063] 3. By combining bidirectional propagation verification with spatial geometric constraints, the accuracy of water network connection based on matching cross sections is improved. It can effectively eliminate false connections caused by terrain, noise or other strong scatterers, and significantly improve the accuracy of water network reconstruction and bridge positioning.

[0064] Experiments show that in complex polarimetric SAR scenarios containing wide rivers, narrow tributaries, bridges of various sizes, and strong interference, the method of this invention can achieve a balance between high recall and high precision, effectively detect numerous small bridges, and has strong immunity to interference from non-river water bodies. The overall detection performance (F1-score, mIoU) is superior to traditional methods.

[0065] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0066] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0067] Figure 1 The overall workflow of the bridge detection method proposed in this invention and the key results of each module are as follows: (a) Flowchart of the proposed method; (b) Polarimetric SAR pseudo-color image; (c) Land-water segmentation results; (d) Extracted water branches; (e) Extracted cross sections (red rectangles); (f) Constructed water network graph, where nodes represent water branches and edges represent matched cross sections; (g) Region of interest (ROI) of the bridge; (h) Final bridge detection results.

[0068] Figure 2 Land-water segmentation results based on the likelihood ratio thresholding method. (a) Pseudo-color image with side lobes from ships and buildings; (b) Segmentation results after effectively suppressing interference; (c) Pseudo-color image of a narrow tributary including a small bridge; (d) Segmentation results of the narrow tributary.

[0069] Figure 3 Bridge shading effect and cross-sectional view. (a) Gray area represents the bridge; (b) Red area represents the cross-section.

[0070] Figure 4 Schematic diagram of a rectangular cross-section model. Indicates the coordinates of the center of the rectangle; Indicates the direction angle of the longer side of the rectangle; For length, For width.

[0071] Figure 5 : Particle filter section initialization. Red dots represent centerline endpoints; green dots represent effective sampling points within the water mask; orange rectangles represent the minimum bounding rectangle of the effective sampling points. Its center is Magenta dots It is past Parallel lines and vertical line The intersection with the water body boundary. Choose the direction of the shorter chord as the initial cross-sectional direction (this direction is closer to being perpendicular to the riverbank).

[0072] Figure 6 The workflow for obtaining cross-sections using particle filtering.

[0073] Figure 7 Bridge region is obtained based on matching cross sections. (a) The red rectangle represents the extracted and successfully matched cross sections. (b) The blue dots represent the vertices determined by the cross sections. The red area enclosed by these cross sections is the bridge region.

[0074] Figure 8Bridge detection results in complex water scenes: (a) pseudo-color polarimetric SAR image; (b) cross-section extraction and matching; (c) bridge localization; (d) final detection results (red box: correctly detected bridges; yellow box: missed bridges; green box: falsely detected bridges) Detailed Implementation

[0075] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0076] This invention aims to solve the challenge of bridge target detection in complex water network and narrow tributary environments, particularly addressing the limitations of existing methods in effectively handling complex, networked scenarios with diverse water and bridge distributions. Observations show that bridges crossing water disrupt the continuity of the originally connected water bodies, resulting in breaks in the water segmentation results. At these breaks, the ends of adjacent water branch branches often form a pair of spatially symmetrical, oriented "cross-sections." These cross-sections exhibit good recognizability and stability in images, effectively characterizing the presence of bridges. Based on this, this invention proposes a bridge detection method integrating "cross-section probabilistic modeling" and "graph topology analysis": first, potential cross-sections of water branch branches are extracted; then, a water network graph model is constructed to analyze the topological connections between branches, thereby achieving robust bridge detection in complex water network and narrow tributary scenarios.

[0077] like Figure 1 As shown in (a), the overall process of this method mainly includes three core modules: water branch extraction, water network construction, and bridge detection. To clearly illustrate the function of each module, Figure 1 (b)–(h) show the key processing results at each stage. In the water branch extraction module, a polarimetric SAR threshold segmentation method based on the likelihood ratio criterion is first used for land-water segmentation. Figure 1 (b) is a polarimetric SAR pseudo-color image, and the corresponding land-water segmentation result is as follows: Figure 1 As shown in (c). Subsequently, individual water branches are extracted from the segmentation results. Figure 1 As shown in (d), this example identifies a total of four water area branches. In the water area network construction module, based on the extracted water area branches, a particle filter algorithm is used to detect potential "cross-sections". Figure 1 The red rectangle in (e) represents the detected cross-section. To achieve accurate cross-section matching, a matching method combining a bidirectional propagation verification mechanism and spatial geometric constraints was designed. Based on the matching results, a water network graph was constructed: nodes in the graph represent water branches, and edges correspond to successfully matched cross-sections, thereby effectively restoring the water connectivity interrupted by bridge obstruction. The final constructed water network graph is shown below. Figure 1As shown in (f). In the bridge detection module, all matching sections in the water network graph are traversed to identify narrow land areas connecting adjacent water branches. These narrow land areas are then identified as bridge targets. Figure 1 (g) and (h) show examples of the final bridge inspection results.

