A catenary sling slackness grading detection method with few sample dependence

Abstract

The present application belongs to the technical field of image processing, and particularly relates to a few-sample-dependent catenary sling relaxation degree grading detection method, comprising the following steps: S1, positioning a sling component region in a catenary inspection image, extracting candidate key points in the sling component region, and obtaining a candidate key point sequence arranged along a sling direction and having a first end and a second end; S2, determining a seed section in the candidate key point sequence; performing spline fitting on the confirmed key point sequence to obtain a sling fitting curve; S3, determining an upper end connecting point and a lower end connecting point on the sling fitting curve, and outputting a relaxation degree of the current sling. The present application does not require a large number of relaxation defect supervision samples, can significantly reduce the sample collection cost, and improve the robustness and reliability of detection.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically relating to a method for graded detection of catenary dropper slack degree based on few samples. Background Technology

[0002] As a key piece of equipment for transmitting electrical energy to electric locomotives in electrified railways, the operating status of the overhead contact system directly affects the safety and stability of railway transportation. The droppers, elastic components connecting the catenary cable and the contact wire, play a crucial role in adjusting the height and maintaining the smoothness of the contact wire. During long-term operation, due to factors such as periodic impacts from the locomotive pantograph, temperature changes, wind loads, and metal fatigue, droppers are prone to slack or even breakage, leading to serious accidents such as poor current collection from the pantograph-catenary system, abnormal wear of the contact wire, or even pantograph breakage. Therefore, accurate and automatic detection and grading of the slack degree of the overhead contact system droppers is an important technical requirement for ensuring the safe operation of railways.

[0003] With the widespread adoption of overhead contact line inspection vehicles and high-speed industrial cameras on their roofs, image processing-based methods for detecting slack in overhead contact lines have gradually become the mainstream direction in research and engineering applications. Existing technologies can be broadly categorized into two types. One type is based on traditional image processing methods, which extract the outline of the overhead contact line from the inspection image using edge detection, Hough transform, skeleton extraction, or least-squares fitting, and then determine slackness based on the curvature, arc height, or global fitting residual of the outline itself. The other type is based on deep learning methods, which rely on convolutional neural networks to supervise the training of a large number of manually labeled normal and slack overhead contact line samples, outputting slack classification labels for the overhead contact lines.

[0004] However, the aforementioned existing technologies still face several prominent problems in practical applications. First, traditional image processing methods typically employ a one-time screening based on global fitting residuals when removing background interference points. This is difficult to adapt to situations where the bending degree of the dropper varies in different sections, and it is easy to misjudge real key points in the bending section as outliers and remove them, thus destroying the restoration of the dropper's true shape. Second, the measurement of dropper slack generally relies solely on the geometric shape of the dropper curve itself, lacking a unified reference benchmark, making it impossible to compare the slack degree of droppers of different lengths and installation angles on the same scale. Third, deep learning methods heavily rely on large-scale supervised samples of slack defects, while samples of mild and severe slack are extremely scarce in engineering practice, and long-term collection is difficult and costly, resulting in limited generalization ability of the detection model. How to achieve robust automatic slack degree classification detection relying only on a small number of normal dropper samples has become an urgent problem to be solved in this field. Summary of the Invention

[0005] Therefore, the main objective of this invention is to provide a method for graded detection of catenary dropper slack with a small sample dependency. This method achieves adaptive screening of key points on the dropper line, avoiding the defect of global fitting methods that misclassify real key points on curved sections as abnormal points. By using a virtual tension baseline and three dimensionless features for joint grading, the slack of droppers of different lengths and installation angles is comparable on the same scale. The grading threshold can be pre-calibrated based on only a small number of normal dropper samples, eliminating the need for a large number of slack defect supervision samples, significantly reducing sample collection costs and improving the robustness and reliability of the detection.

[0006] The technical solution adopted in this invention is as follows: A method for grading the slack of overhead contact line droppers using a few-sample-dependent approach includes the following steps: S1. Locate the dropper component area in the overhead contact line inspection image, extract candidate key points within the dropper component area, and obtain a sequence of candidate key points ordered along the dropper direction and having a first end and a second end; S2. Determine the seed segment in the candidate keypoint sequence; starting from the seed segment, perform fan-shaped propagation guided by the direction field towards the first and second ends respectively: construct the current direction field vector based on the confirmed keypoints, construct a fan-shaped search domain on one side pointed to by the current direction field vector, verify the consistency of direction and propagation spacing of the candidate keypoints in the fan-shaped search domain, include the keypoints that pass the consistency verification into the confirmed keypoint sequence, update the current direction field vector and the fan-shaped search domain, until both bidirectional propagation reaches the termination point; remove the remaining candidate keypoints in the candidate keypoint sequence, and perform spline fitting on the confirmed keypoint sequence to obtain the suspension curve; S3. Determine the upper and lower connection points on the dropper fitting curve, and use the straight line segment connecting the upper and lower connection points as the virtual tension baseline; calculate the normalized curvature feature value, the minimum oblique rectangle width ratio feature value, and the maximum deviation ratio feature value based on the dropper fitting curve and the virtual tension baseline; compare the three feature values ​​with the first-level threshold and the second-level threshold pre-calibrated based on normal dropper samples, and output the current dropper relaxation level.

[0007] Furthermore, in S1, the dropper component region in the catenary inspection image is located by inputting the catenary inspection image into a pre-trained target detection model, outputting the rectangular bounding box coordinates of the dropper component, and using the image range defined by the rectangular bounding box as the dropper component region.

[0008] Furthermore, in S1, candidate key points are extracted within the dropper component region, and a sequence of candidate key points ordered along the dropper direction is obtained. Specifically, the dropper component region is subjected to grayscale conversion and contrast enhancement processing to obtain an enhanced image. The enhanced image is scanned line by line along the image row direction. For each row, the linear texture response value is calculated. The pixel with the largest linear texture response value in each row that reaches a predetermined response threshold is taken as the candidate key point of this row. The candidate key points extracted from all rows constitute a candidate key point set. Principal component analysis is performed on the candidate key point set to obtain the first principal direction. Each candidate key point in the candidate key point set is projected onto the first principal direction to obtain the projection coordinates. The candidate key point set is arranged in ascending order of projection coordinates to obtain a sequence of candidate key points ordered along the dropper direction. The end with the smallest projection coordinate in the candidate key point sequence is defined as the first end, and the end with the largest projection coordinate is defined as the second end.

[0009] Furthermore, in S2, seed segments are determined in the candidate keypoint sequence. Specifically, a sliding window of a predetermined length is moved and scanned segment by segment along the direction of the suspension string in the candidate keypoint sequence. For all candidate keypoints covered by each sliding window, the ratio of the maximum to the minimum Euclidean distance between adjacent candidate keypoints is used as the uniformity evaluation value of this sliding window. The arithmetic mean of the linear texture response values ​​of all candidate keypoints in this sliding window is used as the response intensity evaluation value of this sliding window. In all sliding windows where the response intensity evaluation values ​​reach the predetermined response mean threshold, the sliding window with the uniformity evaluation value closest to 1 is selected as the seed segment. All candidate keypoints contained in the seed segment are included in the confirmed keypoint sequence. The seed segment has a first end point near the first end and a second end point near the second end along the direction of the suspension string.

[0010] Furthermore, S2 also includes: using the median of the Euclidean distance between adjacent candidate keypoints in the seed segment as the baseline spacing, using the product of the baseline spacing and the first spacing coefficient as the lower limit of the continuous spacing interval, and using the product of the baseline spacing and the second spacing coefficient as the upper limit of the continuous spacing interval, wherein the first spacing coefficient is less than 1 and the second spacing coefficient is greater than 1.

[0011] Furthermore, the fan-shaped propagation of the direction field towards the second end in S2 specifically includes: taking the end point of the second end as the starting point of the second end propagation, forming a second end direction reference point group together with the second end propagation starting point and a predetermined number of confirmed key points adjacent to the second end propagation starting point along the direction of the suspension string within the confirmed key point sequence; taking the vector from the confirmed key point with smaller projected coordinates to the confirmed key point with larger projected coordinates in the second end direction reference point group as the current direction field vector of the second end; constructing a fan-shaped search domain on one side towards the second end with the second end propagation starting point as the vertex, the line containing the current direction field vector of the second end as the central axis, a predetermined angle as the half angle, and a predetermined initial maximum radius as the maximum radius; and taking candidate key points in the candidate key point sequence that have not yet been included in the confirmed key point sequence, whose projected coordinates are greater than the projected coordinates of the second end propagation starting point, and are located within the image range defined by the fan-shaped search domain as key points to be verified.

[0012] Furthermore, S2 also includes: performing consistency verification on each key point to be verified: projecting the key point to be verified vertically onto the central axis to obtain a projection point; using the distance between the key point to be verified and the projection point as the lateral deviation distance; using the Euclidean distance between the key point to be verified and the second end propagation starting point as the propagation spacing; using the ratio of the lateral deviation distance to the propagation spacing as the directional consistency error index of this key point to be verified; determining key points to be verified that have passed the consistency verification if the directional consistency error index is less than a predetermined error threshold and the propagation spacing falls within the continuous spacing interval; when there are two or more key points that have passed the consistency verification within the sector search domain constructed in this instance, the directional consistency error index among them is... The smallest key point is selected as the key point to be included in this instance. When the number of key points that pass the consistency verification within the sector search domain constructed in this instance is 1, this key point that passes the consistency verification is selected as the key point to be included in this instance. The key point to be included in this instance is added to the confirmed key point sequence and updated as the second-end propagation starting point. At the same time, the maximum radius of the sector search domain is restored to the predetermined initial maximum radius and the cumulative expansion count is cleared to zero. Based on the updated second-end propagation starting point, the second-end direction reference point group is reconstructed, the current direction field vector of the second end is recalculated, and the sector search domain is reconstructed. The process of selecting key points to be verified, verifying consistency, determining key points to be included in this instance, and updating the second-end propagation starting point is repeated in the direction of the second end.

