Intelligent extraction method for three-dimensional inspection power line in aerial image of unmanned aerial vehicle

Abstract

According to the unmanned aerial vehicle aerial photo three-dimensional inspection power line intelligent extraction method, firstly, a sampling area is drawn on an image through manual intervention, an LSD straight line segment detection algorithm is adopted as a basic algorithm for power line extraction, and according to the gradient symmetry characteristics of the power line, a straight line method is combined to extract the power line; establishing a method suitable for unmanned aerial vehicle inspection image power line extraction; then, based on the linear features of the aerial image power line, matching is conducted by adopting a method based on epipolar constraint, the intersection point of the power line and the epipolar constraint is used as a homonymy point, coordinates of sampling points are automatically calculated by adopting a method based on shape factor constraint, finally, fitting is conducted on the power line through the sampling points and a catenary equation, and a three-dimensional power line preliminary model is obtained; the line hanging point is extracted based on the two-dimensional constraint method and is incorporated into the catenary equation for re-fitting, a more complete three-dimensional power line is extracted, the system stability is good, the space inspection efficiency is high, the power line detection and extraction speed is high, and the accuracy rate is high.

Description

Technical Field

[0001] This application relates to a method for extracting power lines from a three-dimensional inspection by a drone, and in particular to a method for extracting power lines from a drone Figure 3 The invention discloses an intelligent extraction method for power lines during maintenance and inspection, and belongs to the technical field of power line extraction during UAV inspection. Background Art

[0002] Power corridors, particularly ultra-high voltage (UHV) transmission lines, which form the backbone of power grids, are crucial for ensuring the safe and stable operation of power grids. These corridors are characterized by high safety and reliability requirements, long transmission distances, and wide service coverage. However, the operating environment of transmission lines is becoming increasingly complex, posing a threat to traditional transmission safety. For example, the growth of diverse tree species and other vegetation in areas surrounding power corridors, as well as the construction of various types of roads, structures, and canals beneath and near the lines, all pose significant risks to the safe operation of high-voltage transmission lines. To promptly detect changes in the operating environment and accurately track the construction of new crossings and crossings near corridors, traditional two-dimensional line maps are insufficient. Power management departments urgently need three-dimensional power corridors that can visually depict the actual operating directions and spatial distances of transmission lines. This provides complete, readable, and measurable data on the transmission lines, enabling on-site corridor conditions to be displayed and managed using a 3D reality-based platform, assisting in the operation and maintenance of actual lines.

[0003] As a low-altitude remote sensing platform, drones have the characteristics of low cost, fast response, maneuverability, and strong timeliness in the field of surveying and mapping. They can also obtain high-resolution, high-quality aerial images. The use of drones to inspect transmission lines overcomes the shortcomings of traditional manual inspection methods, such as high labor costs, extreme danger, and high labor intensity. The application of drones in the three-dimensional visualization of power corridors can give full play to their advantages of low cost, high image acquisition accuracy, and maneuverability, which is conducive to the realization of real-time browsing and roaming of transmission lines, and also to the visualization application of transmission line detection; power lines can reach 2 to 3 pixels in width on drone images, and the extraction of three-dimensional power lines becomes a reality by combining digital image processing and oblique photogrammetry.

[0004] Due to the complex environment in which transmission lines are located, it is extremely challenging to completely extract power lines from these complex backgrounds. Manual extraction of 3D power lines from aerial images requires first manually identifying and drawing the power lines on the image. Then, through matching, the 3D coordinates of the power lines are calculated. This method requires digitizing each split conductor of each phase of the power line, which is labor-intensive and inefficient. Automatic extraction of 3D power lines from aerial images, however, requires multiple steps, a cumbersome process, and a long time due to the complex background and large amount of image data. Furthermore, if any step fails, the entire model fails and needs to be reprocessed, which is inefficient and difficult. Automatic interactive extraction of 3D power lines, on the other hand, eliminates the labor-intensive and cumbersome process of manual modeling and the complexity of fully automatic modeling. It combines the advantages of both manual and fully automatic modeling, reducing manual intervention while improving extraction efficiency. It offers excellent flexibility, and if any extraction step fails, it can be modified without having to start over. A 3D model of each phase of the power line is then obtained, laying the foundation for the subsequent establishment of 3D power corridors. This is of great significance for strengthening the effective management of power corridors and ensuring the safe and stable operation of transmission lines.

[0005] The existing technology for line extraction usually has poor detection effect when the short straight lines on the image are relatively dense. It is difficult to detect image edges with low pixel grayscale change contrast. It has weak noise resistance and is easily affected by noise. It is also sensitive to broken straight lines and difficult to set parameters. The false detection rate of straight lines is high and the real-time performance is poor. The calculation process is large in amount of computation, high in complexity, large in memory overhead, slow in speed, and may detect false straight lines, resulting in inaccurate extraction results.

[0006] Existing image-based power line extraction algorithms are generally effective for images with simple backgrounds. However, in drone inspection images, the high resolution of transmission lines captured by drones is high due to the close proximity of these images. The background is complex, with both natural features like vegetation and farmland, as well as artificial backgrounds like power towers, insulators, and buildings. Power lines in drone inspection images can be as wide as three to four pixels, making existing extraction algorithms inapplicable. Therefore, it is necessary to explore more effective and accurate power line extraction algorithms based on the inherent characteristics of power lines in drone inspection images.

[0007] The problems that need to be solved in the existing technology of UAV 3D inspection power line extraction and the key technical difficulties of this application include:

[0008] (1) Due to the complex environment in the area where the power transmission lines are located, it is extremely challenging to completely extract the power lines from these complex backgrounds. If the three-dimensional power lines are manually extracted using aerial images, each split conductor of each phase power line needs to be digitized, which is labor-intensive and inefficient. If the three-dimensional power lines are fully automatically extracted using aerial images, due to the complex background of drone aerial photography and the large amount of image data, direct processing requires many steps, a cumbersome process, and a long time. If any link goes wrong, the entire model will fail to be established and needs to be reprocessed, which is inefficient and difficult. The existing straight line extraction technology usually has poor detection effect when the short straight lines on the image are relatively dense. It is difficult to detect the image edge with low pixel grayscale change contrast, has weak anti-noise ability, is easily affected by noise, and is sensitive to broken straight lines. It is difficult to set parameters, has a high false detection rate of straight lines, poor real-time performance, large computational complexity, high memory overhead, slow speed, and may detect pseudo straight lines. The extraction results are not accurate enough. Existing image-based power line extraction algorithms are not suitable for drone-based aerial photography of power lines. However, due to the high resolution of the images captured by drones, the background is complex, including natural features such as vegetation and farmland, as well as artificial backgrounds such as power poles, insulators, and buildings. Power lines in drone inspection images can be as narrow as 3 to 4 pixels, making existing extraction algorithms inadequate. Therefore, it is necessary to explore more effective and accurate power line extraction algorithms based on the inherent characteristics of power lines in drone inspection images.

[0009] (2) The existing technology lacks a method for extracting three-dimensional power lines in an automatic interactive manner, lacks the method of drawing sampling areas on images through manual intervention, lacks the method of using LSD straight line segment detection algorithm as the basic algorithm for power line extraction, does not combine the straight line method based on the gradient symmetry characteristics of the power lines themselves, and does not establish a method suitable for extracting power lines from drone inspection images; lacks the straight line features of power lines based on aerial images, does not use the kernel line constraint method for matching, lacks the method of treating the intersection of power lines and kernel lines as points of the same name, lacks the method of using shape factor constraint method based on their distribution in space, cannot automatically calculate the coordinates of sampling points, lacks the method of fitting power lines using sampling points and catenary equations, cannot obtain a preliminary model of three-dimensional power lines, lacks the method of extracting hanging line points based on two-dimensional constraint methods and incorporating them into the catenary equation for re-fitting, cannot extract complete three-dimensional power lines, or the extracted power lines are of poor quality and slow speed, which does not meet application requirements.

[0010] (3) The existing nuclear line equation will produce certain errors during the calculation process. The intersection error decreases as the angle between the nuclear line and the power line increases. If the nuclear line and the power line are approximately parallel or the angle is very small, the intersection error is large and does not meet the accuracy requirements. In the aerial photos on the same side of the power line, the power line and the nuclear line are approximately parallel or the angle is very small. If such images are selected as the left and right images in the stereo pair for matching, the error will be amplified. When introducing the nuclear line constraint for matching, the correspondence between each split conductor on the left and right images must be determined. During the flight of the drone, the shooting angle will change, resulting in the arrangement order of the conductors in the aerial image being unstable, and the split conductors may overlap. For multiple split conductors, even through human eye recognition, it is impossible to simply determine the correct correspondence. Moreover, if the number of split conductors is too large, the matching efficiency will continue to decrease. Due to the change in the shooting angle during the flight of the drone, the hanging point is usually blocked by insulators or tower bodies, making it difficult to directly extract. When extracting three-dimensional power lines using an automatic interactive method, the strategy adopted is to draw sampling areas as close to both ends of the power line as possible during the manual intervention stage, and use the sampling points at both ends as hanging points for fitting. The three-dimensional power lines fitted in this way can also meet certain accuracy requirements. However, since the sampling points cannot be used as actual hanging points, the split conductors hanging on both sides of the same insulator cannot be connected together. Summary of the Invention

[0011] This application utilizes a multi-rotor drone platform, equipped with data acquisition equipment for power corridors, to acquire high-quality, high-resolution drone inspection images. After pre-processing the data through aerial triangulation, the exterior orientation elements of each image are obtained. Using this pre-processed drone inspection image data, combined with oblique photogrammetry and digital image processing techniques, an automated interactive extraction method is employed to extract three-dimensional power lines. This facilitates efficient subsequent power line diagnosis, troubleshooting, and other related inspections, achieving three-dimensional visualization of power corridors. First, a sampling area is manually drawn on the image. Then, combined with line feature extraction techniques from digital image processing, a program automatically identifies power lines in the aerial image, automatically determines the matching relationship between split conductors, calculates the spatial coordinates of the sampling points, and finally, uses the catenary equation for fitting to extract three-dimensional power lines. For suspension insulators, if power line models are obtained for both sides of the same power tower, a two-dimensional constraint-based method is used to extract the hanging points, which are then incorporated into the catenary equation for further fitting. This results in complete and accurate three-dimensional power lines, laying the foundation for the establishment of digital power corridors and ensuring the safe management of transmission lines.

