Transmission tower tilt detection method and system based on point cloud completion and robust fitting

Abstract

The application discloses a transmission tower tilt detection method based on point cloud completion and robust fitting, comprising: tower point cloud integrity pre-detection; missing area recovery is performed on the point cloud determined as incomplete; K-center robust fitting method is used to calculate the tilt ratio of the complete point cloud; and the final tilt percentage is output according to the tilt percentage difference of the point cloud. The transmission tower tilt detection system based on point cloud completion and robust fitting comprises a tower point cloud integrity pre-detection module, a PFAR Net point cloud completion module, a K-center robust fitting tilt calculation module and a threshold trigger type weighted fusion output module connected in sequence. The transmission tower tilt detection method and system based on point cloud completion and robust fitting enhance sparse structure geometry modeling through a neighborhood-point attention mechanism, and eliminate the splicing boundary cracks through a displacement field fusion refinement network; the completion chamfer distance is reduced compared with the original PF-Net, and the generated point cloud is highly consistent with the true missing area.

Description

Technical Field

[0001] This invention belongs to the field of power line inspection technology, and relates to a method for detecting the tilt of transmission towers based on point cloud completion and robust fitting, as well as a system for detecting the tilt of transmission towers based on point cloud completion and robust fitting. Background Technology

[0002] Tilting detection of transmission towers is a crucial step in ensuring the safe operation of power systems. UAVs equipped with LiDAR (Light Detection and Ranging) can acquire 3D point clouds of the towers, allowing for the calculation of the tilt ratio by extracting the central axis. However, in actual inspections, structural defects often appear in the tower point clouds due to factors such as vegetation obstruction, limited scanning angles, specular reflection, and semantic segmentation errors, directly affecting the accuracy of tilt detection.

[0003] Existing methods for detecting tower tilt based on 2D images fit the tower's centerline through target detection and edge extraction. For example, they utilize YOLOv3 (You Only Look Once version 3, the third-generation single-stage real-time target detection algorithm) and LSD (Line Segment Detector), or an improved U-Net (U-shaped Network) to segment the tower and then extract the principal direction using Principal Component Analysis (PCA). However, these methods rely on 2D projection, lack depth information, are susceptible to perspective distortion, and exhibit significant measurement errors. 3D point cloud-based detection methods directly utilize the tower's spatial geometry. For instance, they segment the tower head and body using elevation histograms and fit the centerline of a truncated pyramid to calculate the tilt ratio, or they cluster the crossarm point cloud using K-Means Clustering and then fit the plane normal vector. However, when the point cloud is missing in key areas, the centerline fitting deviation of these methods increases significantly, and their robustness is insufficient.

[0004] To address point cloud defects, point cloud completion techniques can be introduced. Deep learning point cloud completion networks, such as PF Net (PointFractal Network), employ a strategy of predicting only the missing regions while retaining the original input, making them suitable for asymmetric defect scenarios like poles and towers. However, general completion networks have limited local geometric modeling capabilities on sparse and slender pole and tower structures, resulting in jagged distortion in the generated point clouds. Furthermore, geometric gaps exist at the splicing boundaries between the completed and original point clouds, directly affecting subsequent tilt measurements. In addition, existing completion networks do not incorporate prior knowledge of the symmetry of the pole and tower structure, and there is a lack of quantitative correlation analysis between completion quality and final detection accuracy, making it difficult for completion and detection to work effectively together. Summary of the Invention

[0005] The purpose of this invention is to provide a method for detecting the tilt of transmission towers based on point cloud completion and robust fitting, which solves the problem in the prior art that it is difficult to achieve high-precision tilt detection when the point cloud of transmission towers has structural defects due to occlusion, segmentation errors, etc. during UAV LiDAR inspection.

[0006] Another objective of this invention is to provide a transmission tower tilt detection system based on point cloud completion and robust fitting.

[0007] The technical solution adopted in this invention is a method for detecting the tilt of transmission towers based on point cloud completion and robust fitting, comprising: Step 1: Pre-inspection of the integrity of the tower point cloud; Step 2: Restore the missing regions of the point cloud that is determined to be incomplete; Step 3: Calculate the tilt ratio using the K-center robust fitting method on the complete point cloud; Step 4: Output the final tilt percentage based on the tilt percentage difference of the point cloud.