[0013] Furthermore, S2 also includes: when the number of key points that pass the consistency verification within the constructed sector search domain is zero and the cumulative expansion count is less than the predetermined expansion count limit, the second-end propagation starting point and the current direction field vector of the second end remain unchanged, the maximum radius of the sector search domain is expanded by a predetermined radial step size once to obtain an expanded sector search domain, and the cumulative expansion count is incremented by one to expand the sector search domain and re-execute the screening and consistency verification of the key points to be verified; when the cumulative expansion count reaches the predetermined expansion count limit and the number of key points that pass the consistency verification within the constructed sector search domain is still zero, the current second-end propagation starting point is taken as the second-end termination point. The propagation process towards the second end ends; the first end point is used as the first end propagation starting point, and a first end direction reference point group is constructed in the same way as the second end direction reference point group. The vector pointing from the confirmed key point with the larger projected coordinates to the confirmed key point with the smaller projected coordinates in the first end direction reference point group is used as the first end current direction field vector. The process is repeated towards the first end direction in the same way as the propagation process towards the second end, including the construction of the sector search domain, the screening of key points to be verified, the consistency verification, the determination of key points to be included, the update of the propagation starting point, the expansion of the search domain, and the termination conditions. This process continues until the first end termination point is reached.

[0014] Furthermore, in S3, the upper and lower connection points are determined and a virtual tension baseline is constructed. Specifically, within the dropper component area, the connection positions between the dropper and the catenary clamp, and between the dropper and the contact wire clamp, are obtained through clamp detection. The point on the dropper fitting curve closest to the connection position between the dropper and the catenary clamp is taken as the upper connection point, and the point on the dropper fitting curve closest to the connection position between the dropper and the contact wire clamp is taken as the lower connection point. A straight line segment is formed by connecting the upper and lower connection points. The straight line segment serves as the virtual tension baseline. Points on the dropper fitting curve are projected onto the virtual tension baseline. Multiple projection positions are selected at equal intervals according to the position of the projection points on the virtual tension baseline. Points on the dropper fitting curve corresponding to each projection position are taken as sampling points. A perpendicular line is drawn from each sampling point to the virtual tension baseline. The perpendicular distance from the sampling point to the virtual tension baseline is taken as the normal deviation distance of this sampling point. The normal deviation distances of all sampling points are arranged in the sampling order along the direction of the virtual tension baseline to form a deviation profile.

[0015] Furthermore, S3 also includes: calculating the curvature point-by-point on the dropper fitting curve, and using the product of the maximum curvature and the length of the virtual tensioning baseline as the normalized curvature feature value; obtaining the minimum bounding rectangle of the dropper fitting curve, with the long side of the minimum bounding rectangle following the overall direction of the dropper fitting curve, and using the ratio of the short side length of the minimum bounding rectangle to the length of the virtual tensioning baseline as the minimum bounding rectangle width ratio feature value; using the ratio of the maximum normal deviation distance in the deviation profile to the length of the virtual tensioning baseline as the maximum deviation ratio feature value; pre-collecting a predetermined number of dropper samples in a normal state as normal dropper samples, and calculating the normalized curvature feature value and the minimum bounding rectangle width bit for each normal dropper sample. The eigenvalues ​​and the maximum deviation ratio eigenvalues ​​are used to obtain the mean and standard deviation of each of the three eigenvalues. For each eigenvalue, the sum of the products of its mean, standard deviation, and first multiple is used as its first-level threshold, and the sum of the products of its mean, standard deviation, and second multiple is used as its second-level threshold, where the second multiple is greater than the first multiple. When all three eigenvalues ​​are less than their respective first-level thresholds, the current slack level of the dropper is output as normal. When at least one of the three eigenvalues ​​reaches its respective first-level threshold and all three eigenvalues ​​are less than their respective second-level thresholds, the current slack level of the dropper is output as slightly slack. When at least one of the three eigenvalues ​​reaches its respective second-level threshold, the current slack level of the dropper is output as severely slack.

[0016] By adopting the above technical solutions, this invention achieves the following beneficial effects: First, through a progressive strategy of seed segment positioning, local orientation field construction, point-by-point propagation of the fan-shaped search domain, and point-by-point consistency verification, adaptive screening of key points of the dropper wire is realized. This accurately distinguishes between real key points and abnormal interference points in sections with different degrees of curvature of the dropper wire, avoiding the defect of the one-time screening method based on global fitting residuals that misjudges real key points in curved sections as abnormal points. It effectively preserves the local curvature of the dropper wire body, making the geometric basis for subsequent relaxation grading more faithful and reliable. Second, by introducing a mechanism for graded expansion of the fan-shaped search domain with a predetermined radial step size and a mechanism for clearing and restoring the cumulative expansion times, this method has good tolerance for local imaging breaks of the dropper wire body in the inspection image caused by reflection, occlusion, and transient interference. At the same time, it avoids the problem of false absorption of distant non-dropper wire responses caused by unlimited expansion of the search domain, maintaining high accuracy in key point inclusion while maintaining robustness. Third, by constructing a virtual tension baseline as a unified reference, and using three dimensionless features—normalized curvature characteristic value, minimum oblique rectangle width ratio characteristic value, and maximum deviation ratio characteristic value—for grading determination, the degree of slack in the droppers under different lengths, installation angles, image resolutions, and shooting distances is comparable on the same scale. Furthermore, the three complementary geometric features cover various geometric forms of slack occurring at different locations—end, middle, and overall—improving the stability and reliability of the grading results. Fourth, the grading threshold can be pre-calibrated based on the statistical distribution of only a small number of normal dropper samples, eliminating the need for collecting a large number of mild and severe slack defect samples for supervised training. This significantly reduces sample collection costs and is particularly suitable for the practical application of overhead contact line inspection projects where slack defect samples are extremely scarce. Attached Figure Description

[0017] Figure 1 This is a geometric schematic diagram illustrating the extraction of candidate key points and the sorting along the direction of the dropper in the region of the dropper component, as provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the geometric relationship of a single step incorporating a new key point during the directional field-guided fan-shaped propagation process provided in an embodiment of the present invention. Figure 3 A schematic diagram of the geometric process of expanding the search radius by a predetermined radial step size when there is no key point that passes the consistency verification within the sector search domain, as provided in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the construction of the virtual tension baseline and the geometric meaning of the three normalized relaxation features provided in this embodiment of the invention. Detailed Implementation

[0018] A method for grading the slack of overhead contact line droppers using a few-sample-dependent approach includes the following steps: S1. Locate the dropper component area in the overhead contact line inspection image, extract candidate key points within the dropper component area, and obtain a sequence of candidate key points ordered along the dropper direction and having a first end and a second end; S2. Determine the seed segment in the candidate keypoint sequence; starting from the seed segment, perform fan-shaped propagation guided by the direction field towards the first and second ends respectively: construct the current direction field vector based on the confirmed keypoints, construct a fan-shaped search domain on one side pointed to by the current direction field vector, verify the consistency of direction and propagation spacing of the candidate keypoints in the fan-shaped search domain, include the keypoints that pass the consistency verification into the confirmed keypoint sequence, update the current direction field vector and the fan-shaped search domain, until both bidirectional propagation reaches the termination point; remove the remaining candidate keypoints in the candidate keypoint sequence, and perform spline fitting on the confirmed keypoint sequence to obtain the suspension curve; S3. Determine the upper and lower connection points on the dropper fitting curve, and use the straight line segment connecting the upper and lower connection points as the virtual tension baseline; calculate the normalized curvature feature value, the minimum oblique rectangle width ratio feature value, and the maximum deviation ratio feature value based on the dropper fitting curve and the virtual tension baseline; compare the three feature values ​​with the first-level threshold and the second-level threshold pre-calibrated based on normal dropper samples, and output the current dropper relaxation level.

[0019] Overhead contact line inspection images are typically captured by a high-speed industrial camera mounted on the roof of the inspection vehicle. The typical resolution is 2448×2048 or higher, with a frame rate of 10 to 30 frames per second. The lens's main optical axis is tilted slightly upwards along the track towards the overhead contact line, ensuring the droppers extend roughly vertically or nearly vertically in the image. In tunnels, at night, or in rainy / foggy conditions, the inspection vehicle is equipped with an LED array for synchronous supplemental lighting to prevent large areas of overexposure or underexposure in the images. The overhead contact line structure is characterized by the simultaneous presence of catenary wires, contact lines, positioning tubes, insulators, supports, and multiple droppers in the same image. These components all form linear or edge features in the image. If key points of the droppers are extracted directly from the raw image without regional limitation, the response of the droppers themselves is easily confused with the response of the background structure. Therefore, a two-stage strategy of coarse localization followed by fine processing is adopted.

[0020] The localization of the dropper component region is accomplished by a pre-trained object detection model. Single-stage algorithms such as YOLOv5, YOLOv7, and YOLOv8 can be used, or two-stage algorithms such as Faster R-CNN can be employed, depending on the trade-offs between inference latency and accuracy required by the actual deployment platform. The training data consists of 8,000 to 15,000 manually annotated catenary inspection images, with each dropper labeled with a rectangular bounding box closely attached to the upper and lower clamps of the dropper. The Adam optimizer is used during the training phase, with an initial learning rate of 1×10⁻⁶. Attenuated to 1×10 using cosine annealing. The batch size is set to 16 to 32, and the number of iterations is set to 150 to 200. The model inference outputs the bounding box coordinates of each dropper member. ,in and The x-coordinates of the left and right boundaries of the bounding box. and This represents the ordinate of the upper and lower boundaries. All subsequent processing will only be performed within this range. The search is performed within a limited sub-image area, thus confining the search space to local regions directly related to the dropper components. In multi-dropper scenarios, the model outputs an independent bounding box for each dropper, and subsequent steps are performed independently for each dropper. When the deployment platform has sufficient computing power and requires finer boundary delineation, object detection can be replaced by semantic segmentation based on U-Net or DeepLab, outputting pixel-level foreground masks of the dropper components instead of rectangular bounding boxes. Subsequent processing is performed within the range defined by the mask, which can further suppress background textures in the blind spots of the rectangular bounding boxes.

[0021] refer to Figure 1 The rectangular frame at the outer edge of the image defines the area of ​​the dropper cable component, which is the image range defined by the rectangular bounding box of the dropper cable output by the target detection model in the inspection image. A thick gray band running diagonally from the upper left to the lower right within the frame represents the linear response area formed by the actual imaging of the dropper cable body in the image. Several solid dots distributed along this thick band are candidate key points of the dropper cable body extracted from the line-by-line scanning of the enhanced image in S1. Each candidate key point corresponds to the pixel position in a certain row of the enhanced image where the linear texture response value is the largest and reaches a predetermined response threshold. Several hollow squares scattered outside the thick band within the frame represent non-dropper cable response points that occasionally appear in the background texture, such as pseudo-responses generated by the shadow edges of the catenary cable, reflections from the positioning tube, and slender edges on the far-end column. Their existence indicates that relying solely on the maximum response value within a row is insufficient to guarantee the purity of the candidate key points, and they must be further eliminated in S2 by the directional field fan-shaped propagation mechanism.