[0078] 1. Extraction of water branch

[0079] To achieve accurate water body extraction in polarimetric SAR images, this paper employs a likelihood ratio-based threshold segmentation method. This method first extracts volume scattering power through polarimetric decomposition. Then, utilizing the statistical differences in polarimetric scattering characteristics between water and land, a likelihood ratio testing model is constructed to adaptively determine the optimal segmentation threshold, thereby accurately dividing the image into water and land regions. The likelihood ratio is defined as:

[0080] (1)

[0081] in, The threshold used to distinguish between water and land areas The average power of the entire region. and They represent the first Each region ( The average power and number of pixels. The more uniform the segmentation region, the better. The larger the value, the better. It can be proven that this corresponds to the maximum. threshold This is the optimal threshold. Therefore, the optimal threshold can be determined by searching for the maximum likelihood ratio.

[0082] Unlike other methods that easily misclassify interference areas as land, the likelihood ratio-based thresholding method can achieve accurate land-water segmentation even under sidelobe interference. In polarimetric SAR pseudo-color images (… Figure 2 In (a), strong scattering from ships and surrounding structures can cause interference, but this method can effectively suppress such interference and achieve accurate segmentation. Figure 2 (b)). For narrow tributaries ( Figure 2 (c) This method can also accurately segment water bodies and accurately identify small bridges on tributaries as land. Figure 2 (d) After completing the land-water separation, connectivity analysis is performed on the water mask to extract independent water body branches, and the centerlines of each branch are further calculated. The extracted water body branches and their corresponding centerlines provide a crucial geometric and topological basis for subsequent cross-section detection.

[0083] 2. Cross-sectional probability modeling and extraction

[0084] like Figure 3As shown in (a), the regions connecting the branches of a river correspond to bridges. Due to scattering interference from surrounding structures, the resulting branches often have irregular shapes. Furthermore, the size and shape of bridges vary considerably, making precise positioning based solely on branch boundaries difficult. To achieve precise positioning, the river branches need to be connected. We extract local regions from the ends of the river branches and define these local regions as "sections," such as... Figure 3 (b) shows the red rectangle. Cross-sections typically appear in pairs on both sides of the bridge, exhibiting consistent orientation, spatial symmetry, and stable geometry. By matching these cross-sections, watercourse branches can be connected and a watercourse network can be constructed, thereby enabling bridge inspection.

[0085] 2.1 Cross-section modeling

[0086] To support cross-section matching and waterway branch connections, each cross-section is abstractly modeled as a rectangular model, such as... Figure 4 As shown. The model is defined as follows:

[0087] (2)

[0088] in, Represents the coordinates of the center of the rectangle. Indicates the direction angle of the longer side of the rectangle. For length, The width is defined as the cross-section. This model abstracts each cross-section as a rectangle with directional attributes, thus providing information on location, orientation, and scale.

[0089] 2.2 Cross-section extraction based on particle filtering

[0090] Due to the influence of strong scattering bodies in the surrounding area, the boundaries of watercourse branches are often curved. To obtain accurate cross-sections, a particle filtering algorithm is used for cross-section extraction. Particle filtering is a sequential Monte Carlo method based on Bayesian estimation, which can effectively estimate the state in nonlinear and non-Gaussian environments. In this invention, each particle is represented by a five-dimensional state vector. This is used to parameterize the cross-sectional rectangle. The state transition model uses additive Gaussian noise.

[0091] (3)

[0092] in, The covariance matrix is ​​used to control the perturbation scale. By incorporating a Gaussian perturbation, the particle filter can search within the local state space, thereby enhancing the robustness of cross-section extraction.