[0012] drone aerial photography Figure 3The intelligent extraction method of power lines for maintenance and inspection first draws the sampling area on the image through manual intervention, adopts the LSD straight line segment detection algorithm as the basic algorithm for power line extraction, and based on the gradient symmetry characteristics of the power lines themselves, combines the straight line method to establish a method suitable for power line extraction in drone inspection images; then, based on the straight line characteristics of the power lines in the aerial images, a kernel line constraint method is used for matching, and the intersection of the power lines and the kernel lines is regarded as the same-name points. The power lines adopt a split conductor structure during the transmission process. According to their distribution in space, a shape factor constraint method is used to automatically calculate the coordinates of the sampling points. Finally, the sampling points and the catenary equation are used to fit the power lines to obtain a preliminary three-dimensional power line model. The hanging line points are extracted using a two-dimensional constraint method, and are incorporated into the catenary equation for re-fitting to extract a more complete three-dimensional power line;

[0013] 1) Power line extraction from drone inspection images: The LSD algorithm is used as the basic algorithm for power line extraction from drone inspection images. The algorithm combines the characteristics of drone inspection images to optimize the steps and parameters. Based on the gradient symmetry of power lines in images, the power line directions are calculated and used as a screening criterion to eliminate non-power features. The straight line method is used to fit broken lines and merge the upper and lower edges to extract complete power lines.

[0014] 2) Automatic matching of power lines in aerial images: This method uses a matching method based on kernel line constraints, and uses images taken on both sides of the power line as a stereo pair to improve the accuracy of intersection coordinates. In actual transmission line design, power lines use a split conductor structure, and multiple split conductor points on a vertical plane form a regular polygon. The shape factor, an effective parameter describing the shape, is used to select the optimal result from numerous matching combinations, based on the constraint that the shape factor of a regular polygon is the largest among all polygons.

[0015] 3) Automatic interactive extraction of 3D power lines: After obtaining the coordinates of the sampling points, the 3D coordinates of each point on the power line are calculated according to the catenary equation. Based on the 2D-constrained catenary point extraction algorithm, the 3D curve is projected onto the vertical projection plane. The calculation of the 3D curve intersection is transformed from space to a 2D plane. The obtained catenary points are used to refit the 3D power lines to make them more consistent with the actual situation, and finally the complete 3D power lines are extracted.

[0016] Preferably, for power line extraction from drone inspection images, the LSD algorithm is used as the basic algorithm for power line extraction from drone inspection images. The gradient symmetry characteristics of the split conductors in the image are combined as the conditions for screening power lines. The characteristics of the conductors themselves are considered, and the straight line method is used for fitting. The upper and lower edges are merged as the final extraction result.

[0017] The algorithm flow for extracting power lines from drone inspection images in this application is as follows:

[0018] Process 1: Use the LSD algorithm to detect line features in the image and calculate the direction of each line feature;

[0019] Process 2: Using the symmetry of the gradients on both sides of the power line and the direction of the power line as screening conditions, we can obtain candidate line segments:

[0020] Process 3: Based on the parallel characteristics of the split wires, straight line fitting is performed on the candidate segments, and particularly short segments are deleted;

[0021] Process 4: Merge the upper and lower edges and extract the power lines.

[0022] Preferably, power lines are detected by analyzing local features of the drone image, screening a set of candidate points that may be straight line pixels, verifying them using hypothetical parameters, merging the pixel point set and the error control point set, adaptively controlling the number of straight line segments that may be falsely detected, calculating and performing calculations on the gradient value and gradient direction of each pixel in the image, and determining straight line features in the image based on pixels with large gradient values, similar gradient directions, and adjacent relationships;

[0023] Power line detection steps:

[0024] (1) Image scaling: The original image is scaled using Gaussian downsampling with a scaling factor of 0.8, which means that the number of pixels in both the x and y directions becomes 80% of the original number. The total number of pixels in the downsampled image becomes 64% of the original number of pixels. The image is first filtered using a Gaussian kernel function to avoid quantization pseudo-edges, and then downsampled to reduce subsequent false detections and missed detections.

[0025] (2) Gradient calculation: Use the following Figure 2 The ×2 template is used to calculate the gradient of each pixel and obtain the image gradient. Based on the transition from black to white, the image gradient and the level-to-line angle determine the direction of the image edge. The difference between the image gradient from white to black and the level-to-line angle is 180°. The smallest template is selected to reduce the excessive dependence of pixels on each other in the process of calculating the image gradient. The line segments containing the starting and ending points are extracted, and the starting and ending points of the line segments from white to black and from black to white are exactly opposite. The gradient at (x+0.5, y+0.5) is obtained, and a half-pixel offset occurs. The offset is added to the rectangular coordinates in subsequent processing;

[0026] (3) Obtaining the line support region: Sort the gradients of the image and divide the image from 0 to the maximum gradient amplitude into 1024 bins at equal intervals. Then, distribute the image pixels into these bins according to their own gradient values. First, select the pixel with the largest gradient value as the seed point, and then select from the next bin until all bins are selected.

[0027] After pseudo-sorting the pixel gradients and determining the gradient threshold, a region growing algorithm is used to search for pixels marked as UNUSED within the eight neighborhoods of the seed point. Level-to-line pairs with approximately the same orientation are then merged to form a line segment support domain. If the angle of the line segment support domain and the angle of the next level-to-line pair are both smaller than the set angle tolerance t, the level-to-line pair is added to the line support domain and the angle of the region is updated. The initial angle is calculated from the level-to-line pair of the seed point. This is repeated until no new pixels are added.

[0028] (4) Detecting straight line segments: Find the minimum circumscribed rectangle and obtain a relatively regular straight line area. Use the rectangle as a candidate straight line and calculate the intra-class point density d of the approximate rectangle to determine whether it is greater than the critical value D. If the condition is not met, the rectangle needs to be truncated and d is recalculated until it is greater than D. k is the number of intra-class points in the rectangle, length(r) is the length of the rectangle, width(r) is the width of the rectangle, and D is set to 0.7. The rectangle truncation method includes lowering the angle tolerance critical value and reducing the area radius.

[0029] Evaluate the straight line according to the Helmholtz rule, calculate the NFA, and exclude false straight lines. Suppose there is an image with pixel values ​​representing the angle from level to line, and the angle values ​​independently satisfy the binomial distribution of [0, 2π]. Use the NFA to determine the probability that a rectangle in the detected image has fewer points than the corresponding rectangular box in the hypothetical image. The larger the NFA, the closer the rectangle is to the noise image. Conversely, the more likely it is a true line segment. Set p as the point density within the class and design the critical value e. If NFA < e, the rectangle is judged as a straight line. Otherwise, the rectangular area needs to be re-optimized and judged again.

[0030] Preferably, the power line detection factor is optimized:

[0031] 1) Through manual interaction, a sampling area containing power lines is drawn. The length and width of the sampling area do not exceed 400 pixels, so the image is not Gaussian downsampling according to the scaling of 80%;

[0032] 2) When using the region growing algorithm to obtain the line support region, the angle tolerance t between the level and the line region and the gradient threshold p are set. Given the low contrast between power lines and the background in drone inspection images, more pixels are included in the line support region. The angle tolerance is increased from 22.5° to 30°, which reduces the number of discarded pixels and reduces the missed detection rate.

[0033] 3) Lower the intra-class point density critical value D to avoid discarding more rectangles during the evaluation process, thereby increasing the length of the obtained straight line. In this application, D is set to 0.5.

[0034] Preferably, power line segment screening: after detecting straight line features in the drone inspection image, the correct power line segment is screened from numerous straight line features based on the power line's own features in the image, eliminating interference factors for the final power line extraction;

[0035] Power lines in drone inspection images include the following features;

[0036] a) The drone takes pictures at a short distance, and the aerial image resolution is high, so the width of the power lines in the image is 3 to 5 pixels;

[0037] b) Power lines appear as straight lines in aerial images, and the lines between the split conductors are parallel to each other;

[0038] c) The length of the power lines is long and extends to the border of the image;

[0039] d) Power lines are made of some metal materials, and their spectral properties are similar to those of other power equipment such as power towers;

[0040] Assume that the function z = f(x, y) has a continuous first-order partial derivative in the plane region D. Then the gradient of the function at a point is defined as follows: the gradient is a vector whose direction is the same as the direction of the maximum directional derivative at the point, and its modulus is the maximum value of the directional derivative.

[0041] The difference between adjacent pixels is used as the approximate value of the differential of the continuous signal, and the direction of the strongest grayscale value change at each pixel position is used as the direction of the image gradient. When the pixel is located at the edge of the image, the grayscale changes significantly and the corresponding gradient value is large; when the pixel is located at a position where the grayscale amplitude changes less in the surrounding area, the corresponding gradient value is small. The gradient directions of an image from black to white and from white to black are exactly opposite. Gradient symmetry is a characteristic of power lines in drone inspection images.