[0022] Figure 1 The thick dashed arrow running through the center represents the first principal direction obtained by performing principal component analysis on the candidate keypoint set, denoted as . The arrow falls on the geometric center of all candidate keypoints, marked by an asterisk in the diagram. The asterisk represents the centroid of the set of candidate keypoints. The first principal direction is obtained by calculating the arithmetic mean of the x and y coordinates of all candidate keypoints. The first principal direction is the unit eigenvector corresponding to the largest eigenvalue of the covariance matrix, geometrically corresponding to the direction of the largest variance in the data distribution, and is consistent with the overall extension direction of the dropper. As can be observed in the figure, the first principal direction is not strictly along the vertical axis of the image but has a significant inclination, which matches the actual situation where the dropper typically exhibits an inclined direction in inspection images.

[0023] Figure 1 The thin dashed line segment in the middle, which is formed by several candidate key points leading to the first principal direction axis, represents the direction from these candidate key points. The auxiliary lines obtained by orthographic projection, and the point where each dashed line lands on the principal axis, are the projected coordinates of that candidate key point. Defined as ,in For the first The position vectors of 1 candidate keypoint. All candidate keypoints are ranked according to... Arranging the candidate keypoints from smallest to largest yields a sequence ordered along the suspension cable. The end with the smallest projected coordinates is defined as the first end, corresponding to... Figure 1 The candidate keypoints circled in the upper left corner; the end with the largest projected coordinate is defined as the second end, corresponding to... Figure 1 The candidate key points circled in the lower right corner. The first and second ends are purely geometric symbols used in S2 to represent the two opposite endpoints of bidirectional propagation, and have no fixed correspondence with the physical upper and lower ends of the string; the semantics of the physical upper and lower ends will be completed in S3 by the clamp detection results. Figure 1 The legend in the lower right corner illustrates the meaning of the two types of candidate key points represented by solid circles and hollow squares.

[0024] The sub-image defined by the bounding box is first converted to grayscale. Considering the differences in the red, green, and blue channel responses of industrial inspection images under different lighting conditions, a human visual perception weighting method is used to obtain the grayscale image, i.e. ,in , , Pixels The intensity values ​​of the red, green, and blue channels, The x-coordinate of the pixel is... The vertical coordinate is the pixel coordinate. This refers to the grayscale value after grayscale conversion. Compared to simple averaging, this weighted method better preserves the contrast between the suspension cable itself and the background, such as concrete pillars, sky, and vegetation. In scenes where the suspension cable is dark and the background is bright, the maximum value method can also be used instead. To enhance the prominence of the dark color of the suspension string.

[0025] The grayscale image is then enhanced for contrast. This method uses contrast-limited adaptive histogram equalization as the standard implementation: the grayscale image is divided into several non-overlapping sub-blocks, typically 8×8 pixels in size. Histogram equalization is performed independently within each sub-block, and an upper limit—i.e., a limiting parameter, typically 3.0—is imposed on the cumulative distribution of individual gray levels within the sub-block to suppress noise amplification. Sub-blocks are smoothly transitioned through bilinear interpolation. This processing step is based on the consideration that contact wire inspection images commonly exhibit uneven local exposure under conditions such as tunnel entrances, rain, fog, haze, and strong backlighting. Directly performing line structure detection on the original grayscale image would lead to unstable response values ​​due to the compression of the grayscale difference between the suspension wire and the background. Sub-block equalization simultaneously pulls overexposed and underexposed areas back to a moderate dynamic range, resulting in a stable increase in the contrast of the suspension wire pixels relative to their immediate neighbors. Gamma correction (typically 3.0) can also be used. , To correct the exponential function, homomorphic filtering can be used as an alternative implementation method; gamma correction is suitable for uniform scenes where the entire image is dark, while homomorphic filtering is suitable for scenes where the lighting background changes slowly and it is necessary to separate the illuminance component and the reflection component.

[0026] The enhanced image is obtained after the above preprocessing. The image is then scanned line by line, and the line texture response value is calculated for each line. Specifically, the Hessian matrix of the image is calculated at each pixel location. ;in , These are the second-order partial derivatives of the enhanced image along the horizontal and vertical directions, respectively. The mixed second-order partial derivatives are obtained by convolving the enhanced image with the second-order derivative of the anisotropic Gaussian kernel, and the standard deviation of the Gaussian kernel is... Consider several discrete scales between 1.0 and 3.0. Solve for the two eigenvalues ​​of the Hessian matrix. and And it is agreed that they should be sorted by absolute value. The response value of linear texture is defined as follows: ;in The skewness ratio reflects whether the pixel neighborhood structure tends to be linear or speckled. For structural strength; This is the sensitivity coefficient for differences in skewness, typically taken as 0.5; The intensity scale constant is typically taken as half of the maximum Hessian norm of the enhanced image; That is, pixels The response value of the linear texture at that location. Corresponding to the bright line structure, Corresponding to the dark linear structure, while the suspension wire usually appears as a thin, elongated structure that is darker than the background in the inspection image, therefore the response function only... This results in a non-zero output. The significance of this construction lies in the fact that when the pixel neighborhood is indeed a thin, linear structure, the Hessian matrix possesses an eigenvalue with a significantly large absolute value corresponding to the vertical line direction, and an eigenvalue with a very small absolute value corresponding to the line direction, thus enabling... As the response value approaches zero, it is pushed towards its maximum; if the neighborhood consists of isotropic spots or flat regions, the two eigenvalues ​​are similar or both very small, and the response value will naturally tend towards zero. The multi-scale scheme, through several... The obtained response value is taken as the maximum to account for the representation of hangers of different diameters in the image: The smaller ones fit the thinner suspension strings. Larger ones fit snugly against thick suspension strings or suspension strings magnified in close-up shots.

[0027] To balance computational efficiency, a lighter alternative implementation can also be used. For example, along a set of discrete directions (typically 8 to 12 directions, with angles evenly distributed). One approach is to construct a slender Gaussian kernel—also known as a Gabor filter kernel—and convolve it with the enhanced image to obtain the maximum response value; alternatively, the Steger algorithm can be used to directly find the sub-pixel center through the principal direction of the Hessian matrix. The former involves less computation and is suitable for real-time deployment on embedded devices; the latter offers higher accuracy and is suitable for offline post-processing analysis. The choice in actual deployment depends on available hardware resources.

[0028] After calculating the response value of the linear texture in a row, the pixel with the largest response value is found among all pixels in that row. To avoid false detections caused by noise, a predetermined response threshold is set. Only the response value with the largest value is not less than 1. Only when the condition is met will the position of this pixel be determined as a candidate key point for this row; otherwise, the row is considered to have no reliable response and will not contribute samples to the candidate key point set. The value of is determined using robust statistics relative to the overall graph response distribution. A typical implementation method is as follows: ;in The median of the set of "maximum intra-row response values" for all rows. The absolute deviation of the median of the same set. This is a scaling factor, typically between 2.5 and 3.5. This robust threshold can reliably identify the pixel containing the string in scenes with a large number of background pixels and low response, without relying on a manually set fixed threshold, and can also adaptively adjust across scenes with different illumination levels and distances. It is located at the position with the largest response value. If another local response peak exists within the left and right 5-pixel neighborhoods of a given string, it will not be included as a separate candidate keypoint. This is to prevent the same string body from being identified as multiple candidates in neighboring columns due to subpixel smearing effects. This constraint is equivalent to applying non-maximum suppression to the inline response curve. In some refined implementations, the restriction on single-point extraction within the row can be relaxed, allowing the retention of the top 2 or 3 pixels in response value, thus completely delegating the burden of anomaly removal to the subsequent fan-shaped propagation process. This approach is more suitable for complex scenarios with overlapping projections of multiple strings or severe string bending.

[0029] The candidate key points extracted from all rows are aggregated to form a candidate key point set, denoted as . ,in For the first Key candidate points, , They are respectively x and y coordinates The total number of candidate keypoints, typically between 30 and 200, depending on the vertical size of the sub-image and the proportion of the string in the image. If the value is too small, such as below 20, it means that the positioning deviation of the suspension member area is large or that the image itself has a serious low contrast problem, which can trigger the feedback mechanism to readjust the contrast enhancement parameters or re-examine the detection results; If the threshold is too large, it means that there are redundant responses in the background. In this case, it is not necessary to tighten the threshold excessively in the candidate key point extraction stage. The subsequent orientation field-guided fan-shaped propagation will naturally filter out non-hanging string key points through seed segment localization and fan-shaped search domain screening.

[0030] gather The candidate key points within are not naturally ordered according to the direction of the drop string. If only the vertical axis is considered... When the suspension cable is tilted or the image undergoes an affine transformation, the resulting order deviates systematically from the actual cable trajectory; in extreme cases where the cable tilt angle is close to horizontal, the ordinate sorting may even yield a completely incorrect order. To eliminate this dependency, principal component analysis is introduced to analyze the set... Perform a structured sort.

[0031] For sets Calculate the centroid ;in For set The arithmetic mean position of all candidate keypoints is the geometric center of the set. Each candidate keypoint is then centered. , for The offset vector relative to the centroid. Then, the covariance matrix is ​​constructed. ; It is a 2×2 real symmetric matrix. This represents the transpose of the row vectorized vector. Solve. The characteristic equation yields two nonnegative eigenvalues. and the corresponding unit eigenvector and . for The largest eigenvalue, measuring the data along the path The degree of dispersion in direction; The minimum eigenvalue measures the data along... The degree of dispersion of directions. That is, the first principal direction, which corresponds to the set in the geometric sense of two-dimensional data distribution. The direction with the greatest variance. When the suspension string is nearly vertical in the picture, Approaching the vertical axis of the image; when the suspension is tilted or the image has undergone affine deformation. Adaptively along the overall extension direction of the suspension string. This adaptability is achieved using principal component analysis rather than simply following the general direction of extension. The fundamental consideration in sorting is to transform the physical meaning of "along the direction of the suspension cable" into the statistical meaning of the main direction of data distribution, so that the subsequent sorting results remain unchanged regardless of image rotation or tilt.