[0008] The invention is further characterized by: Step 1 includes: Step 1.1: Align the main axis and normalize the height of the input tower point cloud, and construct a symmetrical reference plane with the direction of the second principal component as the normal vector; Step 1.2: Slice the point cloud along the elevation direction with a fixed step size to obtain several slice point sets; Step 1.3: Calculate the signed vertical distance of each point in each slice point set relative to the reference plane, count the number of points on both sides of the plane, and calculate the symmetry ratio; Step 1.4: Determine the integrity of the tower point cloud; If the cumulative height of the longest consecutive slice interval satisfying the elevation slice symmetry ratio <0.6 exceeds 0.9m, the cumulative height of all slices with an elevation slice symmetry ratio <0.6 accounts for more than 20%, or the proportion of extremely asymmetrical slices satisfying the elevation slice symmetry ratio <0.3 exceeds 8% and the average symmetry ratio of the entire tower is less than 0.85, then the point cloud is determined to be an incomplete tower point cloud and step 2 is executed; otherwise, the tower point cloud is considered complete and step 3 is executed.

[0009] Step 2 includes: Step 2.1: Perform multi-level iterative downsampling of the farthest point and point-by-point feature extraction on the original tower point cloud that is determined to be incomplete by the integrity pre-detection. Transform the geometric information of the overall outline of the tower and the local components of the crossarm and diagonal brace into multi-scale high-dimensional depth feature vectors to complete the encoding of the geometric information of the original point cloud. Step 2.2: First, perform dimensionality compression on the multi-scale high-dimensional depth feature vector, then complete feature upsampling and three-dimensional coordinate regression to generate a coarse missing point cloud with jagged distortion and uneven spatial distribution. Step 2.3: After processing the coarse missing point cloud, a refined missing point cloud is generated; Step 2.4: Assign differentiated labels to the original tower point cloud and the refined missing point cloud. The original tower point cloud is uniformly labeled with label 0, and the refined missing point cloud is uniformly labeled with label 1. The one-dimensional label is used as the fourth-dimensional channel and spliced ​​and fused with the three-dimensional coordinates of the point cloud to generate a four-dimensional combined point cloud that simultaneously contains spatial coordinates and point source identifiers. Step 2.5: Apply hard displacement constraints to the four-dimensional combined point cloud, forcing all original observation points with a label value of 0 to have their displacements reduced to zero, and only applying coordinate fine-tuning to the generated missing points with a label value of 1, finally outputting the three-dimensional displacement field of each point in the corresponding combined point cloud. Step 2.6: Apply the displacement offset to the refined missing point cloud to obtain the set of missing points after coordinate fine-tuning and smoothing. Keep the original tower point cloud coordinate values ​​unchanged, and perform a set union operation on the original observation point cloud and the fine-tuned missing point cloud to obtain the final complete tower point cloud.

[0010] Step 2.3 includes: Step 2.3.1: First, use adaptive convolution to map the 3D coordinates of the coarse missing point cloud to a high-dimensional feature space to generate a deep feature tensor; Step 2.3.2: For each center point, the K-nearest neighbor algorithm is used to filter spatial neighbor points. The local correlation between the center point and the neighbor points is calculated with the help of two sets of learnable linear projection layers, Q and K. Then, the attention weights corresponding to each neighbor point are obtained through normalization. Step 2.3.3: Use the V linear projection layer to perform weighted aggregation of neighborhood features to obtain refined features of the center point; Step 2.3.4: Map the refined features back to the three-dimensional coordinate space, eliminate jagged edges and hole distortions at sparse components of the tower, and output the refined missing point cloud with improved detail accuracy.