[0042] Calculate the line segments that satisfy the gradient symmetry, construct the accumulator H(θ, l), take the length of the line segment as the accumulated amount, and finally take the angle corresponding to the maximum value of l as θ as the direction of the power line. According to the obtained power line direction θ, set a critical value δ, and filter out straight line segments with an angle range of (θ-δ, θ+δ). In this way, many non-power lines are excluded, and the interference line segments are filtered out according to the gradient symmetry and the direction of the power lines to obtain alternative power line features.

[0043] Preferably, the power lines are fitted into straight lines: considering that the split wires appear approximately as straight lines and are continuous in the image, the broken straight lines are fitted, and finally the upper and lower edges after fitting are merged to obtain a complete extraction result;

[0044] 1) When performing straight line fitting, fit the upper and lower edges separately to improve the accuracy;

[0045] 2) During the fitting process, if the two broken lines are far apart, the fitting is abandoned; the distance between the line segments is calculated according to the formula To perform the calculation, assume that the midpoint coordinates of the two line segments are (x1, y1) and (x2, y2), the distance is d, and the critical value D is set to 5 pixels. Fitting is performed only when d < D.

[0046] 3) If the two broken lines have overlapping parts, the fitting is abandoned;

[0047] 4) Calculate the vertical distance between the two broken lines, and perform fitting only if it is less than 3 pixels;

[0048] 5) During the straight line fitting process, the correlation coefficient between the slope and the intercept is calculated. Only when the correlation coefficient is greater than 0.99 is the fitting considered successful. According to the above rules, the selected short straight line segments are connected by straight line fitting;

[0049] After fitting and connecting using the straight line method, short straight lines are deleted and the upper and lower edges of the power lines are retained. For drone inspection images, the width of the power lines is 3 to 5 pixels. The upper and lower edges are merged as the final extraction result and extended to the boundary of the image, making the extracted power lines more accurate and reducing errors.

[0050] Preferably, automatic matching of power lines in aerial images: after extracting power lines from two-dimensional images, automatic matching of power lines in aerial images is performed next. The essence of three-dimensional power line extraction is to obtain the three-dimensional coordinates of points on the power lines. After determining the points of the same name through matching, the spatial coordinates of the points can be calculated based on the collinearity equation by using the forward intersection. The line feature structure of the power lines themselves is used to match based on the kernel line constraint. The intersection of the power lines and the kernel lines is regarded as the points of the same name. Based on the arrangement order of the split conductors in space, each split conductor point is distributed on the vertex of the regular polygon. The matching scheme is determined by using the shape factor constraint method, and the three-dimensional coordinates of the points on the power lines can be obtained by forward intersection.

[0051] Preferably, matching based on shape factor constraints is used: For long-distance transmission lines, each phase power line adopts a split conductor structure. When introducing the core line constraint for matching, the correspondence between each split conductor on the left and right slices must be determined. If a vertical plane is used to cut the split conductors, the intersection between them is exactly at the vertex of the regular polygon.

[0052] A shape factor that describes the shape characteristics of polygons is introduced, and the matching scheme is determined by parameters. The shape factor is not affected by regional rotation, translation, and scale changes. When the number of sides is determined, the shape factor of a regular polygon is the largest, and when the number of sides of a polygon is determined, the value of its shape factor is also determined. The shape factor is used for constraint, and the shape factor of each combination is calculated. The combination corresponding to the maximum shape factor is taken as the best match. The same-name line segments of each split wire in the left slice on the right slice are determined, and the same-name points are determined by the kernel line constraint. Then, the three-dimensional coordinates of the sampling points on the power line are obtained according to the forward intersection in space.

[0053] Preferably, catenary equation fitting: the catenary equation derived and calculated based on the force analysis is an important formula for representing the power line model, which describes the law of how the power line elevation changes at different positions with the change of stress and specific load;

[0054] With A as the origin, establish a coordinate system. Through force analysis, calculate the coordinates of any point according to Equation 1 and Equation 2:

[0055]

[0056] Where: (x, y) is the coordinate of the electric line point on the vertical projection plane; σ0 is the stress, that is, the tension acting on the unit cross-sectional area, the unit is N / mm 2 ; r is the specific load, that is, the load per unit length and unit area of ​​the conductor, the unit is N / mm 2 m; l is the horizontal distance between the first and last endpoints, in meters; h is the vertical distance between the two endpoints, in meters.

[0057] Using the coordinates of points A and B and the spatial coordinates of several sampling points in the middle, the linear iteration method is used to solve the unknown parameters stress σ0 and specific load r, and the coordinates of any point on the power line catenary model are calculated. The unequal height overhead catenary equation is used for fitting to realize the extraction of three-dimensional power lines.

[0058] Preferably, the hanging point extraction based on two-dimensional constraints: a hanging point extraction algorithm based on two-dimensional constraints is used to solve the problem that the hanging points of the same-phase power lines on both sides of the tower body of the suspension insulator are the same;

[0059] By adding two-dimensional constraints, the initial three-dimensional power lines on both sides of the tower are projected onto a vertical projection plane. The two projection curves in this plane intersect, and the intersection point is used as the hanging point. Based on the relationship between the projection coordinate system and the spatial coordinate system, the two-dimensional coordinates of the intersection point on the vertical projection plane are converted into actual coordinates in space. Separate vertical plane coordinate systems are established based on the initial three-dimensional power lines on both sides of the power tower to reduce calculation errors. Two intersection points are calculated, and the average of these two intersection points is finally taken as the final hanging point.

[0060] Assume that the three-dimensional power lines on both sides of a suspension insulator have been obtained. Catenary model 1 and catenary model 2 are the initial three-dimensional power line models suspended on the same insulator and located on the front and rear sides of the power tower. Their projections on the XOY plane are approximately straight lines, namely projection line 1 and projection line 2. First, a vertical coordinate system is established with catenary model 1 as the reference: the direction of projection line 1 of catenary model 1 on the XOY plane is selected as the x-axis, the vertical direction is selected as the y-axis, and the foot o of the perpendicular point O of the original spatial coordinate system on projection line 1 is selected as the origin of the vertical coordinate system. After obtaining the vertical coordinate system, all points on catenary model 1 and catenary model 2 are projected into the coordinate system, and the new coordinates corresponding to each point are calculated. In the vertical coordinate system, find the intersection point between the corresponding projected curves of catenary model 1 and catenary model 2; in the new coordinate system, the type of the projected curve is unknown, and the curve equation cannot be directly found. The curve is regarded as countless straight lines connected end to end, and the curve is divided into several straight lines. The intersection point of the cutting straight lines on the two curves is directly calculated and used as the intersection point of the curve; according to the relationship between the vertical coordinate system and the spatial coordinate system, the two-dimensional coordinates of the intersection point in the vertical coordinate system are converted into actual three-dimensional spatial coordinates; then, with catenary model 2 as the reference, a new vertical coordinate system is established, and the new intersection point is calculated. Finally, the average of the two intersection points obtained with catenary model 1 and catenary model 2 as the reference is taken as the coordinate of the final hanging point;

[0061] Optimization of 2D constraint hanging line point extraction:

[0062] 1) When using the straight line method to fit the projection line of the power line on the XOY plane, the normal line equation is expressed as: ρ = x*cosα + y*sinα, where ρ represents the perpendicular distance from the origin to the straight line, and α represents the inclination angle of the perpendicular line. The normal line equation is used to simplify the calculation;

[0063] 2) Let the coordinates of the origin of the spatial coordinate system O on the projection line of the electric line in the XOY plane be (x0, y0). Then the new coordinates (x, y) of this point in the vertical coordinate system are calculated according to the following rules:

[0064]

[0065] The coordinates of a point on the power line are (X, Y, Z), and the polar coordinates on the XOY horizontal projection plane are (α, ρ).

[0066] Compared with the existing technology, the innovation and advantages of this application are:

[0067] (1) This application utilizes a multi-rotor drone platform and the power corridor data acquisition equipment it carries to obtain high-quality, high-resolution drone inspection images. After the data is pre-processed by aerial triangulation, the exterior orientation elements of each image are obtained. The above pre-processed drone inspection image data is combined with oblique photogrammetry technology and digital image processing technology to achieve the extraction of three-dimensional power lines using an automatic interactive extraction method, so that the power lines can be effectively diagnosed and troubleshooted in the future, and the three-dimensional visualization of the power corridor can be achieved. First, through manual intervention, the sampling area is drawn on the image. Then, combined with the line feature extraction technology in digital image processing, the program is used to automatically identify the power lines in the aerial image, and the matching relationship of the split conductors is automatically determined. The spatial coordinates of the sampling points are calculated, and finally the catenary equation is used for fitting to extract the three-dimensional power lines. In the case of suspended insulators, if the power line models on both sides of the same power tower are obtained, the hanging points are extracted using a two-dimensional constraint-based method, and are incorporated into the catenary equation for fitting again to extract complete and accurate three-dimensional power lines, thereby laying the foundation for the establishment of digital power corridors and providing guarantees for the safe management of transmission lines.