[0093] Particle filtering requires an initial state. This study estimates the initial cross-section based on the endpoints of the centerline of the water body, as follows: First, using the endpoints of the centerline (… Figure 5Centered on the red dot (in the diagram), a set of candidate points P is sampled from a Gaussian distribution. Points falling within the water mask are retained to form an effective subset. ( Figure 5 (The green dots in the image). Then calculate... minimum bounding rectangle and take Geometric Center As the initial cross-section center. Then, through Construct two mutually orthogonal lines. Let... for The direction angle of the longer side, Given the average width of the water branch, the two straight lines can be parameterized as follows:

[0094] (4)

[0095]

[0096] in Indicates relative to the direction along the straight line The signed distance. Calculate. and The points of intersection with the water body boundary are respectively denoted as... and ( Figure 5 (The magenta dot in the image). The corresponding distance is... and Since a shorter distance means a direction closer to being perpendicular to the riverbank, a smaller distance is preferable. or The corresponding direction is used as the initial cross-sectional direction. Finally, the selected direction is compared with... The center coordinates, length, and width are used together as the initial state estimate. This estimate is then replicated to generate... There are 10 particles, and each particle is assigned an equal weight. This forms the initial distribution for particle filtering.

[0097] The initial particle state only provides a rough estimate of the actual cross-section; therefore, an observation model is introduced to iteratively optimize the particle's position and orientation. For each particle, based on its orientation parameters, the two sides of the rectangular cross-section closest to the riverbank are selected. The distances from all points on these two sides to the nearest water boundary are calculated, resulting in a set of distance observations. Let... and Let the mean and standard deviation of these distances be respectively, then the geometric consistency error is defined as:

[0098]

[0099] in, and This is a balancing parameter used to control the trade-off between average deviation and distance distribution stability. This index reflects the fit between the particle rectangle and the true cross-section and serves as an observation term for particle filter updates. The corresponding observation weight function is defined as:

[0100] (7)

[0101] in, Control error tolerance. Geometric consistency error. The smaller the value, the higher the weight of the particle, and the greater the probability that it will be retained during the resampling process.

[0102] Based on the above particle weight distribution, the convergence of the iterative process can be evaluated. This study adopts a dual termination criterion: on the one hand, a maximum number of iterations is set to limit the running time; on the other hand, the convergence is dynamically evaluated based on the particle weights. The iteration is terminated early when the weight of any particle meets the following condition:

[0103] (8)

[0104] in, This is a preset weight threshold. At this point, the estimated rectangle is geometrically consistent with the actual cross-sectional height. Figure 6 The overall process of cross-section extraction is shown.

[0105] 3. Waterway Network Construction

[0106] 3.1 Graphical Model

[0107] The water network is modeled as a graph , where each vertex Represents a branch of a water area, each edge This represents the spatial topological connection between two water branches based on a matching cross section.

[0108] 3.2 Section Matching

[0109] To establish effective node connections in a water network graph, candidate cross-sections need to be matched. This matching process consists of two stages: coarse matching and fine matching. In the coarse matching stage, a two-way propagation verification mechanism is used to quickly filter potential connection pairs. Specifically, for two candidate cross-sections... and A set of extended detection points is generated from their respective center points along the cross-sectional direction. Then, the spatial affiliation of these extended points is verified using the connected water area defined by the land-water separation result: if from... The extended detection point falls Within its respective waterway branch, simultaneously from The extended detection points also fell Within their respective water areas, the two cross sections are considered topologically bidirectionally reachable, thus forming a potential matching pair. Based on the candidate cross sections selected through coarse matching, geometric features are introduced for fine matching to ensure the structural rationality of the connection. Specifically, the connection is first constructed... and The central axis of the centroid. Then, extract the boundary line segments of the two rectangular sections that intersect this axis, denoted as... and To verify the geometric consistency of the cross-section, the following two constraints must be satisfied simultaneously:

[0110] ① Length similarity: The difference in line segment lengths should not exceed a preset threshold. :

[0111] (9)

[0112] ② Directional consistency: The angle between the principal directions of the two line segments should be less than the angle tolerance. :

[0113] (10)

[0114] in Represents line segment Length, Its orientation angle (defined relative to the horizontal axis). Only when both conditions are met is the section considered a valid match and included in the water network diagram. Establish the corresponding edges in the middle.

[0115] 3.3 Removal of non-river water bodies

[0116] To prevent non-river water bodies such as ponds and lakes from introducing erroneous connections in network construction, this study designs a subgraph filtering mechanism based on geometric and topological attributes. Specifically, the minimum bounding rectangle of each connected subgraph is first calculated to evaluate its aspect ratio. Since rivers typically have a slender shape, subgraphs with smaller aspect ratios can be initially identified as non-river water bodies. Subsequently, a compactness index is introduced for further differentiation, defined as follows:

[0117] (11)

[0118] Where A represents the water area and p is the perimeter. Circular structures exhibit the highest compactness, while elongated structures have lower compactness. Combining the aspect ratio and compactness, the proposed filtering mechanism effectively identifies and removes non-river water bodies, thus preventing false connections in the water network. Specifically, if the aspect ratio is less than a first threshold and the compactness is greater than a second threshold, the sub-image is determined to be a non-river water body and is removed.