[0011] Step 3 includes: Step 3.1, Discretization of tower point cloud elevation direction slices: Discretize the input point cloud into multiple overlapping horizontal slices along the elevation direction, and filter the valid slices by the number of points threshold; Step 3.1.1: Set the slice thickness and step size according to the tower pitch and point cloud density; Step 3.1.2: Generate several horizontal slices sequentially along the elevation direction. Perform point count verification on the point set of each slice. If the number of points in a slice is less than a preset threshold, it is determined to be an invalid slice and is skipped. The point set data of all valid slices are retained. Step 3.2, Extraction of the center point of the slice tower body based on KMeans clustering: Perform clustering operation on the planar coordinates of each valid slice, calculate the center of the slice tower body by the geometric mean of the cluster centers, and obtain the sequence of center points in the elevation direction; Step 3.2.1: Read the point set of each valid slice in sequence, extract the XY plane coordinates of all points, perform KMeans clustering operation on the two-dimensional coordinate set, set the number of clusters and fix the random seed, and obtain the cluster center after the operation; Step 3.2.2: Take the geometric mean of the cluster centers as the tower center point of the current slice. After traversing all valid slices, obtain the tower center point sequence arranged in order of elevation. Step 3.3, RANSAC robust linear fitting and slope ratio calculation: Step 3.3.1: Receive the sequence of tower center points sorted by elevation, and use the RANSAC random sampling consensus algorithm to perform spatial straight line fitting on the sequence to obtain the direction vector of the central axis, and select two points A and B on the fitted line; Step 3.3.2: Calculate the horizontal offset and tower height based on the coordinates of the two points respectively; The horizontal offset is the projection length of vector AB on the horizontal plane, and the tower height is the projection length of vector AB in the vertical direction. Step 3.3.3: Calculate the tower tilt ratio and tilt percentage.

[0012] Step 4 includes: outputting the final tilt percentage q based on the tilt percentage difference Δq of the point cloud using a three-segment rule. final : If Δq≤0.1%, then q final =q comp ; If 0.1% < Δq ≤ 0.5%, then q final =0.3×q orig +0.7×q comp ; If Δq > 0.5%, then q final =min(q) orig q comp ); The percentage difference in tilt of the point cloud is Δq = |q comp -q orig |; Where, q orig q is the tilt percentage based on the original residual cloud. comp This represents the tilt percentage based on the completed point cloud.

[0013] Another technical solution adopted in this invention is a transmission tower tilt detection system based on point cloud completion and robust fitting, comprising a tower point cloud integrity pre-detection module, a PFAR Net (Point Fractal Attention Refinement Network) point cloud completion module, a K-center robust fitting tilt calculation module, and a threshold-triggered weighted fusion output module connected in sequence. The tower point cloud integrity pre-detection module and the K-center robust fitting tilt calculation module are connected. Another feature of the technical solution of the present invention is that: The tower point cloud integrity pre-detection module consists of a main axis alignment and height normalization unit, an elevation slice division unit, a slice symmetry ratio calculation unit, and an integrity judgment unit connected in series. The main axis alignment and height normalization unit first performs main axis alignment and height normalization processing on the input tower point cloud, and constructs a symmetry reference plane with the direction of the second principal component as the normal vector. The elevation slice division unit divides the point cloud into several slice point sets along the elevation direction with a fixed step size, decomposing the three-dimensional tower structure into multiple horizontal slices. The slice symmetry ratio calculation unit calculates the signed vertical distance of each point in each slice relative to the symmetry reference plane, counts the number of point clouds on both sides of the reference plane and calculates the symmetry ratio, quantifying the degree of symmetry of the point cloud at each height layer. The integrity judgment unit outputs the final judgment result according to three types of preset judgment rules. If the point cloud is judged to be incomplete, it is sent to the PFAR Net point cloud completion module; otherwise, it is judged to be complete and directly sent to the K-center robust fitting tilt calculation module.