[0068] (2) In response to the shortcomings of manual and fully automatic extraction of power lines, this application proposes a method for extracting three-dimensional power lines using an automatic interactive method, that is, first, a sampling area is drawn on the image through manual intervention, then the program automatically calculates the coordinates of the sampling points, and finally, three-dimensional power line extraction is achieved based on catenary fitting. First, the power lines of the drone inspection image are extracted, and the gradient symmetry characteristics of the power lines themselves are combined to obtain candidate line segments; then, the straight line method is used for fitting, and the broken straight lines are connected into complete line segments; finally, the upper and lower edges of the power lines are merged as the final extraction results. Then, the matching relationship of the split conductors is automatically determined to obtain the three-dimensional coordinates of the sampling points. A matching method based on kernel line constraints is adopted, and the intersection of the power line and the kernel line is regarded as the matching point with the same name, and the images on both sides of the power line are selected as the left and right pieces for matching. In this way, the photographic baseline is almost perpendicular to the power line, and the intersection angle between the power line and the kernel line is large, thereby improving the calculation accuracy of the three-dimensional coordinates. Based on the characteristic that the split conductor forms a regular polygon on the vertical plane, with each split conductor point located exactly at a vertex, this application proposes determining the matching relationship based on shape factor constraints and obtaining the spatial coordinates of the split conductor points through forward intersection. Finally, the power line hanging point extraction is proposed. If the 3D power lines on both sides of the same power tower have been obtained, the hanging point is obtained based on 2D constraints and re-incorporated into the catenary equation to obtain a more complete 3D power line. The extracted power line is of high quality and fast, meeting the application requirements.

[0069] (3) The present application proposes a method for extracting three-dimensional power lines in an automatic interactive manner, namely, firstly, a sampling area is drawn on the image through manual intervention, and the LSD straight line segment detection algorithm is used as the basic algorithm for power line extraction. Based on the gradient symmetry characteristics of the power lines themselves, combined with the straight line method, a method suitable for extracting power lines from drone inspection images is established; then, based on the straight line characteristics of the power lines in the aerial images, a kernel line constraint method is used for matching, and the intersection of the power lines and the kernel lines is regarded as a point of the same name. The power lines adopt a split conductor structure during the transmission process. According to their distribution in space, a shape factor constraint method is used to automatically calculate the coordinates of the sampling points. Finally, the sampling points and the catenary equation are used to fit the power lines to obtain a preliminary three-dimensional power line model. The hanging line points are extracted using a two-dimensional constraint method, and are incorporated into the catenary equation for fitting again to extract more complete three-dimensional power lines. The system has good stability, high spatial inspection efficiency, fast power line detection and extraction speed, and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flowchart for the automatic interactive extraction of 3D power lines.

[0071] Figure 2 It is a schematic diagram of the intersection accuracy of the epipolar line and the power line.

[0072] Figure 3 This is a schematic diagram of a transmission line that uses a split conductor structure for each phase of power line for long-distance transmission.

[0073] Figure 4 This is a schematic diagram of the split wire in the image.

[0074] Figure 5 It is a schematic diagram of the catenary model of this application.

[0075] Figure 6 This is a schematic diagram of plane constraint hanging line point extraction.

[0076] Figure 7 This is a schematic diagram of the sampling area drawn during the experiment.

[0077] Figure 8 It is a schematic diagram of experimental acquisition and calculation of sampling point coordinates.

[0078] Figure 9 This is a schematic diagram of the catenary model of power lines generated in CloudCompare.

[0079] Figure 10 This is a schematic diagram of the result of projecting the fitted power lines onto the image.

[0080] Figure 11 This is a schematic diagram of the power line translation in the experiment.

[0081] Figure 12 This is a schematic diagram of the extraction results after the power lines are shifted in the experiment. DETAILED DESCRIPTION

[0082] Below is a diagram of the drone aerial photography provided by this application. Figure 3 The technical solution of the intelligent extraction method for maintenance and inspection power lines is further described so that those skilled in the art can better understand the present application and implement it.

[0083] Drone inspections of power lines overcome the drawbacks of traditional manual inspections, such as high cost, high risk, and high labor intensity. Reconstructing 3D models of power lines based on drone inspection images is a key focus of building digital power corridors. Existing methods for extracting power lines from images are extremely challenging due to the complex environments and numerous interference factors in the areas where transmission lines are located. Consequently, research on image-based 3D power line model reconstruction is limited. In view of the characteristics of UAV inspection images such as high resolution, complex background, large data volume, and difficulty in power line extraction, this application proposes a method for extracting three-dimensional power lines in an automatic interactive manner, namely, firstly, a sampling area is drawn on the image through manual intervention, and the LSD straight line segment detection algorithm is used as the basic algorithm for power line extraction. Based on the gradient symmetry characteristics of the power lines themselves, combined with the straight line method, a method suitable for power line extraction from UAV inspection images is established; then, based on the straight line characteristics of the power lines in the aerial images, a kernel line constraint method is used for matching, and the intersection of the power lines and the kernel lines is regarded as the same-name points. The power lines adopt a split conductor structure in the transmission process, and according to their distribution in space, a shape factor constraint method is used to automatically calculate the coordinates of the sampling points. Finally, the sampling points and the catenary equation are used to fit the power lines to obtain a preliminary three-dimensional power line model, and the hanging line points are extracted based on the two-dimensional constraint method, and are incorporated into the catenary equation for fitting again to extract more complete three-dimensional power lines; the automatic interactive extraction process of three-dimensional power lines is as follows Figure 1 .

[0084] 1. Power line extraction from drone inspection images: The LSD algorithm is used as the basic algorithm for power line extraction from drone inspection images. Combined with the characteristics of drone inspection images, the steps and parameters are optimized. Based on the gradient symmetry of power lines in the image, the direction of the power lines is calculated and used as a screening condition to eliminate non-power features. The broken straight lines are fitted and connected using the straight line method, and the upper and lower edges are merged to extract complete power lines. Experimental results show that the method proposed in this application can extract power lines under different backgrounds in drone inspection images.

[0085] 2. Automatic matching of power lines in aerial images: This method uses a matching method based on kernel line constraints, and uses images taken on both sides of the power line as a stereo pair to improve the accuracy of intersection coordinates. In actual transmission line design, power lines use a split conductor structure, which makes it difficult to match multiple split conductors. Considering that the points of multiple split conductors form a regular polygon on a vertical plane, the shape factor, an effective parameter describing the shape, is combined with the constraint that the shape factor of the regular polygon is the largest among all polygons. This parameter is used to select the optimal result from multiple matching combinations.

[0086] 3. Automatic interactive extraction of 3D power lines: After obtaining the coordinates of the sampling points, the 3D coordinates of each point on the power line are calculated according to the catenary equation. Based on the 2D-constrained catenary point extraction algorithm, the 3D curve is projected onto the vertical projection plane. The calculation of the 3D curve intersection is converted from space to a 2D plane. The obtained catenary points are used to refit the 3D power lines to make them more consistent with the actual situation, and finally the complete 3D power lines are extracted.

[0087] 1. Power Line Extraction from UAV Inspection Images

[0088] Due to uncertain weather conditions, complex terrain, the inherent instability of drone platforms, and the limitations of cameras, aerial images are susceptible to interference, resulting in inconsistent image quality and uncertainty. The high-resolution features of drone inspection images also facilitate accurate power line location extraction during 3D power line extraction.

[0089] In the power industry, high-voltage power lines may consist of one or more loops, each of which is composed of three-phase power lines A, B, and C. To minimize power loss during transmission, and taking into account the characteristics of high-voltage transmission lines, the power lines adopt a split conductor structure, with a large number of power lines between each span. To minimize the impact on human safety during transmission, power companies generally install transmission lines in areas far from human settlements, such as forests, mountains, and fields. As a result, the background in drone inspection images is very complex. Factors that affect power line extraction include vegetation, power towers, insulators, roads, ditches, and bare land. In drone inspection images, power lines have the following characteristics:

[0090] (1) The split wires are approximately straight lines in the aerial image. The width of each wire can reach 2 to 3 pixels. The split wires of the same phase do not intersect and are parallel to each other. There are many split wires in the entire image.

[0091] (2) The aerial photography background is complex and has a great noise impact. The presence of vegetation, roads, and towers increases the difficulty of extracting power lines.

[0092] The LSD algorithm is used as the basic algorithm for power line extraction from UAV inspection images. The gradient symmetry characteristics of the split conductors in the image are combined as the condition for screening power lines. Considering the characteristics of the conductors themselves, the straight line method is used for fitting, and the upper and lower edges are merged as the final extraction result.

[0093] The algorithm flow for extracting power lines from drone inspection images in this application is as follows:

[0094] Process 1: Use the LSD algorithm to detect line features in the image and calculate the direction of each line feature;

[0095] Process 2: Using the symmetry of the gradients on both sides of the power line and the direction of the power line as screening conditions, we can obtain candidate line segments:

[0096] Process 3: Based on the parallel characteristics of the split wires, straight line fitting is performed on the candidate segments, and particularly short segments are deleted;

[0097] Process 4: Merge the upper and lower edges and extract the power lines.

[0098] (1) Detection of power lines

[0099] By analyzing the local features of drone images, a set of candidate points that may be straight line pixels is screened out, verified using hypothetical parameters, and the pixel point set and error control point set are merged. The number of straight line segments that may be falsely detected is adaptively controlled. The gradient value and gradient direction of each pixel in the image are calculated and calculated. The straight line features in the image are determined based on the pixels with large gradient values, similar gradient directions and adjacent relationships.

[0100] 1. Power line detection steps

[0101] (1) Image scaling: The original image is scaled using Gaussian downsampling with a scaling factor of 0.8, which means that the number of pixels in both the x and y directions becomes 80% of the original number. The total number of pixels in the downsampled image becomes 64% of the original number of pixels. The image is first filtered using a Gaussian kernel function to avoid quantization pseudo-edges, and then downsampled to reduce subsequent false detections and missed detections.