[0032] Project each candidate keypoint onto the first principal direction to obtain the projected coordinates. ,in For vector dot product, for exist Scalar components in direction. The set according to Arrange them in ascending order to obtain the candidate keypoint sequence. ,in For the projected coordinates of the first Small candidate key points, i.e., along the direction of the suspension string. The key points of the position. The end with the smallest projected coordinate is denoted as the first end, and the end with the largest projected coordinate is denoted as the second end.

[0033] The eigenvectors obtained from principal component analysis have uncertainty in sign, i.e. and Mathematically equivalent, this means there is no fixed correspondence between the combination of the first and second ends and the physical upper and lower ends of the dropper. This uncertainty does not pose a problem in this method because the subsequent processing of constructing the virtual tension baseline determines the upper and lower connection points based on the geometric position of the clamp detection. The physical orientation semantics of "along the dropper's direction" are completed by the real structure at that stage. Under this arrangement, the first and second ends are purely geometric symbols used to represent two opposite endpoints in the subsequent bidirectional propagation. The advantage is that it avoids making any assumptions about the dropper's physical orientation during the candidate key point extraction stage, thus making the output of this step equally applicable to installation postures where the catenary is at the top of the screen, the contact line is at the bottom of the screen, or vice versa, thus possessing stronger deployment universality.

[0034] After the above processing, the candidate keypoint sequence possesses two properties necessary for subsequent processing: first, the keypoint positions have been filtered by linear texture response and intra-row nonmaximum suppression, ensuring that the vast majority of keypoints truly fall on the main body of the dropper; second, the order between keypoints is determined by the main direction of the data distribution, independent of the specific tilt angle of the dropper within the image. These two properties together constitute the prerequisite for stable execution of the fan-shaped directional field propagation.

[0035] While the candidate keypoint sequence output in stage S1 is ordered along the dropper's direction, it doesn't guarantee that every candidate keypoint accurately falls on the dropper itself. In actual inspection images, lens projections of adjacent contact lines, the slender edges of distant cement supports, shadows cast by positioning pipes under supplementary lighting, rainwater marks, lens smudges causing blurring, and fence railings are all identified as local peaks by the Hessian linear response and thus enter the candidate keypoint set. These false keypoints and those actually falling on the dropper often intersect in the projected coordinates. If a one-time polynomial or least-squares fitting is directly performed on the candidate keypoint sequence, and then deviations are eliminated based on the fitting residuals, the local bending segments of the dropper itself—which are the most significant geometric features of the dropper under relaxation defects—will be incorrectly treated as deviation segments with large residuals and eliminated. This processing method not only destroys the restoration of the dropper's true shape but also causes the relaxation features that this method aims to detect to be eliminated by the preprocessing process. The overall design of the S2 stage treats the dropper as a spatial curve with local continuity. Starting from the most reliable segment, it progresses point by point along the local direction of the curve, eliminating deviations in real time. This local tracking strategy aligns with the characteristics of the dropper as a physically continuous flexible component and preserves the true curvature of the dropper better than global fitting.

[0036] First, the most reliable segment is determined from the candidate keypoint sequence as the starting point for propagation, called the seed segment. Specifically, a segment of length is defined as follows: The sliding window moves position by position along the candidate keypoint sequence from the first end to the second end. The number of candidate keypoints is typically between 7 and 15. If the window size is too small, the stability of local statistics is insufficient, and a single outlier can significantly affect the window metrics; if the window size is too large, it is difficult to accurately pinpoint truly dense and uniform small segments. After each window is defined, two metrics are calculated for all candidate keypoints within the window.

[0037] The first is the uniformity evaluation value, denoted as... Let the candidate key points within the window be arranged in an orderly manner along the direction of the suspension cable, denoted as . ,in For the first in the window There are 10 candidate keypoints. Calculate the Euclidean distance between adjacent candidate keypoints. , , Let be the Euclidean norm. The uniformity evaluation value is defined as follows: That is, the ratio of the maximum to the minimum spacing between adjacent elements within the window. The closer the value is to 1, the more evenly the candidate keypoints are arranged within the window. This metric is based on the fact that the image of the dropper body is continuous, and the single-point extraction process within a row contributes at most one true keypoint to each row. Therefore, the spacing between adjacent candidate keypoints that actually fall on the dropper should be roughly consistent. Conversely, false responses in the background are often concentrated in certain scattered sections, where the adjacent spacing can exhibit both minimum and maximum values, thus... Significant deviation from 1.

[0038] The second is the response intensity evaluation value, denoted as... Defined as ;in for The Hessian linear texture response values ​​obtained in S1, This is the arithmetic mean of the response values ​​corresponding to the candidate keypoints within the window. The consideration for introducing a response intensity evaluation value is that relying solely on uniformity can easily misclassify coincidentally uniform non-dropper responses—such as distant power line projections or fence edges—as seed segments; after adding a response intensity threshold, candidate seed segments must be both uniformly arranged and possess sufficient dropper body feature intensity. First, a predetermined response mean threshold is used. Eliminate windows that are not responding well. Typically, the median response value of candidate keypoints in the whole image is taken as 1.0 to 1.2 times. In the remaining window, all candidate keypoints covered by the window with the uniformity evaluation value closest to 1 are selected as seed segments, and these candidate keypoints are included in the confirmed keypoint sequence.

[0039] The seed segment has two endpoints along the direction of the suspension string; the endpoint closer to the first end is designated as the first endpoint, and the endpoint closer to the second end is designated as the second endpoint. The seed segment also provides an important parameter for subsequent propagation—the reference spacing. Specifically, this is achieved by calculating the median Euclidean distance between adjacent candidate keypoints within the seed segment. , This represents the "natural spacing" of adjacent keypoints on the dropper body at the current image resolution and shooting distance. The median, rather than the mean, is used to maintain robustness to the small number of edge defects that may exist within the seed segment. Based on Further define the continuous spacing interval , For the first spacing coefficient, This is the second spacing coefficient. Typically, the value is between 0.6 and 0.8. Typically, the value is set between 1.4 and 2.0. This range ensures that the subsequent propagation process no longer relies on a fixed pixel threshold to determine the distance between adjacent candidate keypoints, but rather adaptively couples with image resolution, shooting distance, and lens focal length: for long-distance shooting... As the scale naturally shrinks, the continuous spacing also contracts to a smaller scale; when shooting at close range or at high resolution... As the range increases, the corresponding interval expands outward. This adaptive coupling is the key to the stable generalization ability of this method across different inspection vehicle configurations and different route scenarios.

[0040] After the seed segment is determined, fan-shaped propagation guided by the direction field is performed towards the first and second ends respectively. The processing logic of the two directions is completely symmetrical. The following is a detailed explanation of the propagation towards the second end. The propagation towards the first end only requires a corresponding reversal in the direction.

[0041] refer to Figure 2 , Figure 2 The left half consists of six solid dots arranged in a row, representing several confirmed keypoints in the confirmed keypoint sequence at a certain moment. The four consecutive confirmed keypoints closest to the right are enclosed by a dashed elliptical outline, forming a direction reference point group. Currently, the propagation process is proceeding towards the second end; therefore, the vector direction from the confirmed keypoint with smaller projected coordinates to the confirmed keypoint with larger projected coordinates in the direction reference point group is taken as the current direction field vector of the second end, denoted as... This is indicated by a short, thick horizontal arrow emanating from the solid dot at the right end of the confirmed keypoint sequence. The end of this arrow marks the starting point of the second propagation. That is, the confirmed key point with the largest projected coordinates in the direction reference point group.

[0042] by As vertices, with The straight line is the central axis, with a predetermined angle. For half an angle, with a predetermined initial maximum radius For the maximum radius, in The side that is pointed to constructs Figure 2 The right half of the fan-shaped region, i.e., the fan-shaped search area. The angle between the upper edge of the fan and the central axis. Depend on Figure 2 middle The nearby small arc marker, this included angle is also formed between the lower edge of the sector and the central axis. Maximum radius of the sector. From the lower edge of the fan A double-headed arrow pointing to the apex of the arc is given. The central axis itself is represented in the diagram as a thin dashed line running through the fan shape.

[0043] Figure 2 There are four candidate keypoints distributed within the sector, denoted as follows: , , , . Located near the central axis, this is a key point included in this inclusion after consistency verification, and is therefore represented by a solid circle; the other 3 points... , , All are presented as hollow circles, representing three typical different handling scenarios. Near the upper edge of the sector, the angle formed with the central axis is close to half an angle. That is, the direction consistency error index It has approached the predetermined error threshold. It is on the verge of being eliminated due to excessive deviation from its intended direction. Two geometric quantities used to demonstrate conformance verification and Definition: From Draw a perpendicular line to the central axis. The projection point of the perpendicular line segment onto the central axis is the length of the perpendicular line itself, which is the lateral deviation distance. The small label near the vertical line segment Identification; from to Draw a double-headed arrow; the length of the arrow represents the propagation distance. The small label near the midpoint of the arrow Identification. The orientation consistency error index is defined as follows: Geometrically Compared to Position vector and The sine of the angle between them. Located near the outer edge of the far end of the fan, its propagation spacing Exceeding the continuous spacing range The upper limit is reached, therefore even if the direction consistency error index is qualified, it cannot pass the consistency verification. When multiple key points that have passed the consistency verification exist simultaneously within the sector search domain, The smallest one was the key factor for inclusion in this study.

[0044] The second end of the seed segment is taken as the current second end propagation starting point, denoted as... Within the confirmed key point sequence, from... Starting from the direction of the suspension cable, take the adjacent cable in the opposite direction. One confirmed key point, For the predetermined quantity, typically 4 to 6, together with itself The confirmed key points constitute the second set of end-direction reference points. If the value is too small, for example, equal to 2, the direction estimation is easily dragged down by the positional error of a single key point; If the value is too large, the direction estimation will be slow and unable to keep up with the actual curvature of the dropper. The smallest projected coordinate in the direction reference point set will be denoted as... The largest of the projected coordinates is denoted as , Near the first end Near the second end, the direction vector between the two That is, the current direction field vector at the second end. It is a unit vector. Here, the line connecting the first and last points is used as the direction estimate, instead of the direction obtained by least-squares straight-line fitting of the direction reference point group. This is because the local orientation of the dropper changes gradually. When the dropper bends, the line connecting the first and last points in the direction reference point group of the local bending segment is closer to the true tangent at the very end than the fitted straight line. Using the first and last point connection means that the newly added key points contribute a larger proportion to the direction field update, making the direction field more sensitive to the local bending of the dropper and able to closely follow the dropper's trend, rather than prematurely "smoothing out" the bending segment with a seemingly smooth straight line. In some cases, especially when the dropper itself is relatively straight near the seed segment, the direction reference point group can also be used instead. The principal direction of least squares line fitting at each point is taken as... This implementation is more resistant to positional noise, but sacrifices response speed to sudden bending.