[0014] The PFAR Net point cloud completion module consists of a missing region generation and N2P (Neighborhood-to-Point Attention) refinement branch, a label encoding splicing transition unit, and an FRN (Field Refinement Network) branch connected in series. The missing region generation and N2P refinement branch includes a multi-scale point cloud encoder unit, a multi-scale feature stitching and transformation unit, a reconstruction decoder unit, and an N2P neighborhood point attention refinement unit. The multi-scale point cloud encoder unit downsamples the original point cloud to three spatial scales through two-level iterative point downsampling, and then performs point-by-point feature extraction through a cascaded multilayer perceptron, simultaneously capturing multi-scale geometric information of the overall outline of the tower and local components. The multi-scale feature stitching and transformation unit first stitches three sets of depth features at different scales along the feature channel dimension, and then performs feature dimension regularization and adaptation through a multilayer perceptron, integrating global structural features and local detail features into a unified multi-scale feature tensor. The reconstruction decoder unit adopts an architecture of linear layers, fully connected layers and one-dimensional convolutions in series to complete feature upsampling and three-dimensional coordinate regression, generating a coarse-grained point cloud of missing regions with local jagged distortion. The N2P neighborhood point attention refinement unit selects spatial neighborhood points for each center point through the K nearest neighbor algorithm, calculates local correlation and attention weights with three sets of linear projection layers (Q, K, V), adaptively weights and aggregates neighborhood geometric features, and outputs a refined missing point cloud with smooth details. The label encoding and splicing transition unit splices and merges the one-dimensional label as the fourth-dimensional channel with the three-dimensional coordinates of the point cloud to generate a four-dimensional combined point cloud with point source identifiers; The FRN displacement field fusion refinement branch includes an encoder feature extraction unit, a residual block feature enhancement unit, a decoder displacement regression unit, and a displacement constraint and point cloud fusion unit; The encoder feature extraction unit consists of four convolutional layers connected in series, progressively expanding the network's receptive field and deeply extracting geometric features at the splicing boundary, capturing coordinate deviations and density jumps at the intersection of the original and generated points. The residual block feature enhancement unit fuses shallow contour features and deep boundary features through internal jump connections. The decoder displacement regression unit consists of four convolutional layers, applying a Dropout regularization strategy after the first two convolutional layers to gradually map high-dimensional features back to three-dimensional coordinate space, regressing to obtain the three-dimensional displacement field corresponding to each point. The displacement constraint and point cloud fusion unit applies hard displacement constraints based on the label channel of the four-dimensional point cloud, forcing the displacement of the original observation point with label 0 to be zero, and only applying three-dimensional coordinate fine-tuning to the generated missing points with label 1 to correct geometric cracks at the splicing boundary. Finally, the fine-tuned missing point cloud is merged with the original observation point cloud to output a geometrically continuous, crack-free complete tower point cloud.

[0015] The K-center robust fitting tilt calculation module consists of an elevation slice discretization unit, a KMeans cluster center point extraction unit, and a RANSAC robust linear fitting and tilt calculation unit connected in series. The elevation slice discretization unit discretizes the input point cloud into multiple overlapping horizontal slices along the elevation direction, setting the slice thickness to be greater than the step size, and filtering out sparse and invalid slices through a point count threshold; the KMeans clustering center point extraction unit performs KMeans clustering operation on the XY plane coordinates of each valid slice, sets the number of clusters and fixes the random seed, takes the geometric mean of the four cluster centers as the tower center point of the current slice, and obtains the tower center point sequence arranged in elevation order after traversing all valid slices; the RANSAC robust linear fitting and tilt calculation unit uses the random sampling consensus algorithm to perform spatial linear fitting on the center point sequence, automatically removes local outlier center points, and after fitting the direction vector of the tower's central axis, calculates the horizontal offset and vertical tower height based on two points on the central axis, and finally derives the tower tilt ratio and tilt percentage; The threshold-triggered weighted fusion output module includes a dual-path tilt percentage calculation unit, a difference calculation unit, and a three-segment rule output unit connected in sequence. The dual-path tilt percentage calculation unit simultaneously calculates the tilt percentage based on the original incomplete point cloud and the tilt percentage based on the completed point cloud; the difference calculation unit calculates the absolute difference between the two tilt percentages; the three-segment rule output unit executes the corresponding output strategy according to the three threshold intervals of the difference to obtain the final tilt percentage result.