[0102] (2) Gradient calculation: Use the following Figure 2 The ×2 template is used to calculate the gradient of each pixel and obtain the image gradient. Based on the transition from black to white, the image gradient and the level-to-line angle determine the direction of the image edge. The difference between the image gradient from white to black and the level-to-line angle is 180°. The smallest template is selected to reduce the excessive dependence of pixels on each other in the process of calculating the image gradient. The line segments containing the starting and ending points are extracted, and the starting and ending points of the line segments from white to black and from black to white are exactly opposite. The gradient at (x+0.5, y+0.5) is obtained, and a half-pixel offset occurs. The offset is added to the rectangular coordinates in subsequent processing;

[0103] (3) Obtaining the line support region: Sort the gradients of the image and divide the image from 0 to the maximum gradient amplitude into 1024 bins at equal intervals. Then, distribute the image pixels into these bins according to their own gradient values. First, select the pixel with the largest gradient value as the seed point, and then select from the next bin until all bins are selected.

[0104] After pseudo-sorting the pixel gradients and determining the gradient threshold, a region growing algorithm is used to search for pixels marked as UNUSED within the eight neighborhoods of the seed point. Level-to-line pairs with approximately the same orientation are then merged to form a line segment support domain. If the angle of the line segment support domain and the angle of the next level-to-line pair are both smaller than the set angle tolerance t, the level-to-line pair is added to the line support domain and the angle of the region is updated. The initial angle is calculated from the level-to-line pair of the seed point. This is repeated until no new pixels are added.

[0105] (4) Detecting straight line segments: Find the minimum circumscribed rectangle and obtain a relatively regular straight line area. Use the rectangle as a candidate straight line and calculate the intra-class point density d of the approximate rectangle to determine whether it is greater than the critical value D. If the condition is not met, the rectangle needs to be truncated and d is recalculated until it is greater than D. k is the number of intra-class points in the rectangle, length(r) is the length of the rectangle, width(r) is the width of the rectangle, and D is set to 0.7. The rectangle truncation method includes lowering the angle tolerance critical value and reducing the area radius.

[0106] Evaluate the straight line according to the Helmholtz rule, calculate the NFA, and exclude false straight lines. Suppose there is an image with pixel values ​​representing the angle from level to line, and the angle values ​​independently satisfy the binomial distribution of [0, 2π]. Use the NFA to determine the probability that a rectangle in the detected image has fewer points than the corresponding rectangle in the hypothetical image. The larger the NFA, the closer the rectangle is to the noise image. Conversely, the more likely it is a true line segment. Set p as the point density within the class and design the critical value e. If NFA < e, the rectangle is judged as a straight line. Otherwise, the rectangular area needs to be re-optimized and judged again.

[0107] The further optimization method is divided into the following steps:

[0108] Step 1: p = p / 2;

[0109] Step 2: Reduce the short side of the rectangle by one row;

[0110] Step 3: Reduce the long side of the rectangle by one line;

[0111] Step 4: Reduce the long side of the rectangle by another line;

[0112] Step 5: Recursively repeat steps 1 to 4 until the rectangle that meets the critical value e is too small and is rejected, or recurs 5 times and p becomes 1 / 32 of the original value.

[0113] 2. Power line detection factor optimization

[0114] 1) In the actual 3D power line automatic interactive extraction process, the entire image does not need to be processed. Instead, a sampling area containing the power lines needs to be drawn through manual interaction. The length and width of the sampling area do not exceed 400 pixels, so Gaussian downsampling is not performed on the image at a zoom scale of 80%;

[0115] 2) When using the region growing algorithm to obtain the line support region, the angle tolerance t between the level and the line region and the gradient threshold p are set. Given the low contrast between power lines and the background in drone inspection images, more pixels are included in the line support region. The angle tolerance is increased from 22.5° to 30°, which reduces the number of discarded pixels and reduces the missed detection rate.

[0116] 3) If the intra-class point density is set too high, the approximate rectangle in the image will be easily truncated, and there will be more broken short straight lines in the final detection result. Therefore, the intra-class point density critical value D is lowered to avoid discarding more rectangles in the evaluation process, thereby obtaining a longer straight line length. In this application, D is set to 0.5.

[0117] (2) Extracting power lines

[0118] 1. Power line segment screening

[0119] In the drone inspection image, after detecting the straight line features, the correct power line segments are screened out from the numerous straight line features based on the power line’s own characteristics in the image, eliminating interference factors for the final power line extraction.

[0120] Power lines in drone inspection images have the following characteristics;

[0121] a) The drone takes pictures at a short distance, and the aerial image resolution is high, so the width of the power lines in the image is 3 to 5 pixels;

[0122] b) Power lines appear as straight lines in aerial images, and the lines between the split conductors are parallel to each other;

[0123] c) The length of the power lines is long and extends to the border of the image;

[0124] d) Power lines are made of some metal materials, and their spectral properties are similar to those of other power equipment such as power towers;

[0125] Assume that the function z = f(x, y) has a continuous first-order partial derivative in the plane region D. Then the gradient of the function at a point is defined as follows: the gradient is a vector whose direction is the same as the direction of the maximum directional derivative at the point, and its modulus is the maximum value of the directional derivative.

[0126] The difference between adjacent pixels is taken as the approximate value of the continuous signal differential, and the direction of the strongest grayscale value change at each pixel position is taken as the direction of the image gradient. When the pixel is located at the edge of the image, the grayscale changes significantly and the corresponding gradient value is large; when the pixel is located at a position where the grayscale amplitude changes less in the surrounding area, the corresponding gradient value is small. The gradient directions of an image from black to white and from white to black are exactly opposite. Gradient symmetry is a characteristic of power lines in drone inspection images.

[0127] Calculate the line segments that satisfy the gradient symmetry, construct the accumulator H(θ, l), take the length of the line segment as the accumulated amount, and finally take the angle corresponding to the maximum value of l as θ as the direction of the power line. According to the obtained power line direction θ, set a critical value δ, and filter out straight line segments with an angle range of (θ-δ, θ+δ). In this way, many non-power lines are excluded, and the interference line segments are filtered out according to the gradient symmetry and the direction of the power lines to obtain alternative power line features.

[0128] 2. Power line fitting straight line

[0129] The extracted power line segments are divided into upper and lower edges. Due to occlusion or image quality, the complete power line may be broken into several parts. Considering that the split wires appear approximately as straight lines and are continuous in the image, the broken straight lines are fitted and the upper and lower edges are finally merged to obtain the complete extraction result.

[0130] 1) When performing straight line fitting, fit the upper and lower edges separately to improve the accuracy;

[0131] 2) During the fitting process, if the two broken lines are far apart, the fitting is abandoned; the distance between the line segments is calculated according to the formula To perform the calculation, assume that the midpoint coordinates of the two line segments are (x1, y1) and (x2, y2), the distance is d, and the critical value D is set to 5 pixels. Fitting is performed only when d < D.

[0132] 3) If the two broken lines have overlapping parts, the fitting is abandoned;

[0133] 4) Calculate the vertical distance between the two broken lines, and perform fitting only if it is less than 3 pixels;

[0134] 5) During the straight line fitting process, the correlation coefficient between the slope and intercept is calculated. The fit is considered successful only if the correlation coefficient is greater than 0.99. According to the above rules, the selected short straight line segments are connected by straight line fitting.

[0135] After fitting and connecting using the straight line method, short straight lines are deleted, and the upper and lower edges of the power lines are retained. For drone inspection images, the width of the power lines is 3 to 5 pixels. If only the upper or lower edge is retained as the final extraction result, a small amount of offset will be generated. The upper and lower edges are merged as the final extraction result and extended to the boundary of the image, making the extracted power lines more accurate and reducing errors.

[0136] 2. Automatic Matching of Power Lines in Aerial Images

[0137] After extracting power lines from a two-dimensional image, the next step is to automatically match the power lines in the aerial image. The essence of three-dimensional power line extraction is to obtain the three-dimensional coordinates of points on the power lines. After determining the same-name points through matching, the spatial coordinates of the points can be calculated using forward intersection based on the collinearity equation. This application utilizes the line feature structure of the power lines themselves and matches based on the kernel line constraint. The intersection of the power lines and the kernel line is regarded as the same-name points. Based on the arrangement order of the split conductors in space, each split conductor point is distributed at the vertex of a regular polygon. A method based on shape factor constraints is used to determine the matching scheme, and then the three-dimensional coordinates of the points on the power lines can be obtained through forward intersection.

[0138] (1) Automatic matching of power lines

[0139] 1. Core line constraint drives power line matching

[0140] In the process of matching power lines, the core line constraint is introduced, and the intersection of the power line and the core line is regarded as the matching point with the same name, such as Figure 2 shown.

[0141] The kernel equation will produce a certain error in the calculation process. Assuming that its plane error is m x , then the intersection error m p It is m p =m x / sinθ, θ is the angle between the epipolar line and the power line. The intersection error decreases as the angle between the epipolar line and the power line increases. If the epipolar line and the power line are approximately parallel or the angle is very small, the intersection error is large and does not meet the accuracy requirements. During drone aerial photography, in the aerial photos taken on the same side of the power line, the power line and the epipolar line are approximately parallel or the angle is very small. If such images are selected as the left and right images in a stereo pair for matching, the error will be amplified; in the aerial photos taken on both sides of the power line, the power line and the epipolar line are approximately perpendicular or the angle is very large. Selecting such photos as a stereo pair will greatly reduce the matching error. Therefore, when matching power lines, this application selects photos taken on both sides of the power line as the matching stereo pair.

[0142] 2. Matching scheme based on shape factor constraints

[0143] Transmission lines for long distance transmission use split conductor structure for each phase of power line (such as Figure 3 In the figure, (1), (2), and (3) correspond to the cases of four-split wires, six-split wires, and eight-split wires, respectively. Therefore, when introducing the kernel constraint for matching, the corresponding relationship between each split wire on the left and right slices must be determined. During the flight of the drone, the shooting angle will change, resulting in an unfixed arrangement order of the wires on the aerial image, and the split wires may overlap. Figure 4 , the arrangement order of the split conductors shown in 1 and 2 is different, and the four split conductors in 3 overlap into two.