[0045] Sure After that, with As vertices, with The straight line is the central axis, with a predetermined angle. For half an angle, with a predetermined initial maximum radius For the maximum radius, in Construct a sector-shaped search domain on the side that is being pointed to. Typically, the temperature is between 15 and 30 degrees Celsius. If the value is too small, the dropper string may leave the search domain at points of sudden, significant bends, causing the propagation to terminate prematurely. If the value is too large, it will allow non-suspended responses far from the directional field's central axis to enter the candidate range, increasing the risk of false absorption. Typical That is, twice the reference spacing - this choice leaves room for "crossing over occasional missed detections" in single-step propagation. Even if a real key point does not enter the candidate key point set in S1 due to background occlusion or instantaneous reflection, the fan-shaped search domain can still reach the next real key point.

[0046] Next, the candidate keypoint sequence is screened for keypoints to be verified. Specifically, candidate keypoints that simultaneously meet the following three conditions are identified and designated as keypoints to be verified. The first condition is that they have not yet been included in the confirmed keypoint sequence. The second condition is that their projected coordinates are greater than [a certain value]. The projected coordinates are located on the side facing the second end along the direction of the suspension cable. The third condition is that it falls on the side with... For vertices, For the central axis, For half an angle, Within the geometric range of the sector with the maximum radius. The second condition is introduced to prevent propagation from backtracking in directions already traversed. When the suspension string bends significantly or the axis of the direction field drifts slightly during the update process, the sector search domain may geometrically cover the area where the direction reference point group is located. If it is not mandatory that the new key point is located closer to the second end along the suspension string, the confirmed key points will be repeatedly "rediscovered," causing the propagation process to oscillate or even regress.

[0047] For each key point to be verified Perform consistency verification. First, calculate two geometric quantities. One is the lateral deviation distance. ,Right now Perpendicular distance to the central axis of the direction field: ;in for Compared to The position vector in Projected length in the direction, The projection vector itself is the result; subtracting the two gives the result. Relative to the vertical component of the central axis, we then take its Euclidean norm to obtain... Second, the propagation distance. ,Right now and Euclidean distance between them: ;based on and Further define the direction consistency error index ; Geometrically equal to Compared to Position vector and The sine of the angle between them, therefore The smaller, the more it means The more precisely it falls near the central axis of the direction field. (Introduction) Instead of using directly As a deviation criterion, it is because of the simple Distance The standards are too lenient on distant key points to be verified and too strict on nearby key points—the same angular deviation is converted to a different value at a more distant point. Larger, proximal conversion Smaller. As a relative quantity, this distance dependency is normalized, ensuring that key points to be verified at different distances are on the same discriminative scale. When Less than the predetermined error threshold and Falling within a continuous interval At that time, It is determined to be a critical point that passes the consistency verification; otherwise, it fails. Typical values ​​range from 0.20 to 0.35, corresponding to a directional deviation angle of approximately 11.5 to 20.5 degrees.

[0048] Within the sector search domain, there may be more than one keypoint that passes the consistency verification. This situation typically occurs when the dropper image is slightly thick, the inline single-point extraction is split at the edges, or parallel interference lines with similar phases appear below the dropper. For this multi-candidate scenario, our method handles it by selecting from all keypoints that have passed the consistency verification... The smallest one is the key point for inclusion in this study, denoted as... This means that the selected key point for inclusion is the one that is closest to the central axis of the direction field. Only when there is only one key point that passes the consistency verification within the sector search domain is that key point directly used as the key point for inclusion. This selection strategy follows the consideration of "choosing the one that best fits the local direction continuity among multiple seemingly reasonable candidates", which can reliably avoid being swayed by side interference.

[0049] This will be included as a key point. Incorporate the confirmed key point sequence, and at the same time Updated to the new second-end propagation starting point; and the maximum radius of the sector search domain is restored to The cumulative expansion count is reset to zero. The radius recovery and count reset steps are crucial in engineering: each successful inclusion of a new key point means the image of the dropper body at that location is clearly visible. The next propagation should start from a "standard search range" again; otherwise, the cumulative expansion of the search radius on long-distance droppers will continue to increase, eventually including distant non-dropper responses in the fan-shaped search domain. After inclusion and state update, based on the new second-end propagation starting point, using the same directional reference point group selection rules, the same directional field vector calculation formula, and the same fan-shaped search domain geometric parameters, the second-end directional reference point group is reconstructed, the current directional field vector of the second end is recalculated, and the fan-shaped search domain is rebuilt. This process continues repeatedly towards the second-end direction, performing the screening of key points to be verified, consistency verification, determination of the included key points, and updating of the second-end propagation starting point.

[0050] During the propagation process, there may be instances where no key points that have passed consistency verification exist within a single constructed sector search domain. This typically corresponds to a localized imaging break in the dropper body due to factors such as contact line reflection, supplementary lighting glare, or obstruction by construction signs, preventing S1 from contributing candidate key points at that location. In such cases, this method maintains... and Keeping the maximum radius of the sector search domain unchanged, adjust it according to a predetermined radial step size. Expanding the sector once yields an expanded sector search area; Typical to Within the expanded sector search domain, re-execute the screening and consistency verification of the key points to be verified, and increment the cumulative expansion count by 1. If no key points pass the consistency verification after expansion, continue as follows. Expand; if a critical point passes consistency verification after an expansion, it is included according to the aforementioned rules, and the initial maximum radius and count are restored. Set a predetermined upper limit for the number of expansions. Typically, 3 to 5 are taken; when the cumulative number of expansions reaches... If no key point passes the consistency verification within the sector search domain, it is considered that the visible portion of the suspension string in that direction has been processed, and the current... As the second termination point, the propagation process towards the second end ends. The radius is expanded in stages rather than being enlarged to a large value all at once. This is because, in the common case where a new key point is successfully included in the first expansion, the search radius only deviates from the standard value briefly; and it avoids the side effect of "allowing the search radius to expand indefinitely to deal with occasional breaks".

[0051] refer to Figure 3 , Figure 3 The left half shows the confirmed keypoint sequence consisting of four solid dots, with the rightmost solid dot being the current second-end propagation starting point. .from The short, thick horizontal arrow at the starting point indicates the current direction field vector at the second end. .

[0052] Figure 3 The core is to For common vertices, with The three concentric sectors, sharing a common central axis and extending towards the second end at the same half-angle, are formed by three layers of concentric sectors. The innermost sector is closed by a solid arc, corresponding to a predetermined initial maximum radius. The initial sector search domain is defined; the middle sector is closed by a short dashed arc, and the radius increases to... This corresponds to the sector search domain after being expanded once; the outermost sector is closed by a dotted line arc, and its radius is further increased to... This corresponds to the sector search domain after being expanded twice. The predetermined radial step size is indicated by a bidirectional arrow between adjacent layers along the outer edge of the sector, appearing at the first and second expansions, respectively. The progression from the innermost to the outermost layer reflects the successive expansion process when no consensus verification key points exist in either the initial sector search domain or the sector search domain after one expansion; during the expansion process... and All remain unchanged. From the outer edge of the sector The double-headed arrow pointing to the innermost arc apex indicates the initial maximum radius. The lower outer edge of the three-layered fan-shaped structure is marked by three lines of brief text: Initial, Expanded 1st, and Expanded 2nd.

[0053] Figure 3 A solid dot appeared within the outermost sector, representing the first included critical point that passed consistency verification within the sector search domain after two expansions. This represents the following engineering scenario: the dropper body failed to contribute as a candidate critical point within the initial and expanded sector search domains due to contact wire reflection, supplementary lighting glare, and obstruction by construction signs, until the sector search domain was expanded to... Only then did we reach the next real, visible candidate key point for the suspension cable. Once this key point is confirmed, the maximum radius of the sector search domain is restored to the predetermined initial maximum radius. The cumulative expansion count is reset to zero to prevent the search radius from continuously expanding on long-range droppers and eventually including distant non-dropper responses in the sector search domain. When the cumulative expansion count reaches the predetermined expansion count limit... If there are still no key points that pass the consistency verification within the sector search domain, then the current... As the second termination point, the propagation process towards the second end ends; the propagation towards the first end adopts a completely symmetrical logic.

[0054] The propagation towards the first end follows a completely symmetrical logic to that towards the second end. Specifically, the first end of the seed segment is taken as the starting point of the first-end propagation, and adjacent nodes are taken in the positive direction along the suspension string starting point. The confirmed key points together constitute the first-end direction reference point group. The vector pointing from the largest projected coordinate to the smallest projected coordinate in the first-end direction reference point group is taken as the first-end current direction field vector. Here, the direction of the first-end current direction field vector is opposite to that of the second-end current direction field vector, so that the sector search domains in the two directions extend towards their respective endpoints. The remaining processing—including the geometric parameters of the sector search domain, the selection rules for the key points to be verified, consistency verification, selection of the best among multiple candidates, updating of the key points included in this time, and the expansion and termination conditions of the sector search domain—is consistent with the propagation towards the second-end direction; the only difference is that the constraint on the projected coordinates of the key points to be verified in the first-end direction is changed to "projected coordinates less than the first-end propagation starting point" to ensure that the propagation advances towards the first end without regressing. This continues until the cumulative expansion reaches a certain number. If there are still no key points that pass the consistency verification within the sector search domain, the current first end propagation starting point is taken as the first end termination point, and the propagation process towards the first end ends.