[0016] The beneficial effects of this invention are: Integrity pre-detection utilizes the prior symmetry of the tower structure and makes rapid judgments based solely on the symmetry ratio of the slices. It achieves an accuracy of 96.8% on the joint simulation and experimental datasets, with almost no complete samples being misjudged and sent to the completion network, thus avoiding unnecessary computational overhead. The improved PFAR Net enhances sparse structure geometry modeling through a neighborhood-point attention mechanism and eliminates splicing boundary cracks by refining the network through displacement field fusion. At missing rates of 10%, 20%, and 30%, the completion chamfer distance (CD) is reduced by 28.5%, 19.3%, and 16.1% compared to the original PF-Net, respectively, and the generated point cloud closely matches the actual missing regions. Experiments show that the Pearson correlation coefficient between the completed CD and the final tilt detection error is 0.671, demonstrating that higher completion accuracy leads to lower detection error and validating the effectiveness of the completed detection framework. The K-center robust fitting method suppresses interference from auxiliary structures such as crossarms and ladders by using four cluster centers. Combined with RANSAC (Random Sample Consensus) robust fitting, it is more robust in extracting the central axis under defective scenarios. With the addition of a threshold-triggered weighted fusion strategy, the tilt detection error is only 0.3869% at a 10% missing rate, which is 65.5% lower than directly using the residual point cloud. At a 30% severe missing rate, the error is 0.9529%, which is still far lower than existing methods (such as least squares method 3.0597%, PCA (Principal Component Analysis) method 3.2261%), etc., which greatly improves the accuracy and robustness of tower tilt detection under point cloud defect conditions. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the transmission tower tilt detection method based on point cloud completion and robust fitting of the present invention. Figure 2 A schematic diagram of the symmetrical proportional distribution of complete samples and their corresponding point clouds in the pre-inspection of tower point cloud integrity; Figure 3 A schematic diagram of the symmetrical proportion distribution of slices of missing samples and their corresponding point clouds in the pre-inspection of the integrity of tower point clouds; Figure 4 This is a schematic diagram of the PFAR Net used in the embodiments of the present invention. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 This embodiment proposes a method for detecting the tilt of transmission towers based on point cloud completion and robust fitting, such as... Figure 1 As shown, it includes: Step 1: Pre-inspection of the integrity of the tower point cloud; Step 2: Restore the missing regions of the point cloud that is determined to be incomplete; Step 3: Calculate the tilt ratio using the K-center robust fitting method on the complete point cloud; Step 4: Output the final tilt percentage based on the tilt percentage difference of the point cloud.

[0020] Example 2 Based on Example 1, this example proposes that step 1 includes: Step 1.1: Align the main axis and normalize the height of the input tower point cloud, and construct a symmetrical reference plane with the direction of the second principal component as the normal vector; Step 1.2: Slice the point cloud along the elevation direction with a fixed step size to obtain several slice point sets; Step 1.3: Calculate the signed vertical distance of each point in each slice point set relative to the reference plane, count the number of points on both sides of the plane, and calculate the symmetry ratio; In one embodiment of the present invention, the signed vertical distance of each point relative to the reference plane is calculated. Count the number of points on both sides of the plane and Calculate the symmetrical proportions ,in, d(p) For point p The signed perpendicular distance to the symmetric reference plane. p This is the position vector of a single point to be calculated in a 3D point cloud. Let be the position vector of the reference point on the symmetric reference plane; This is the unit normal vector corresponding to the second principal component, i.e., the unit normal vector of the symmetric reference plane; k This is the sequence number of the elevation slice; The number of point clouds located to the left of the symmetric reference plane in the k-th slice; The number of point clouds located to the right of the symmetric reference plane in the k-th slice; The symmetry ratio of the k-th slice directly reflects the degree of symmetry of the point cloud at each height level with respect to the reference plane. Figure 2 and Figure 3 The results of typical samples are shown: in a complete tower, the number of point clouds on both sides of the reference plane is balanced, such as... Figure 2 The elevation histogram is shown; while the missing towers show continuous low values ​​in the missing area, such as... Figure 3 As shown, the low-value range in the histogram matches the geometrically missing locations in the actual point cloud; Step 1.4: Determine the integrity of the tower point cloud; If the cumulative height of the longest consecutive slice interval satisfying the elevation slice symmetry ratio <0.6 exceeds 0.9m, the cumulative height of all slices with an elevation slice symmetry ratio <0.6 accounts for more than 20%, or the proportion of extremely asymmetrical slices satisfying the elevation slice symmetry ratio <0.3 exceeds 8% and the average symmetry ratio of the entire tower is less than 0.85, then the point cloud is determined to be an incomplete tower point cloud and step 2 is executed; otherwise, the tower point cloud is considered complete and step 3 is executed.