[0144] Even with the human eye, it's difficult to easily determine the correct correspondence for multiple split conductors. Furthermore, if there are too many split conductors, the time required to manually determine the corresponding line segments for each split conductor on the left and right slices increases exponentially, reducing matching efficiency. Careful observation reveals that if a perpendicular plane is used to intersect the split conductors, their intersection points lie exactly at the vertices of a regular polygon.

[0145] Therefore, this application introduces a shape factor that describes the shape characteristics of a polygon, and uses parameters to determine the matching scheme. The shape factor is not affected by regional rotation, translation, and scale changes. When the number of sides is determined, the shape factor of a regular polygon is the largest, and when the number of sides of a polygon is determined, the value of its shape factor is also determined. Therefore, the shape factor is used for constraint, and the shape factor of each combination is calculated. The combination corresponding to the maximum value of the shape factor is taken as the best match, and the same-name line segments of each split wire in the left piece on the right piece are determined. The same-name points are determined through the kernel line constraint, and the three-dimensional coordinates of the sampling points on the power line are obtained based on the forward intersection in space.

[0146] 3. Automatic interactive extraction of 3D power lines

[0147] Transmission lines are supported by power towers. Due to the influence of gravity, power lines suspended on different insulators at both ends exhibit a catenary-like geometric shape. Through force analysis, a three-dimensional power line can be represented using the catenary equation. By sampling the power line at regular intervals, calculating the coordinates of the sampling points, and fitting the catenary equation to obtain the coordinates of other points on the power line, a complete three-dimensional power line model can be generated.

[0148] Therefore, an automatic interactive extraction method is adopted. First, through manual intervention, a rectangular frame is drawn on the image at intervals along the direction of the power line as a sampling area. Then, the power lines within the range are automatically extracted and matched, and the coordinates of the sampling points in the sampling area are calculated. After obtaining the coordinates of the sampling points in different sampling areas, the catenary equation is used for fitting to obtain complete three-dimensional power lines, narrow the power line extraction range, select areas with obvious contrast and low extraction difficulty, and improve the extraction speed and accuracy. Compared with manual extraction and fully automatic extraction methods, it can not only reduce manual operations and workload, but also use automatic calculation to improve efficiency and have higher flexibility. Among them, the key to affecting the accuracy of the three-dimensional power line model is the determination of the hanging point. Therefore, for the case of suspension insulators, this application uses the preliminary three-dimensional model of the power lines on both sides of the power tower, adopts a hanging point extraction algorithm based on two-dimensional constraints, calculates the coordinates of the hanging points, and re-corrects the three-dimensional model of the power lines to make the calculated model more accurate, thereby extracting the complete three-dimensional power lines.

[0149] (1) Catenary equation fitting

[0150] In high-voltage transmission lines, due to the long distance between adjacent power towers and the influence of the conductor's own gravity, the power line between the two suspension points presents a catenary shape in the air. Based on this, the catenary equation derived and calculated based on force analysis is an important formula for representing the power line model. It describes the law of change of power line elevation at different positions with changes in stress and specific load.

[0151] Figure 5 This is a schematic diagram of the catenary model. With A as the origin, a coordinate system is established. Through force analysis, the coordinates of any point are calculated according to Equations 1 and 2:

[0152]

[0153] Where: (x, y) is the coordinate of the electric line point on the vertical projection plane; σ0 is the stress, that is, the tension acting on the unit cross-sectional area, the unit is N / mm 2 ; r is the specific load, that is, the load per unit length and unit area of ​​the conductor, the unit is N / mm 2 m; l is the horizontal distance between the first and last endpoints, in meters; h is the vertical distance between the two endpoints, in meters.

[0154] Using the coordinates of points A and B and the spatial coordinates of several sampling points in the middle, the linear iteration method is used to solve the unknown parameters stress σ0 and specific load r, and the coordinates of any point on the power line catenary model are calculated. The unequal height overhead catenary equation is used for fitting to realize the extraction of three-dimensional power lines.

[0155] (2) Extraction of hanging line points based on two-dimensional constraints

[0156] During power transmission, power lines are installed via power poles and towers. Key to this installation lies in the insulators fixed to the tower arms. Depending on the installation method, insulators are categorized as suspension insulators or tension insulators. If suspension insulators are suspended vertically or in a V-shape, the power lines on either side of the tower hang from the same insulators, with the same-phase power lines hanging from the same points. If tension insulators are suspended horizontally, parallel to the ground, to bear the conductor tension, the insulators on either side of the tower hang from two different sets of insulators, with the same-phase power lines hanging from different points.

[0157] This application adopts a two-dimensional constrained hanging point extraction algorithm to solve the problem that the hanging points of the same-phase power lines on both sides of the tower body of the suspension insulator are the same.

[0158] When fitting power lines using the catenary equation, the hanging points at both ends are crucial. Due to changes in the shooting angle when the drone is flying, the hanging points are usually blocked by insulators or tower bodies, making them difficult to extract directly. When extracting three-dimensional power lines using an automatic interactive method, the strategy adopted is to draw sampling areas as much as possible to both ends of the power lines during the manual intervention stage, and to fit the sampling points at both ends as hanging points. The three-dimensional power lines fitted in this way can also meet certain accuracy requirements, but because the sampling points cannot be used as real hanging points, the split conductors hanging on both sides of the same insulator cannot be connected together. Gaps appeared in the power lines that should have been connected together. In order to make the extracted three-dimensional power lines more consistent with the actual situation, for suspended insulators (the situation where the power lines on both sides of the power tower body are hung on the same insulator), this application uses a two-dimensional constraint-based hanging point extraction algorithm to calculate the hanging points, and incorporates the extracted hanging points into the catenary equation for re-fitting to obtain a more complete three-dimensional power line.

[0159] In a plane, two non-collinear straight lines must have an intersection, but in space, this conclusion does not hold true. If the extracted three-dimensional power lines on both sides of the suspension insulator are extended directly to both ends, due to the influence of errors and the limited accuracy of automatic interactive modeling, the two catenaries after extension may not intersect (assuming that each split conductor is extended forward, there is no guarantee that there must be an intersection between them). Based on the principle that two non-collinear straight lines in a plane must intersect, this application projects the initial three-dimensional power lines on both sides of the tower body onto a vertical projection plane by adding two-dimensional constraints. The two projection curves in the plane intersect, and the intersection is used as the hanging point. According to the relationship between the projection coordinate system and the space coordinate system, the two-dimensional coordinates of the intersection on the vertical projection plane are converted into actual coordinates in space. The initial three-dimensional power lines on both sides of the power tower are used as references to establish their respective vertical coordinate systems, reduce calculation errors, calculate two intersections, and finally take the average of the two intersections as the final hanging point.

[0160] Assume that the three-dimensional electric lines on both sides of a suspension insulator have been obtained, such as Figure 6 As shown, catenary model 1 and catenary model 2 are initial three-dimensional power line models suspended on the same insulator and located on the front and rear sides of the power tower. Their projections on the XOY plane are approximately straight lines, namely projection line 1 and projection line 2. First, a vertical coordinate system is established based on catenary model 1: the direction of projection line 1 of catenary model 1 on the XOY plane is selected as the x-axis, the vertical direction is the y-axis, and the foot o of the origin O of the original space coordinate system on the projection line 1 is used as the origin of the vertical coordinate system. After obtaining the vertical coordinate system, all points on catenary model 1 and catenary model 2 are projected into the coordinate system to obtain the new coordinates corresponding to each point. In the vertical coordinate system, the new coordinates corresponding to each point are obtained. The intersection of the corresponding projection curves of catenary model 1 and catenary model 2; in the new coordinate system, the type of the projection curve is unknown, and the curve equation cannot be directly calculated. The curve is regarded as countless straight lines connected end to end, and the curve is divided into several straight lines. The intersection of the cutting straight lines on the two curves is directly calculated and used as the intersection of the curves; according to the relationship between the vertical coordinate system and the spatial coordinate system, the two-dimensional coordinates of the intersection in the vertical coordinate system are converted into actual three-dimensional spatial coordinates; then, with catenary model 2 as the benchmark, a new vertical coordinate system is established, and the new intersection is calculated. Finally, the average of the two intersection points obtained based on catenary model 1 and catenary model 2 is taken as the coordinate of the final hanging point.

[0161] Optimization of 2D constraint hanging line point extraction:

[0162] 1) When using the straight line method to fit the projection line of the power line on the XOY plane, the normal line equation is expressed as: ρ = *cosa + y*sina, where ρ represents the perpendicular distance from the origin to the straight line, and α represents the inclination angle of the perpendicular line. The normal line equation is used to simplify the calculation;

[0163] 2) Let the coordinates of the origin of the spatial coordinate system O on the projection line of the electric line in the XOY plane be (x0, y0). Then the new coordinates (x, y) of this point in the vertical coordinate system are calculated according to the following rules:

[0164]

[0165] The coordinates of a point on the power line are (X, Y, Z), and the polar coordinates on the XOY horizontal projection plane are (α, ρ).