[0119] 3.4 Network Analysis and Bridge ROI Extraction

[0120] After constructing the water network map and removing irrelevant water bodies, the next step is to analyze the network structure to extract potential regions of interest (ROIs) for bridges. This is done by traversing the water network map. edge set For each edge The corresponding matching cross-sections are extracted. Then, the geometric relationships between the cross-sections are used to achieve precise bridge positioning. Specifically, for each pair of matching cross-sections, the closest boundary segments between the two rectangles are first identified; these segments correspond to the boundaries between the bridge and the water body on both sides. Next, the endpoints of these segments are extracted, and the nearest points are found on the boundaries of the corresponding water body branches to ensure that the bridge boundaries are precisely aligned with the actual water body contours. By obtaining two corresponding boundary points on each side, a total of four precise vertices can be determined. These vertices together constitute the planar extent of the bridge, thus achieving accurate bridge positioning. Figure 7 As shown in (a), the red rectangle represents the extracted and matched cross-sections; in Figure 7 In (b), the blue dots are the vertex positions determined according to the cross-sectional geometry, and the red area formed by these vertices is the spatial range of the bridge.

[0121] Experimental verification:

[0122] Experiments were conducted using GF3 single-look fully polarimetric SAR data from the Zhongshan area. The data size was [data size missing]. The resolution is Detection performance was evaluated using recall, precision, F1-score, and mean inter-union ratio (mIoU).

[0123] In the cross-section extraction process, particle filter modeling assumes that each state dimension is independent, and the perturbation covariance matrix is ​​set as follows: Corresponding position ,direction and size Specifically, a variance of 3 confines particles to a locally optimal region, a variance of 10 adapts to irregular changes in boundary direction, and a variance of 5 adapts to changes in river width and imaging, while avoiding excessive deformation of the rectangular model. In the cross-section matching step, the weights in the consistency error function are set to... = That is, for the mean with standard deviation Assign equal importance. Set the maximum weight threshold to... =0.10. When + When the value is 2, the corresponding particle weight is 0.14, which exceeds the threshold, indicating that the cross-section is reliable. In water network construction, the matching tolerance parameter... Based on the adaptive setting of the two cross-sectional side lengths: This setting balances scale differences, prevents distortion caused by matching short and long sides, and improves robustness under noisy conditions. For directional constraints, the angle difference threshold is set to... This design allows for the natural meandering of rivers while avoiding false connections. Analysis revealed that typical rivers are elongated with an aspect ratio greater than 4 and a compactness of less than 0.45; sub-maps exceeding these limits were classified as non-river bodies.

[0124] like Figure 8 (a) The Pauli false-color image shows a complex water system scene, including a wide main channel, narrow tributaries, and significantly varying river widths. Numerous bridges of varying sizes, orientations, and structures are distributed throughout the scene. Furthermore, non-river bodies of water such as ponds and lakes exist within the area, which could easily lead to false positives. Figure 8 (b) shows the results of the cross-section matching, with the adjacent red boxes indicating the matched cross-sections; Figure 8 (c) The location results of the bridge are shown, with the bridge area in red; Figure 8 (d) shows the final detection map, where red boxes represent correctly detected bridges, yellow boxes represent missed detections, and green boxes represent false detections. Observation shows that most bridges were correctly detected, including several small bridges. Missed detections were mainly due to weak backscattering from some bridges, leading to their misclassification as water. False detections primarily occurred in areas of strong scattering, where water was incorrectly classified as land. The proposed method achieves accurate detection of bridges on narrow tributaries in complex water systems, with a recall of 89%, precision of 92%, F1-score of 91%, and mIoU of 0.77.

[0125] The experimental results show that the present invention can achieve bridge target detection in complex water network and narrow tributary environments, and can adapt to strong noise interference and small-sized bridge detection in narrow river branches.