[0021] Example 3 Based on Example 1, this example proposes that step 2 includes: The point cloud identified as incomplete is processed sequentially through the PFAR Net internal encoder, reconstruction decoder, N2P neighborhood point attention module, label encoding and splicing unit, and FRN network for basic encoding, coarse missing point generation, local detail refinement, multi-source point cloud label splicing, boundary displacement fine-tuning, and complete point cloud fusion output. Finally, the missing area of ​​the tower is repaired and a geometrically continuous complete tower point cloud without splicing cracks is output. Step 2.1: Perform multi-level iterative downsampling of the farthest point and point-by-point feature extraction on the original tower point cloud that is determined to be incomplete by the integrity pre-detection. Transform the geometric information of the overall outline of the tower and the local components of the crossarm and diagonal brace into multi-scale high-dimensional depth feature vectors to complete the encoding of the geometric information of the original point cloud. Step 2.2: First, perform dimensionality compression on the multi-scale high-dimensional depth feature vector, then complete feature upsampling and three-dimensional coordinate regression to generate a coarse missing point cloud with jagged distortion and uneven spatial distribution. Step 2.3: After processing the coarse missing point cloud, a refined missing point cloud is generated.

[0022] Step 2.3.1: First, use adaptive convolution to map the 3D coordinates of the coarse missing point cloud to a high-dimensional feature space to generate a deep feature tensor; Step 2.3.2, for each center point The K-nearest neighbor algorithm with K=32 is used to select spatial neighbor points. The local correlation between the center point and its neighboring points is calculated using two sets of learnable linear projection layers, Q and K. Then, the attention weights corresponding to each neighborhood point are obtained by normalization using the softmax function. , Normalized attention weights for each neighboring point: , , in, This represents the attention weight of the j-th neighboring point corresponding to the i-th center point; That is, the normalized exponential function. It is a local correlation measurement function between the center point and its neighboring points; The feature vector of the i-th center point corresponds to a single generated point in the missing point cloud that needs to be refined and optimized. The feature vector representing the j-th neighboring point of the i-th center point; The dimension of the feature vector output by the linear projection of Q and K; It is a linear projection layer for querying data; It is a linear projection layer of the key; Step 2.3.3: Use the V-linear projection layer to perform weighted aggregation of neighborhood features to obtain refined features of the center point: f i = Σa ij ·V ( ); in, The refined feature vector representing the i-th center point; This represents the attention weight of the j-th neighboring point corresponding to the i-th center point; It is a linear projection layer of the value; This represents the feature vector of the j-th neighboring point of the i-th center point; Step 2.3.4: Map the refined features back to 3D coordinate space to eliminate jagged edges and hole distortions at sparse components of the tower, and output the refined missing point cloud with improved detail accuracy. ; Step 2.4: Analyze the original tower point cloud. With Refined Missing Point Cloud Differentiated label assignment is performed: the original tower point cloud is uniformly labeled with label 0, and the refined missing point cloud is uniformly labeled with label 1. The one-dimensional label is used as a fourth-dimensional channel and spliced ​​and fused with the three-dimensional x, y, z coordinates of the point cloud to generate a four-dimensional composite point cloud that simultaneously contains spatial coordinates and point location identifiers. ; Step 2.5: Combine the four-dimensional point cloud Apply hard displacement constraints to force all original observation points with a label value of 0 to zero displacement, and apply coordinate fine-tuning only to the generated missing points with a label value of 1, and finally output the three-dimensional displacement field of each point in the corresponding combined point cloud. Step 2.6: Adjust the displacement offset. Superimposed effect on the refined missing point cloud The set of missing points after coordinate fine-tuning and smoothing is obtained. Preserve the original tower point cloud Without changing the coordinate values, perform a union operation on the original observation point cloud and the fine-tuned missing point cloud to obtain the final complete tower point cloud. .