[0166] 4. 3D Power Line Automatic Interactive Extraction Experiment

[0167] The data used in this experiment is drone inspection images of a 500 kV transmission line in a certain area. The data has been pre-processed using aerial triangulation. The power lines in this line are divided into three phases, each containing four split conductors. The experiment was implemented using PowerTower software and C++ programming. The following are the specific steps for the automatic interactive extraction experiment:

[0168] (1) Draw sampling areas: Use PowerTower software to draw four sampling areas between each span, such as Figure 7 This is a schematic diagram of the sampling areas. The first and fourth sampling areas are located near the towers at both ends of the line, and the second and third are located in the center of the line. The four sampling areas are evenly distributed to improve the accuracy of subsequent catenary fitting.

[0169] (2) Obtaining sampling point coordinates: The algorithm is implemented in the PowerTower software using C++ programming. First, the power lines within each sampling area are extracted. Then, the matching scheme is automatically determined based on the shape factor using the kernel line constraint method. The sampling point coordinates are obtained by forward intersection. Figure 8 As shown, six images are displayed in the PowerTower software. The frame represents a sample area, and the points are the projections of the sample points obtained by the automatically determined matching scheme. In each image, the projected straight lines of the extraction results coincide with the power lines on the image, demonstrating that the matching method proposed in this application is correct and can meet the accuracy requirements. The coordinates of three points on each split conductor are evenly selected as the sampling points of the sampling area.

[0170] (3) Initial fitting of the catenary equation: The coordinates of the sampling points in the four sampling areas are used as the initial values ​​of the catenary equation to calculate the coordinates of the points on the power line between the two towers. Figure 9 This is the result of the power line display in CloudCompare. From the figure, we can see that the four split conductors are parallel to each other and all present a catenary shape. Figure 10 It is the result of projecting the fitted power lines onto the image. From the figure, it can be seen that the projection of the three-dimensional power lines obtained after fitting onto the image approximately coincides with the actual power lines in the image, indicating that the fitting accuracy is high.

[0171] (4) Obtain the hanging line points and refit: Select the three-dimensional power lines on the front and back sides of a power tower to extract the power lines that should be connected together in space, and there will be a gap;

[0172] Using a two-dimensional constraint method, this approach was implemented through programming: Based on the preliminary 3D power line model for the front and rear sides of the power tower, the hanging points were calculated and incorporated into the catenary equation for a refit. The refit results displayed in CloudCompare can be magnified to show that the bolded points are the hanging points, indicating that the power lines on both sides of the power tower are connected, consistent with the actual situation. When the refitted 3D power lines are projected onto the image, the hanging points are located exactly at the junction of the insulator and the power lines. The projected power lines coincide with the power lines in the image, demonstrating that the calculated 3D hanging points are correctly located and that the power lines fitted using the catenary equation are highly accurate.

[0173] (5) Power line translation: Figure 11 , using the obtained B-phase power line to translate to both sides, automatically obtain the sampling area, calculate the sampling point coordinates, which can reduce human intervention, automatically execute the above process, and obtain the three-dimensional power lines of phases A and C ( Figure 12 Each phase of the power lines on both sides of the power tower are connected together, the hanging points are positioned correctly, the extracted 3D power lines are consistent with the actual situation, and the projected straight lines on the image coincide with the actual power lines. The complete 3D power lines were obtained using automatic interactive extraction.

Claims

1. An intelligent method for extracting power lines from three-dimensional inspection images taken by drones, characterized by: First, a sampling area is drawn on the image through manual intervention. The LSD line segment detection algorithm is used as the basic algorithm for power line extraction. Based on the gradient symmetry characteristics of the power lines themselves, combined with the straight line method, a method suitable for power line extraction from UAV inspection images is established. Then, based on the straight line features of the power lines in the aerial images, a method based on core line constraints is used for matching. The intersection of the power lines and core lines is regarded as a point of the same name. The power lines adopt a split conductor structure during the transmission process. According to their distribution in space, a method based on shape factor constraints is used to automatically calculate the coordinates of the sampling points. Finally, the sampling points and the catenary equation are used to fit the power lines to obtain a preliminary three-dimensional power line model. The hanging line points are extracted using a two-dimensional constraint method and incorporated into the catenary equation for further fitting to extract a more complete three-dimensional power line. 1) Power line extraction from drone inspection images: The LSD algorithm is used as the basic algorithm for power line extraction from drone inspection images. The algorithm combines the characteristics of drone inspection images to optimize the steps and parameters. Based on the gradient symmetry of power lines in images, the power line directions are calculated and used as a screening criterion to eliminate non-power features. The straight line method is used to fit broken lines and merge the upper and lower edges to extract complete power lines. 2) Automatic matching of power lines in aerial images: This method uses a matching method based on kernel line constraints, and uses images taken on both sides of the power line as a stereo pair to improve the accuracy of intersection coordinates. In actual transmission line design, power lines use a split conductor structure, and multiple split conductor points on a vertical plane form a regular polygon. The shape factor, an effective parameter describing the shape, is used to select the optimal result from numerous matching combinations, based on the constraint that the shape factor of a regular polygon is the largest among all polygons. 3) Automatic interactive extraction of 3D power lines: After obtaining the coordinates of the sampling points, the 3D coordinates of each point on the power line are calculated according to the catenary equation. Based on the 2D-constrained catenary point extraction algorithm, the 3D curve is projected onto the vertical projection plane. The calculation of the 3D curve intersection is transformed from space to a 2D plane. The obtained catenary points are used to refit the 3D power lines to make them more consistent with the actual situation, and finally the complete 3D power lines are extracted.

2. The method for intelligently extracting power lines from three-dimensional inspection images of drone aerial photography according to claim 1 is characterized in that: Power line extraction from drone inspection images: The LSD algorithm is used as the basic algorithm for power line extraction from drone inspection images. The gradient symmetry characteristics of split conductors in the image are combined as a condition for screening power lines. The conductor's own characteristics are considered, and the straight line method is used for fitting. The upper and lower edges are merged as the final extraction result. The algorithm flow for extracting power lines from drone inspection images in this application is as follows: Process 1: Use the LSD algorithm to detect line features in the image and calculate the direction of each line feature; Process 2: Using the symmetry of the gradients on both sides of the power line and the direction of the power line as screening conditions, we can obtain candidate line segments: Process 3: Based on the parallel characteristics of the split wires, straight line fitting is performed on the candidate segments, and particularly short segments are deleted; Process 4: Merge the upper and lower edges and extract the power lines.

3. The intelligent extraction method for three-dimensional inspection power lines from drone aerial images according to claim 1 is characterized in that: Detecting power lines: By analyzing the local features of drone images, a set of candidate points that may be straight line pixels is screened and verified using hypothetical parameters. The pixel point set and the error control point set are merged to adaptively control the number of straight line segments that may be falsely detected. The gradient value and gradient direction of each pixel in the image are calculated and then the straight line features in the image are determined based on the pixels with large gradient values, similar gradient directions, and adjacent relationships. Power line detection steps: (1) Image scaling: The original image is scaled using Gaussian downsampling with a scaling factor of 0.8, which means that the number of pixels in both the x and y directions becomes 80% of the original number. The total number of pixels in the downsampled image becomes 64% of the original number of pixels. The image is first filtered using a Gaussian kernel function to avoid quantization pseudo-edges, and then downsampled to reduce subsequent false detections and missed detections. (2) Gradient calculation: Use the 2×2 template shown below to calculate each pixel and obtain the gradient of the image. Based on the transition from black to white, the image gradient and the level-to-line angle determine the direction of the image edge. The difference between the image gradient and the level-to-line angle from white to black is 180°. The smallest template size is selected to reduce the excessive dependence of pixels on each other in the process of calculating the image gradient. The line segments containing the starting and ending points are extracted, and the starting and ending points of the line segments from white to black and from black to white are exactly opposite. The gradient at (x+0.5, y+0.5) is obtained and offset by half a pixel. The offset is added to the rectangular coordinates in subsequent processing; (3) Obtaining the line support region: Sort the gradients of the image and divide the image from 0 to the maximum gradient amplitude into 1024 bins at equal intervals. Then, distribute the image pixels into these bins according to their own gradient values. First, select the pixel with the largest gradient value as the seed point, and then select from the next bin until all bins are selected. After pseudo-sorting the pixel gradients and determining the gradient threshold, a region growing algorithm is used to search for pixels marked as UNUSED within the eight neighborhoods of the seed point. Level-to-line pairs with approximately the same orientation are then merged to form a line segment support domain. If the angle of the line segment support domain and the angle of the next level-to-line pair are both smaller than the set angle tolerance t, the level-to-line pair is added to the line support domain and the angle of the region is updated. The initial angle is calculated from the level-to-line pair of the seed point. This is repeated until no new pixels are added. (4) Detecting straight line segments: Find the minimum circumscribed rectangle and obtain a relatively regular straight line area. Use the rectangle as a candidate straight line and calculate the intra-class point density d of the approximate rectangle to determine whether it is greater than the critical value D. If the condition is not met, the rectangle needs to be truncated and d is recalculated until it is greater than D. k is the number of intra-class points in the rectangle, length(r) is the length of the rectangle, width(r) is the width of the rectangle, and D is set to 0.

7. The rectangle truncation method includes lowering the angle tolerance critical value and reducing the area radius. Evaluate the straight line according to the Helmholtz rule, calculate the NFA, and exclude false straight lines. Suppose there is an image with pixel values ​​representing the angle from level to line, and the angle values ​​independently satisfy the binomial distribution of [0, 2π]. Use the NFA to determine the probability that a rectangle in the detected image has fewer points than the corresponding rectangular box in the hypothetical image. The larger the NFA, the closer the rectangle is to the noise image. Conversely, the more likely it is a true line segment. Set p as the point density within the class and design the critical value e. If NFA < e, the rectangle is judged as a straight line. Otherwise, the rectangular area needs to be re-optimized and judged again.