[0126] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis, characterized in that: Includes the following steps: Step S1: Perform land-water segmentation on the input polarimetric SAR image to obtain a water mask; Connectivity analysis is performed on the water mask to extract independent water branches and calculate the centerline of each water branch; Step S2: For each branch of the waterway, in its terminal region, a particle filter algorithm is used to perform Bayesian estimation of the cross-sectional state, extracting the cross-section represented by a rectangular model; the rectangular model is: in, Represents the coordinates of the center of the rectangle. Indicates the direction angle of the longer side of the rectangle. For length, Width; Step S3: Construct the graph , where each vertex Represents a branch of a water area, each edge This represents the spatial topological connection between two water branches based on matched cross sections, wherein a two-stage matching strategy is used to connect cross sections to construct graph edges; the graph is then analyzed based on geometric features. Filter the connected subgraphs in the graph and remove those that are determined to be non-river water bodies; Step S4: Traverse the graph For all edges in the array, for each matching section corresponding to an edge, the boundary vertices of the bridge are determined based on the geometric relationship between the two sections, and the area enclosed by the boundary vertices is the detected bridge target.

2. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 1, characterized in that: In step S1, the input polarimetric SAR image is segmented into land and water using a threshold segmentation method based on likelihood ratio testing; the likelihood ratio is defined as: in, The threshold used to distinguish between water and land areas The average power of the entire region. and They represent the first Each region ( The average power and number of pixels; by searching to make Maximum threshold To determine the optimal segmentation threshold.

3. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 1, characterized in that: In step S2, the Bayesian estimation of the cross-sectional state using the particle filter algorithm includes the following sub-steps: First, a set of particles is initialized based on the endpoints of the water branch centerline and geometric features; Then, an observation model is defined, and the particle weights are evaluated by calculating the geometric consistency error between the rectangle represented by the particle and the boundary of the real water body. Finally, through the iterative process of state prediction, weight update and resampling, the particle swarm converges to the optimal cross-sectional parameters, achieving robust estimation of the cross-sectional shape and position.

4. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 3, characterized in that: In step S2, the process of initializing the particles is as follows: Centered on the endpoint of the centerline, a set of candidate points P is sampled from the Gaussian distribution; points falling within the water mask are retained to form an effective subset. ;calculate minimum bounding rectangle and take Geometric center As the initial cross-section center; through Construct two mutually orthogonal lines: in for The direction angle of the longer side, The average width of the water branch, Indicates relative to the direction along the straight line The signed distance; calculate and The points of intersection with the water body boundary are respectively denoted as... and The corresponding distance is and Choose the smaller one or The corresponding direction is taken as the initial cross-sectional direction; the selected direction is compared with... The center coordinates, length, and width are used together as the initial state estimate; this estimate is then copied to generate... There are 10 particles, and each particle is assigned an equal weight. This forms the initial distribution for particle filtering.

5. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 3, characterized in that: In step S2, the geometric consistency error is defined as: in and These are the distance observation values, which are the distances from all points on the two sides closest to the riverbank in the rectangular cross-section to the nearest water boundary. and For balancing parameters.

6. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 1, characterized in that: In step S3, the two-stage matching strategy is divided into coarse matching and fine matching. In the coarse matching stage, a bidirectional propagation verification mechanism is used to screen potential connection pairs as candidate pairs. In the fine matching stage, spatial geometric constraints are used to screen the candidate pairs.

7. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 6, characterized in that: The bidirectional propagation verification mechanism is as follows: For two candidate cross sections, probes are extended from their center points along the cross section direction to the opposite water area. If both probe points can fall into the water branch of the other's water area, they are topologically reachable and a candidate pair is formed.

8. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 6, characterized in that: The spatial geometric constraints are as follows: For the two cross sections in the candidate pair and , build connections and The central axis of the centroid is used to extract the boundary line segments of the two rectangular sections that intersect this axis, denoted as... and Constraints: The difference in line segment lengths does not exceed a preset threshold. : The angle between the principal directions of the two line segments is less than the angle tolerance. : in Represents line segment Length, Its direction angle.

9. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 1, characterized in that: In step S3, based on the graph The aspect ratio and compactness of the minimum bounding rectangle of the connected subgraph are used to filter the connected subgraph: if the aspect ratio is less than a first threshold and the compactness is greater than a second threshold, the subgraph is determined to be a non-river water body and is removed.

10. The polarimetric SAR bridge detection method integrating cross-sectional probabilistic modeling and graph topology analysis according to claim 1, characterized in that: In step S4, the water network map is traversed. For each edge in the matching section, the precise boundary line between the two sides of the bridge and the water is determined based on the nearest boundary line segment between the two section rectangles. By finding the nearest point of the endpoint of the boundary line segment on the water branch contour, four precise vertices are obtained. The area enclosed by this is then determined and located as the bridge target.

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