[0023] Example 4 Based on Example 1, this example proposes that step 3 includes: For the complete tower point cloud after completion or the original tower point cloud that is determined to be complete by pre-detection, the K-center robust fitting method is used to extract the tower body centerline and calculate the tilt ratio. The elevation slice discretization, cluster center point extraction, and robust linear fitting are completed in sequence. The interference of the attached structure is suppressed by clustering and the influence of outliers is resisted by RANSAC. Finally, a stable and reliable tilt ratio result is output. Step 3.1, Discretization of tower point cloud elevation direction slices: Discretize the input point cloud into multiple overlapping horizontal slices along the elevation direction, and filter the effective slices by the number of points threshold to provide a layered data basis for the subsequent extraction of the tower center point and avoid elevation sampling blind spots; Step 3.1.1: The elevation range of the complete tower point cloud P is... The slice thickness δ and step size Δh are set according to the tower pitch and point cloud density, and δ>Δh is set to ensure that adjacent slices overlap and eliminate sampling blind spots in the elevation direction. Step 3.1.2: Generate several horizontal slices sequentially along the elevation direction, with the center height of the i-th slice being... The corresponding slice point set is denoted as Perform point count verification on each slice point set. If the number of points in a slice is less than a preset threshold, it is determined to be an invalid slice and is skipped. The point set data of all valid slices are retained and passed down. The overlapping slice design avoids the component omission problem that may occur in fixed step size sampling, and the point number threshold screening eliminates sparse and invalid slices, ensuring the data reliability of subsequent center point calculation; the layered slice decomposes the three-dimensional tower body centerline fitting problem into a multi-layer two-dimensional center estimation problem, reducing the overall computational complexity.

[0024] Step 3.2, Extraction of the center point of the slice tower body based on KMeans clustering: Perform a quaternion operation on the planar coordinates of each valid slice, calculate the center of the slice tower body by the geometric mean of the quaternion centers, suppress the interference of crossarms, ladders and other auxiliary structures on the center positioning, and obtain the center point sequence in the elevation direction; Step 3.2.1: Read the point set S of each valid slice in sequence. i Extract the XY plane coordinates of all points, perform KMeans clustering operation on the two-dimensional coordinate set, set the number of clusters k=4 and fix the random seed to ensure that the results are reproducible, and obtain four cluster centers c1, c2, c3 and c4 after the operation. Step 3.2.2: Take the geometric mean of the four cluster centers as the tower body center point of the current slice; after traversing all valid slices, obtain the tower body center point sequence arranged in order of elevation; The sequence of the tower's center points is as follows: , Among them, O irepresents the three-dimensional coordinates of the tower center point corresponding to the i-th elevation slice, which is a three-dimensional point vector containing the horizontal coordinate, vertical coordinate, and elevation information; i is the sequence number of the elevation slice, used to identify the i-th horizontal slice divided along the tower elevation direction; j is the sequence number of the cluster center, ranging from 1 to 4, corresponding to the 4 cluster centers obtained by KMeans clustering within a single slice; c xj c represents the x-coordinate value of the j-th cluster center, that is, the coordinate component of the cluster center on the x-axis of the horizontal coordinate system; yj h represents the ordinate value of the j-th cluster center, that is, the coordinate component of the cluster center on the Y-axis of the horizontal coordinate system; i This represents the center height corresponding to the i-th elevation slice, that is, the center elevation value of the slice in the vertical direction; This invention utilizes the geometric characteristics of the four corners of the tower body corresponding to the four cluster centers to effectively filter out the interference of external auxiliary structures such as crossarms, ladders, and foot spikes on the center calculation. Compared with the method of directly taking the centroid, it is closer to the real geometric center of the tower body and significantly improves the center point extraction accuracy in the scenario where defects and auxiliary structures coexist. Step 3.3, RANSAC robust linear fitting and tilt ratio calculation: The random sampling consensus algorithm is used to perform spatial linear fitting on the center point sequence to resist the interference of local outlier center points, extract the tower centerline and calculate the tilt ratio and tilt percentage; Step 3.3.1: Receive the sequence of tower center points sorted by elevation, and use the RANSAC random sampling consensus algorithm to perform spatial straight line fitting on the sequence to obtain the direction vector d of the central axis. Select two points A and B on the fitted line for subsequent geometric calculations. Step 3.3.2: Calculate the horizontal offset and tower height based on the coordinates of the two points respectively; The horizontal offset S is the projected length of vector AB on the horizontal plane, and the tower height H is the projected length of vector AB in the vertical direction. The corresponding calculation formulas are as follows: , , in, This refers to the horizontal offset of the tower. The vertical height of the tower; These are two spatial points on the central axis obtained through fitting; Step 3.3.3: Calculate the tower tilt ratio q and tilt percentage. The calculation formula is as follows: , in The tower tilt ratio; This is the horizontal offset; The vertical tower height is given. Multiplying the tilt ratio by 100% gives the tilt percentage; this formula characterizes the overall tilt of the tower, with a larger value indicating a more severe tilt.