[0055] After both-way propagation is complete, the confirmed key point sequence is the dropper key point sequence identified by this method. All candidate key points in the candidate key point sequence that were not included in the confirmed key point sequence are judged as outliers and removed. In some application scenarios, these removed points, along with their coordinates in the original image, can be retained as auxiliary information for subsequent diagnosis—for example, recording the locations of linear responses that were judged as outliers in the inspection log, in order to check for parallel interference from non-dropper components, camera lens contamination, or suspected defects that need to be focused on in the next inspection.

[0056] Finally, spline fitting is performed on the confirmed key point sequence to obtain the suspension string fitting curve. Specifically, the confirmed key point sequence is sorted along the suspension string direction (i.e., according to the projected coordinates from smallest to largest) and used as the model points for spline interpolation. One implementation method is to use cubic splines: based on the projected coordinates... As parameters, respectively for the x-axis with the vertical axis Construct a piecewise cubic polynomial and Adjacent segments maintain continuity of function values, first derivatives, and second derivatives at nodes; natural boundary conditions are applied to endpoints, i.e., the second derivative is set to zero at both endpoints, thus avoiding overshoot, a common phenomenon in spline interpolation, near the endpoints. Another implementation method uses cubic B-splines: using the confirmed keypoint sequence as control points, a fitting curve is constructed according to a uniform node vector; the local support characteristics of B-splines ensure that the positional error of a single keypoint only affects the local curve segment, providing better noise resistance for the overall shape of long droppers. Yet another implementation method uses Catmull-Rom splines: the curve strictly passes through each confirmed keypoint, and the tangent at the node is determined by the line connecting adjacent keypoints, faithfully preserving the geometric features of the dropper relaxation shape. The dropper fitting curves obtained from all three implementation methods can be used as inputs for subsequent relaxation feature calculations in engineering; the specific choice depends on the application's preference for endpoint smoothness, noise resistance, and shape fidelity.

[0057] After the S2 stage processing, the candidate key point sequence on the dropper that was originally noisy and mixed with interference points has been processed into a continuous and smooth curve that fits the real shape, and the local curvature of the dropper is faithfully preserved - which is the geometric basis on which the subsequent relaxation degree determination is based.

[0058] While the dropper fitting curve output in stage S2 accurately reflects the actual shape of the dropper in the image, it's difficult to determine whether the dropper is slack based solely on the curve's geometric properties. This is because droppers have different suspension lengths at different installation locations—droppers near the positioning point are only about 20 cm, while those further away can reach 80 cm or even over 1 meter. Geometric parameters such as the lifting of the catenary cable on different supports, the contact wire pull-out value, and the rail surface superelevation also cause variations in the dropper's installation angle. If the maximum curvature or bending amplitude of the dropper curve itself is used as the criterion, long droppers exhibit significant bending even when slack is not severe, while short droppers show limited geometric amplitude even when significantly slack, making it impossible to unify the criteria for judgment. The core idea of ​​stage S3 is to use the "shape that the dropper should present" under tension as a reference benchmark, and to use the deviation of the actual dropper shape from this benchmark as the basis for slack quantification, thus placing droppers of different lengths and inclination angles on the same comparative scale.

[0059] In this method, this reference datum is represented as a virtual tension baseline. To establish the virtual tension baseline, it is first necessary to find the positions on the physical object where the dropper connects to the clamps at the upper and lower ends—these correspond to the two real endpoints of the dropper curve in the image. Considering that the dropper fitting curve obtained by S2 may slightly extend near the endpoints due to the boundary effect of spline interpolation, or that the imaging of the clamp body overlaps with the imaging of the dropper, directly taking the minimum and maximum points of the dropper fitting curve in the projected coordinates may not accurately correspond to the physical endpoints. This method uses clamp detection to anchor the real endpoints.

[0060] Specifically, clamp detection within the dropper member area can be performed by a lightweight object detection model. This model can share a backbone with the dropper member object detection and output its own independent detection head, or it can be trained independently. In the training data, the upper and lower clamps of each dropper are individually labeled with rectangular bounding boxes. The number of labeled clamps for each type is comparable to the number of labeled dropper members, typically 5,000 to 10,000 samples per type. The model inference outputs two rectangular bounding boxes, corresponding to the positions where the dropper connects to the catenary clamp and the contact wire clamp, respectively. The catenary clamp is installed on the catenary side and is usually located above the dropper in the image; the contact wire clamp is installed on the contact wire side and is usually located below the dropper. Under normal catenary installation posture, the vertical coordinate of the catenary clamp connection position in the image is smaller, while the vertical coordinate of the contact wire clamp connection position is larger. However, when the posture of the inspection vehicle changes, the camera tilts, or the image undergoes affine transformation, this vertical relationship is not constant. Therefore, this method does not rely on the vertical coordinate as a criterion, but directly uses the two semantic categories of the clamp detection output—catenary clamp connection position and contact wire clamp connection position—as identification.

[0061] After obtaining the two bounding boxes for the wire clamp detection, the geometric center of each is taken as the representative point of the wire clamp connection position, denoted as . and , The geometric center of the connection point between the dropper and the catenary clamp. This is the geometric center of the connection point between the dropper wire and the contact wire clamp. The dropper wire fitting curve is represented as a parametric curve. , For arc length parameters, , They are respectively The x and y coordinates of the points on the curve, For the curve in The position vector at that point. Solve for it on the fitting curve of the suspension cable: ;in For Euclidean norm, To make the curve point reach The parameter value with the smallest distance. To make the curve point reach The parameter value that minimizes the distance. Solving the above two minimization problems can be done by following... Discrete search with a step size of 0.001 typically takes less than 1 millisecond. The golden section method or Newton's iteration method can also be used to obtain subpixel-level accuracy. This refers to the point on the fitting curve of the dropper that is closest to the connection point between the dropper line and the catenary cable clamp, i.e., the upper connection point; This is the point on the fitting curve of the dropper that is closest to the connection point between the dropper and the contact wire clamp, i.e., the lower connection point.

[0062] The "nearest point" is introduced as the endpoint localization strategy, instead of simply using the center of the clamp bounding box as the endpoint, because the clamp itself is a metal component of a certain area in the image, and its geometric center may not be on the extended line of the dropper's image. Forcing the endpoints onto the dropper's fitted curve preserves the semantic identity verification provided by clamp detection while ensuring that the upper and lower connection points are themselves true points on the dropper curve. Subsequent operations such as integration, sampling, and curvature calculation on the curve segment will not result in the endpoints jumping off the curve. In degenerate scenarios with low clamp detection confidence or missed detection of a single clamp, the two ends of the intersection of the dropper foreground mask obtained from semantic segmentation and the curve can be used as the upper and lower connection points as an alternative degenerate processing implementation.

[0063] Determine the upper connection point Connection point to the lower end Then, connecting the two ends forms a straight line segment, which serves as the virtual tension baseline. Physically, this straight line segment corresponds to the geometric shape that the dropper should exhibit under ideal conditions—fully tensioned, with negligible self-weight and deflection—a straight line stretched directly from the upper clamp to the lower clamp. Any bending or displacement deviating from this line can be considered a deviation of the dropper from the ideal tension state.

[0064] The dropper fitting curve and the virtual tension baseline are unified into a local coordinate system that facilitates calculation. Specifically, the lower end connection point... With the origin as the coordinate origin, the direction from the upper connection point to the lower connection point is defined as one axis of the local coordinate system (called the reference direction axis), and the direction perpendicular to the reference direction axis and defined according to the right-hand rule is defined as the other axis (called the normal axis), thus establishing a two-dimensional local coordinate system. In this local coordinate system, the virtual tension baseline is the line along the reference direction axis from 0 to... A section, The length of the virtual tension baseline is the Euclidean distance between the upper and lower connection points. The deviation of the suspension fitting curve from the virtual tension baseline can be decomposed into two parts: the longitudinal position in the reference direction and the lateral displacement in the normal direction.

[0065] Next, samples are taken at equal intervals along the virtual tension baseline on the dropper fitting curve to construct the offset profile. Specifically, samples are taken at equal intervals from the lower connection point to the upper connection point on the virtual tension baseline. Each projection position, Typically, the range is 100 to 200, denoted as , For the first The distance from each projection position to the lower connection point , Corresponding to the lower connection point, Corresponding to the upper connection point. For each... Find the corresponding sampling points on the fitting curve of the suspension string. , making After drawing a perpendicular line from the virtual tension baseline, the foot of the perpendicular will be positioned exactly on the virtual tension baseline. With the projection positions arranged at equal intervals, the sampling along the curve direction is not strictly equidistant, but it is strictly equidistant along the reference direction. The advantage of doing so is that when calculating the normal deviation distance laterally, the "horizontal scale" of all sampling points is aligned, and the resulting deviation profile corresponds one-to-one with the reference direction axis in scale, which facilitates the lateral comparison between suspensions of different lengths.

[0066] For each sampling point Draw a perpendicular line to the virtual tension baseline, and let the foot of the perpendicular be... ,but Vertical distance to the virtual tension baseline That is, the normal deviation distance of the sampling point. The dimension is pixels. The normal deviation distances of all sampling points are arranged in the sampling order along the virtual tension baseline to form the deviation profile. A dropper string in a fully taut state deviates from its outline. In all The values ​​above are close to 0; a slack suspension string deviates from the contour. A distinct peak will appear in the middle section, and the position and amplitude of this peak together reflect the degree and shape of relaxation.

[0067] Next, based on the fitting curve of the suspension string and the virtual tension baseline, three relaxation eigenvalues ​​are calculated. These three eigenvalues ​​are complementary in a physical and geometric sense, and their combined use can maintain the stability of the discrimination ability under different relaxation states.

[0068] The first term is the normalized curvature eigenvalue. This is the arc length parameter along the suspension fitting curve. Calculate curvature point by point ;in , They are respectively , right The first derivative, , They are respectively for The second derivative, for The curvature of the curve is measured in units of the reciprocal of pixels. In cubic spline or B-spline implementations, these first and second derivatives can be analytically derived from the spline coefficients without numerical differencing. A set of densely sampled points (typically 500 to 1000) is discretized on the curve, and the maximum curvature is selected from these. The maximum curvature reflects the degree of local bending of the suspension string itself; the more severe the slack, the more severe the bending. The larger. However It inherently has the dimension of the reciprocal of pixels, so you can use it directly. As a criterion, the values ​​will drift across different image resolutions and shooting distances, making it impossible to share a threshold across different samples. This method will... Length of virtual tension baseline Multiplying them together yields the normalized curvature eigenvalues. ; The dimension of is the reciprocal of the pixel. The dimension of both is pixels, and their product is a dimensionless quantity, allowing for direct lateral comparisons between suspension strings of different lengths and resolutions. This normalization method considers the idea of ​​using the "image resolution information" carried by curvature, also based on pixels, to represent this information. The degree of relaxation is truly reflected in the pure geometric curvature that remains after the cancellation.