4. The method for intelligently extracting power lines from three-dimensional inspection images of drone aerial photography according to claim 1 is characterized in that: Power line detection factor optimization: 1) Through manual interaction, a sampling area containing power lines is drawn. The length and width of the sampling area do not exceed 400 pixels, so the image is not Gaussian downsampling according to the scaling of 80%; 2) When using the region growing algorithm to obtain the line support region, the angle tolerance t between the level and the line region and the gradient threshold p are set. Given the low contrast between power lines and the background in drone inspection images, more pixels are included in the line support region. The angle tolerance is increased from 22.5° to 30°, which reduces the number of discarded pixels and reduces the missed detection rate. 3) Lower the intra-class point density critical value D to avoid discarding more rectangles during the evaluation process, thereby increasing the length of the obtained straight line. In this application, D is set to 0.

5.

5. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1 is characterized in that: Power line segment screening: After detecting straight line features in drone inspection images, the correct power line segments are screened from numerous straight line features based on the power line characteristics in the image, eliminating interference factors for the final power line extraction. Power lines in drone inspection images include the following features; a) The drone takes pictures at a short distance, and the aerial image resolution is high, so the width of the power lines in the image is 3 to 5 pixels; b) Power lines appear as straight lines in aerial images, and the lines between the split conductors are parallel to each other; c) The length of the power lines is long and extends to the border of the image; d) Power lines are made of some metal materials, and their spectral properties are similar to those of other power equipment such as power towers; Assume that the function z = f(x, y) has a continuous first-order partial derivative in the plane region D. Then the gradient of the function at a point is defined as follows: the gradient is a vector whose direction is the same as the direction of the maximum directional derivative at the point, and its modulus is the maximum value of the directional derivative. The difference between adjacent pixels is used as the approximate value of the differential of the continuous signal, and the direction of the strongest grayscale value change at each pixel position is used as the direction of the image gradient. When the pixel is located at the edge of the image, the grayscale changes significantly and the corresponding gradient value is large; when the pixel is located at a position where the grayscale amplitude changes less in the surrounding area, the corresponding gradient value is small. The gradient directions of an image from black to white and from white to black are exactly opposite. Gradient symmetry is a characteristic of power lines in drone inspection images. Calculate the line segments that satisfy the gradient symmetry, construct the accumulator H(θ, l), take the length of the line segment as the accumulated amount, and finally take the angle corresponding to the maximum value of l as θ as the direction of the power line. According to the obtained power line direction θ, set a critical value δ, and filter out straight line segments with an angle range of (θ-δ, θ+δ). In this way, many non-power lines are excluded, and the interference line segments are filtered out according to the gradient symmetry and the direction of the power lines to obtain alternative power line features.

6. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1, characterized in that: Power line fitting: Considering that the split wires appear approximately as straight lines and are continuous in the image, the broken lines are fitted and the upper and lower edges are finally merged to obtain a complete extraction result. 1) When performing straight line fitting, fit the upper and lower edges separately to improve the accuracy; 2) During the fitting process, if the two broken lines are far apart, the fitting is abandoned; the distance between the line segments is calculated according to the formula To perform the calculation, assume that the midpoint coordinates of the two line segments are (x1, y1) and (x2, y2), the distance is d, and the critical value D is set to 5 pixels. Fitting is performed only when d < D. 3) If the two broken lines have overlapping parts, the fitting is abandoned; 4) Calculate the vertical distance between the two broken lines, and perform fitting only if it is less than 3 pixels; 5) During the straight line fitting process, the correlation coefficient between the slope and the intercept is calculated. Only when the correlation coefficient is greater than 0.99 is the fitting considered successful. According to the above rules, the selected short straight line segments are connected by straight line fitting; After fitting and connecting using the straight line method, short straight lines are deleted and the upper and lower edges of the power lines are retained. For drone inspection images, the width of the power lines is 3 to 5 pixels. The upper and lower edges are merged as the final extraction result and extended to the boundary of the image, making the extracted power lines more accurate and reducing errors.

7. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1, characterized in that: Automatic matching of power lines in aerial images: After extracting power lines from two-dimensional images, the next step is to automatically match power lines in aerial images. The essence of three-dimensional power line extraction is to obtain the three-dimensional coordinates of points on the power lines. After determining the points of similarity through matching, the spatial coordinates of the points can be calculated using the forward intersection method based on the collinearity equation. The line feature structure of the power lines themselves is used for matching based on the kernel line constraint. The intersection of the power lines and the kernel line is regarded as the points of similarity. Based on the arrangement order of the split conductors in space, each split conductor point is distributed at the vertex of a regular polygon. The matching scheme is determined based on the shape factor constraint method, and the three-dimensional coordinates of the points on the power lines can be obtained through the forward intersection method.

8. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1, characterized in that: Matching based on shape factor constraints: Long-distance transmission lines use a split conductor structure for each phase. When introducing core line constraints for matching, the correspondence between each split conductor on the left and right slices must be determined. If a vertical plane is used to intersect the split conductors, their intersection points will be located at the vertices of a regular polygon. A shape factor that describes the shape characteristics of polygons is introduced, and the matching scheme is determined by parameters. The shape factor is not affected by regional rotation, translation, and scale changes. When the number of sides is determined, the shape factor of a regular polygon is the largest, and when the number of sides of a polygon is determined, the value of its shape factor is also determined. The shape factor is used for constraint, and the shape factor of each combination is calculated. The combination corresponding to the maximum shape factor is taken as the best match. The same-name line segments of each split wire in the left slice on the right slice are determined, and the same-name points are determined by the kernel line constraint. Then, the three-dimensional coordinates of the sampling points on the power line are obtained according to the forward intersection in space.

9. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1, characterized in that: Catenary equation fitting: The catenary equation derived from stress analysis is an important formula for representing the power line model. It describes how the power line elevation changes at different locations as stress and specific load change. With A as the origin, establish a coordinate system. Through force analysis, calculate the coordinates of any point according to Equation 1 and Equation 2: Where: (x, y) is the coordinate of the electric line point on the vertical projection plane; σ0 is the stress, that is, the tension acting on the unit cross-sectional area, the unit is N / mm 2 ; r is the specific load, that is, the load per unit length and unit area of ​​the conductor, the unit is N / mm 2 m; l is the horizontal distance between the first and last endpoints, in meters; h is the vertical distance between the two endpoints, in meters. Using the coordinates of points A and B and the spatial coordinates of several sampling points in the middle, the linear iteration method is used to solve the unknown parameters stress σ0 and specific load r, and the coordinates of any point on the power line catenary model are calculated. The unequal height overhead catenary equation is used for fitting to realize the extraction of three-dimensional power lines.

10. The method for intelligently extracting power lines from three-dimensional inspection images taken by unmanned aerial vehicles according to claim 1, characterized in that: 2D Constrained Hanging Point Extraction: A 2D constrained hanging point extraction algorithm is used to solve the problem of identical hanging points on both sides of the tower of a suspension insulator. By adding two-dimensional constraints, the initial three-dimensional power lines on both sides of the tower are projected onto a vertical projection plane. The two projection curves in this plane intersect, and the intersection point is used as the hanging point. Based on the relationship between the projection coordinate system and the spatial coordinate system, the two-dimensional coordinates of the intersection point on the vertical projection plane are converted into actual coordinates in space. Separate vertical plane coordinate systems are established based on the initial three-dimensional power lines on both sides of the power tower to reduce calculation errors. Two intersection points are calculated, and the average of these two intersection points is finally taken as the final hanging point. Assume that the three-dimensional power lines on both sides of a suspension insulator have been obtained. Catenary model 1 and catenary model 2 are the initial three-dimensional power line models suspended on the same insulator and located on the front and rear sides of the power tower. Their projections on the XOY plane are approximately straight lines, namely projection line 1 and projection line 2. First, a vertical coordinate system is established based on catenary model 1: the direction of projection line 1 of catenary model 1 on the XOY plane is selected as the x-axis, the vertical direction is the y-axis, and the foot o of the perpendicular to the projection line 1 of the original space coordinate system is taken as The origin of the vertical coordinate system; after obtaining the vertical coordinate system, project all points on catenary model 1 and catenary model 2 into the coordinate system and calculate the new coordinates corresponding to each point; in the vertical coordinate system, calculate the intersection between the corresponding projected curves of catenary model 1 and catenary model 2; in the new coordinate system, the type of the projected curve is unknown and the curve equation cannot be directly calculated. Treat the curve as a number of straight lines connected end to end, divide the curve into several straight lines, and directly calculate the intersection of the cutting lines on the two curves, and use it as the intersection point of the curve; According to the relationship between the vertical coordinate system and the spatial coordinate system, the two-dimensional coordinates of the intersection point in the vertical coordinate system are converted into actual three-dimensional spatial coordinates; then, a new vertical coordinate system is established based on the catenary model 2, and the new intersection point is calculated. Finally, the average of the two intersection points obtained based on the catenary model 1 and the catenary model 2 is taken as the coordinate of the final hanging point; Optimization of 2D constraint hanging line point extraction: 1) When using the straight line method to fit the projection line of the power line on the XOY plane, the normal line equation is expressed as: ρ = *cosa + y*sina, where ρ represents the perpendicular distance from the origin to the straight line, and α represents the inclination angle of the perpendicular line. The normal line equation is used to simplify the calculation; 2) Let the coordinates of the origin of the spatial coordinate system О on the projection line of the electric line in the XOY plane be (x0, y0). Then the new coordinates (x, y) of this point in the vertical coordinate system are calculated according to the following rules: y=Z Formula 3 The coordinates of a point on the power line are (X, Y, Z), and the polar coordinates on the XOY horizontal projection plane are (α, ρ).

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