[0069] refer to Figure 4 , Figure 4 It consists of a broken line fixed at both ends and an arc in between. Located in Figure 4 The small gray square in the upper left corner, along with the solid dot inside, represents the upper clamp and upper connection point of the suspension string; located in Figure 4 The small gray square in the lower right corner, along with the solid dot inside the square, represents the lower clamp and lower connection point of the dropper. The upper connection point is the point on the dropper fitting curve closest to the connection between the dropper and the catenary clamp, and the lower connection point is the point on the dropper fitting curve closest to the connection between the dropper and the contact wire clamp.

[0070] Figure 4 The thick dashed line segment extending directly from the upper connection point to the lower connection point is the virtual tension baseline, representing the ideal geometric shape that the suspension cable should exhibit under full tension, with negligible self-weight and deflection. The length of this virtual tension baseline is denoted as... That is, the Euclidean distance between the upper and lower connection points, which is... Figure 4 The label in the middle section is close to the right side of the baseline. The solid curve that bulges significantly to the left between the upper and lower connection points is the dropper fitting curve, representing the true geometric shape of the dropper body; the bulging direction of this curve relative to the virtual tension baseline is the direction in which the dropper deviates from the tensioned position due to slack.

[0071] Figure 4 The dashed rectangle enclosing the entire fitting curve of the suspension string is the minimum bounding rectangle, with its longer side arranged along the overall direction of the fitting curve. The length of the shorter side of the minimum bounding rectangle is indicated by a double-headed arrow starting from the lower right corner of the rectangle, denoted as . This reflects the maximum unfolded width of the suspension string in its normal direction.

[0072] Figure 4 Another solid line segment connects a point on the suspension wire fitting curve perpendicularly to the virtual tension baseline. The lower end of this solid line segment is a fork-shaped marker on the suspension wire fitting curve, corresponding to the sampling point with the largest normal deviation distance in the deviation profile obtained by sampling at equal intervals along the virtual tension baseline direction; the length of this solid line segment itself is the maximum normal deviation distance in the deviation profile, denoted as [missing information]. Labels near the solid line segment Logo.

[0073] Figure 4 The hollow dot located in the lower part of the fitted curve of the suspension string indicates the maximum curvature. The location is where the curvature is calculated point by point along the arc length parameter on the fitted curve of the suspension string. The maximum value is then taken. Based on the above geometric quantities, the three normalized relaxation eigenvalues ​​are as follows: , , All three are dimensionless quantities, making the slack of the suspension wires of different lengths and installation angles comparable.

[0074] The second term is the minimum slant rectangle width ratio eigenvalue. The goal is to find the minimum circumscribed slant rectangle of the suspension string fitting curve, which is the rectangle with the smallest area among all possible rotation angles that can cover the entire curve. Its long side should be aligned along the overall direction of the curve. The solution for the minimum circumscribed slant rectangle can be derived from the rotating caliper algorithm: first, calculate the convex hull of the discrete sampling points on the suspension string fitting curve; then, enumerate each edge of the convex hull, constructing a circumscribed rectangle along that edge as its long side, and selecting the rectangle with the smallest area in all directions as the minimum circumscribed slant rectangle. Let the length of the long side of the minimum circumscribed slant rectangle be... The length of the shorter side is , Approximately equal to the end-to-end span of the suspension cable. It is the maximum width of the dropper curve in the direction perpendicular to its overall orientation. The length of the shorter side reflects the extent of the dropper's "swing" in the normal direction of its orientation; the more severe the slack, the more the dropper deviates in the normal direction due to loss of tension. The larger. But Also affected by image scale, this method divides it by the length of the virtual tension baseline. Obtain the eigenvalue of the dimensionless minimum width ratio of the oblique rectangle. ;Will Instead As a denominator, because Representing the distance between the actual endpoints, it is physically more stable than the "long side of the curve envelope"; in cases of severe relaxation, It will be slightly smaller due to the bending of the suspension string. ,by The denominator is always the geometric scale under tension, and the resulting proportion reflects the degree of relaxation relative to the physical reference quantity.

[0075] The third item is the maximum deviation ratio characteristic value. (This refers to the deviation from the contour.) Take the maximum value from the middle , It is the maximum normal deviation of the dropper curve relative to the virtual tension baseline, reflecting the deviation of the dropper from the point furthest from the tensioned position in the slack state. Then... Divide by the length of the virtual tension baseline get ; Also a dimensionless quantity, geometrically equivalent to the "ratio of the maximum normal deviation to the end-to-end length of the suspension string," this is the most intuitive and physically interpretable quantitative indicator for slack. (Short suspension string) With long suspension They cannot be directly compared, but they are normalized to... After that, they are on the same scale. It is the feature with the most direct physical meaning and the strongest correlation with the degree of relaxation in this method, and it has the highest discrimination contribution in most practical scenarios.

[0076] Of the three features, Highlighting the most severe bending in a specific area, Emphasizing overall lateral expansion, Emphasize the proportion of deviation of the maximum point from the tension reference. The relaxation patterns "seen" by these three methods each have their own emphasis: It is more sensitive to a sharp bend in a small section of the suspension string (for example, the upper fixing bolt of the suspension string is loose, causing only the upper half to sag), but if the suspension string sags evenly as a whole and the bends are relatively gentle in all places, It may not be significant; It is particularly sensitive to the most common slack form, which is drooping in the middle of the suspension string, but has limited response to cases where there is only a small angular shift at the end; It provides a significant response to situations where the suspension wire exhibits a large S-shaped or C-shaped bend, given that... and The three features are used in combination, enabling this method to cover various geometric shapes when relaxation occurs at different locations—end, middle, and overall—avoiding blind spots for specific relaxation shapes by a single feature.

[0077] The threshold calibration phase is completed before the system is put into online detection. Specifically, a predetermined number of thresholds are collected in advance from historical inspection data. Images of droppers with roots in a normal state are used as normal dropper samples. Typically, 30 to 100 wires are selected. The determination of "normal condition" can be completed by manual review by someone experienced in overhead contact line maintenance. The sample's corresponding droppers must be confirmed to be taut and without slack during visual inspection, tension testing, or manual tactile testing. For each normal dropper sample, stages S1 and S2 are performed sequentially to obtain the dropper fitting curve, and then stage S3 is calculated accordingly. , , .set up The feature value sequence obtained from the normal dropper sample is as follows , , , Indicates the first Root normal suspension cable sample number eigenvalues, Calculate the mean for each characteristic value. ; and standard deviation ; For the first The arithmetic mean of the eigenvalues ​​on the normal dropper sample. For the first The sample standard deviation of the eigenvalues ​​on a normal dropper sample. The first-level threshold of the feature value is taken The second-level threshold is taken as follows: ;in This is a multiple of the first value, typically 2 to 3, corresponding to a probability of approximately 2.3% to 0.13% in the tail of the normal distribution; It is a multiple of the second, typically 4 to 6. Greater than . As a boundary indicating that the distribution is beginning to deviate from the normal distribution, This serves as the alarm boundary for "significant deviation from the normal distribution." This threshold determination method, based on the mean plus a multiple of the standard deviation, only requires normal string samples for calibration. It does not require collecting a large number of slightly relaxed and severely relaxed fault samples, nor does it require supervised classification training on fault samples. This is the fundamental reason why this method is named "few-sample dependent." When the number of normal samples is small ( In scenarios where the value is below 50, or where the sample distribution is significantly skewed, a more robust statistical approach can be adopted: using the median instead. Replace the absolute deviation of the median with 1.4826 (to make it an unbiased estimate of the standard deviation under a normal distribution). This can effectively reduce the impact of individual outliers on the threshold. Alternatively, the threshold can be determined directly using quantiles, for example, taking the 95th percentile as the threshold. The 99th percentile as This approach does not rely on assumptions about the shape of the distribution and is suitable for eigenvalues ​​that are not normally distributed.

[0078] During the online detection phase, after completing the initial processing steps S1, S2, and S3 for the current dropper, three characteristic values ​​of the current dropper are obtained. , , , and the pre-calibrated threshold , ( The relaxation level is determined by comparison. The specific determination rules are as follows: when... and and When all three feature values ​​are less than their respective first-level thresholds, the current suspension level is output as normal. When at least one of the three feature values ​​reaches its respective first-level threshold, but all three feature values ​​are still less than their respective second-level thresholds, the current suspension level is output as slightly relaxed. When at least one of the three feature values ​​reaches its respective second-level threshold, the current suspension level is output as severely relaxed. The three-level judgment result can be used as the final output label for the current suspension, written into the inspection log along with the specific values ​​of the three feature values, and accompanied by a visual annotation of the suspension fitting curve, virtual tension baseline, and the location of the maximum deviation point overlaid on the original image for maintenance personnel to review. This maximum value aggregation strategy of "upgrading if any feature value exceeds the level" reflects the low tolerance for false negatives in relaxation detection—the three feature values ​​have different geometric sensitive directions, and triggering any one of them means that the suspension has deviated significantly in at least some geometric shape. For driving safety considerations, the system should tend to issue an alarm rather than relying on multiple features to trigger simultaneously to upgrade the level. In scenarios where false alarms are more sensitive, a majority voting strategy can also be used—the level is only upgraded when at least two of the three feature values ​​reach the corresponding threshold. This alternative implementation slightly increases the false alarm rate in exchange for a decrease in the false alarm rate.

[0079] After processing in the S3 stage, this method outputs a clear slack level label for each dropper, along with three traceable feature values, completing the end-to-end detection from image to grading determination. Moreover, the entire set of judgment thresholds can be calibrated using only normal dropper samples, making it suitable for actual overhead contact line inspection projects where samples of mild and severe slack faults are extremely scarce.

[0080] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these specific embodiments are merely illustrative. Those skilled in the art can omit, substitute, and modify the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, combining the above method steps to perform substantially the same function and achieve substantially the same result according to substantially the same method falls within the scope of the present invention. Therefore, the scope of the present invention is defined only by the appended claims.

Claims

1. A method for grading the slack degree of overhead contact line droppers based on few samples, characterized in that, Includes the following steps: S1. Locate the dropper component area in the overhead contact line inspection image, extract candidate key points within the dropper component area, and obtain a sequence of candidate key points ordered along the dropper direction and having a first end and a second end; S2. Determine the seed segment in the candidate keypoint sequence; starting from the seed segment, perform fan-shaped propagation guided by the direction field towards the first and second ends respectively: construct the current direction field vector based on the confirmed keypoints, construct a fan-shaped search domain on one side pointed to by the current direction field vector, verify the consistency of direction and propagation spacing of the candidate keypoints in the fan-shaped search domain, include the keypoints that pass the consistency verification into the confirmed keypoint sequence, update the current direction field vector and the fan-shaped search domain, until both bidirectional propagation reaches the termination point; remove the remaining candidate keypoints in the candidate keypoint sequence, and perform spline fitting on the confirmed keypoint sequence to obtain the suspension curve; S3. Determine the upper and lower connection points on the dropper fitting curve, and use the straight line segment connecting the upper and lower connection points as the virtual tension baseline; calculate the normalized curvature feature value, the minimum oblique rectangle width ratio feature value, and the maximum deviation ratio feature value based on the dropper fitting curve and the virtual tension baseline; compare the three feature values ​​with the first-level threshold and the second-level threshold pre-calibrated based on normal dropper samples, and output the current dropper relaxation level.

2. The method according to claim 1, characterized in that... In S1, the dropper component region in the catenary inspection image is located by inputting the catenary inspection image into the pre-trained target detection model, outputting the rectangular bounding box coordinates of the dropper component, and taking the image range defined by the rectangular bounding box as the dropper component region.

3. The method according to claim 2, characterized in that... In step S1, candidate key points are extracted within the dropper component region, and a sequence of candidate key points ordered along the dropper direction is obtained. Specifically, the dropper component region is grayscaled and contrast-enhanced to obtain an enhanced image. The enhanced image is scanned line by line along the image row direction. For each row, the linear texture response value is calculated. The pixel with the largest linear texture response value in each row that reaches a predetermined response threshold is taken as the candidate key point of this row. The candidate key points extracted from all rows constitute a candidate key point set. Principal component analysis is performed on the candidate key point set to obtain the first principal direction. Each candidate key point in the candidate key point set is projected onto the first principal direction to obtain the projection coordinates. The candidate key point set is arranged in ascending order of projection coordinates to obtain a sequence of candidate key points ordered along the dropper direction. The end with the smallest projection coordinate in the candidate key point sequence is defined as the first end, and the end with the largest projection coordinate is defined as the second end.

4. The method according to claim 1, characterized in that... In S2, seed segments are determined from the candidate keypoint sequence. Specifically, a sliding window of a predetermined length is moved and scanned segment by segment along the direction of the suspension string in the candidate keypoint sequence. For all candidate keypoints covered by each sliding window, the ratio of the maximum to the minimum Euclidean distance between adjacent candidate keypoints is used as the uniformity evaluation value of this sliding window. The arithmetic mean of the linear texture response values ​​of all candidate keypoints in this sliding window is used as the response intensity evaluation value of this sliding window. Among all sliding windows where the response intensity evaluation values ​​reach the predetermined response mean threshold, the sliding window with the uniformity evaluation value closest to 1 is selected as the seed segment. All candidate keypoints contained in the seed segment are included in the confirmed keypoint sequence. The seed segment has a first end point near the first end and a second end point near the second end along the direction of the suspension string.

5. The method according to claim 4, characterized in that... S2 further includes: taking the median of the Euclidean distance between adjacent candidate keypoints in the seed segment as the baseline spacing, taking the product of the baseline spacing and the first spacing coefficient as the lower limit of the continuous spacing interval, and taking the product of the baseline spacing and the second spacing coefficient as the upper limit of the continuous spacing interval, wherein the first spacing coefficient is less than 1 and the second spacing coefficient is greater than 1.

6. The method according to claim 5, characterized in that... S2, the fan-shaped propagation guided by the direction field towards the second end, specifically includes: taking the end point of the second end as the starting point of the second end propagation, forming a second end direction reference point group together with the second end propagation starting point and a predetermined number of confirmed key points adjacent to the second end propagation starting point along the direction of the suspension wire in the confirmed key point sequence; taking the vector from the confirmed key point with smaller projection coordinates to the confirmed key point with larger projection coordinates in the second end direction reference point group as the current direction field vector of the second end; constructing a fan-shaped search domain on one side towards the second end with the second end propagation starting point as the vertex, the line containing the current direction field vector of the second end as the central axis, a predetermined angle as the half angle, and a predetermined initial maximum radius as the maximum radius; and taking candidate key points in the candidate key point sequence that have not yet been included in the confirmed key point sequence, whose projection coordinates are greater than the projection coordinates of the second end propagation starting point, and are located within the image range defined by the fan-shaped search domain as key points to be verified.

7. The method according to claim 6, characterized in that... S2 also includes: performing consistency verification on each key point to be verified: projecting the key point to be verified vertically onto the central axis to obtain a projection point; using the distance between the key point to be verified and the projection point as the lateral deviation distance; using the Euclidean distance between the key point to be verified and the second end propagation starting point as the propagation spacing; using the ratio of the lateral deviation distance to the propagation spacing as the directional consistency error index of this key point to be verified; determining the key points to be verified that have passed the consistency verification as having a directional consistency error index less than a predetermined error threshold and a propagation spacing falling within a continuous spacing interval; when there are two or more key points that have passed the consistency verification within the sector search domain constructed in this instance, selecting the key point with the smallest directional consistency error index. The key points are used as the key points to be included in this time; when the number of key points that have passed the consistency verification in the sector search domain constructed in this time is 1, this key point that has passed the consistency verification is used as the key point to be included in this time; the key point to be included in this time is added to the confirmed key point sequence and updated as the second end propagation starting point, while the maximum radius of the sector search domain is restored to the predetermined initial maximum radius and the cumulative expansion number is cleared to zero; based on the updated second end propagation starting point, the second end direction reference point group is reconstructed, the current direction field vector of the second end is recalculated, the sector search domain is reconstructed, and the screening of key points to be verified, consistency verification, determination of key points to be included in this time and updating of the second end propagation starting point are repeatedly performed in the second end direction.

8. The method according to claim 7, characterized in that... S2 further includes: when the number of key points that pass the consistency verification within the constructed sector search domain is zero and the cumulative expansion count is less than the predetermined expansion count limit, the second-end propagation starting point and the current direction field vector of the second end remain unchanged, the maximum radius of the sector search domain is expanded by a predetermined radial step size by 1 to obtain an expanded sector search domain, and the cumulative expansion count is incremented by 1 to expand the sector search domain and re-execute the screening and consistency verification of the key points to be verified; when the cumulative expansion count reaches the predetermined expansion count limit and the number of key points that pass the consistency verification within the constructed sector search domain is still zero, the current second-end propagation starting point is taken as the second-end termination point, and the process ends. The propagation process towards the second end direction: taking the first end endpoint as the first end propagation starting point, constructing the first end direction reference point group according to the same selection method as the second end direction reference point group, taking the vector of the confirmed key point with larger projected coordinates pointing to the confirmed key point with smaller projected coordinates in the first end direction reference point group as the first end current direction field vector, and repeatedly executing towards the first end direction according to the same fan-shaped search domain construction method, key point screening method, consistency verification method, key point inclusion determination method, propagation starting point update method, search domain expansion method and termination condition as the propagation process towards the second end direction, until the first end endpoint is reached.

9. The method according to claim 1, characterized in that... In S3, the upper and lower connection points are determined and a virtual tensioning baseline is constructed. Specifically, within the area of ​​the dropper member, the connection positions between the dropper and the catenary clamp and between the dropper and the contact wire clamp are obtained through clamp detection. The point on the dropper fitting curve closest to the connection position between the dropper and the catenary clamp is taken as the upper connection point, and the point on the dropper fitting curve closest to the connection position between the dropper and the contact wire clamp is taken as the lower connection point. The upper and lower connection points are connected to form a straight line segment, which is used as the virtual tensioning baseline. Points on the dropper fitting curve are projected onto the virtual tensioning baseline. Multiple projection positions are selected at equal intervals according to the position of the projection points on the virtual tensioning baseline. Points on the dropper fitting curve corresponding to each projection position are taken as sampling points. A perpendicular line is drawn from each sampling point to the virtual tensioning baseline. The perpendicular distance from the sampling point to the virtual tensioning baseline is taken as the normal deviation distance of the sampling point. The normal deviation distances of all sampling points are arranged in the sampling order along the direction of the virtual tensioning baseline to form a deviation profile.

10. The method according to claim 9, characterized in that... S3 further includes: calculating the curvature point by point on the dropper fitting curve, and using the product of the maximum curvature and the length of the virtual tensioning baseline as the normalized curvature feature value; obtaining the minimum bounding rectangle of the dropper fitting curve, with the long side of the minimum bounding rectangle along the overall direction of the dropper fitting curve, and using the ratio of the length of the short side of the minimum bounding rectangle to the length of the virtual tensioning baseline as the minimum bounding rectangle width ratio feature value; using the ratio of the maximum normal deviation distance in the deviation profile to the length of the virtual tensioning baseline as the maximum deviation ratio feature value; pre-collecting a predetermined number of dropper samples in normal condition as normal dropper samples, and calculating the normalized curvature feature value and the minimum bounding rectangle width ratio feature value for the normal dropper samples respectively. The mean and standard deviation of each of the three eigenvalues ​​are obtained by comparing the maximum deviation ratio eigenvalue with the mean. For each eigenvalue, the sum of the products of its mean, standard deviation, and first multiple is used as its first-level threshold, and the sum of the products of its mean, standard deviation, and second multiple is used as its second-level threshold, where the second multiple is greater than the first multiple. When all three eigenvalues ​​are less than their respective first-level thresholds, the current slack level of the dropper is output as normal. When at least one of the three eigenvalues ​​reaches its respective first-level threshold and all three eigenvalues ​​are less than their respective second-level thresholds, the current slack level of the dropper is output as slightly slack. When at least one of the three eigenvalues ​​reaches its respective second-level threshold, the current slack level of the dropper is output as severely slack.

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