[0025] In this invention, the RANSAC algorithm can automatically remove local outlier center points, avoiding the influence of center point deviation caused by individual defects or attached structures on the overall centerline fitting. Compared with global fitting methods such as least squares, it has stronger robustness and can still obtain stable and reliable tilt detection results in point cloud local defect scenarios.

[0026] Example 5 Based on Example 1, this example proposes step 4, which includes: outputting the final tilt percentage q using a three-segment rule based on the tilt percentage difference Δq of the point cloud. final : If Δq≤0.1%, then q final =q comp ; If 0.1% < Δq ≤ 0.5%, then q final =0.3×q orig +0.7×q comp ; If Δq > 0.5%, then q final =min(q) orig q comp ); The percentage difference in tilt of the point cloud is Δq = |q comp -q orig |; Where, q orig q is the tilt percentage based on the original residual cloud. comp This represents the tilt percentage based on the completed point cloud.

[0027] Example 6 This embodiment proposes a transmission tower tilt detection system based on point cloud completion and robust fitting, including a tower point cloud integrity pre-detection module, a PFAR Net point cloud completion module, a K-center robust fitting tilt calculation module, and a threshold-triggered weighted fusion output module connected in sequence. The tower point cloud integrity pre-detection module is connected to the K-center robust fitting tilt calculation module.

[0028] Example 7 Based on Example 6, this example proposes a tower point cloud integrity pre-detection module that utilizes the prior symmetry of the tower structure to quickly determine whether there are structural defects in the point cloud, thus avoiding unnecessary computational overhead caused by the entry of complete point clouds into the completion network; It consists of a main axis alignment and height normalization unit, an elevation slice division unit, a slice symmetry ratio calculation unit, and an integrity judgment unit connected in series.

[0029] The main axis alignment and height normalization unit first performs main axis alignment and height normalization on the input tower point cloud, and constructs a symmetric reference plane with the direction of the second principal component as the normal vector to provide a unified geometric benchmark for subsequent layered analysis. The elevation slice division unit divides the point cloud into several slice point sets along the elevation direction with a fixed step size, decomposing the three-dimensional tower structure into multiple horizontal slices to simplify the analysis dimensions. The slice symmetry ratio calculation unit calculates the signed vertical distance of each point in each slice relative to the symmetric reference plane, counts the number of point clouds on both sides of the reference plane and calculates the symmetry ratio to quantify the degree of symmetry of the point cloud at each height layer. The integrity judgment unit outputs the final judgment result according to three types of preset judgment rules. If the point cloud is judged to be incomplete, it is sent to the PFAR Net point cloud completion module; otherwise, it is judged to be complete and directly sent to the K-center robust fitting tilt calculation module.

[0030] The PFAR Net point cloud completion module restores the missing areas of the tower point cloud that is determined to be incomplete. While preserving the original observation point cloud, it repairs the missing structure and eliminates the geometric cracks at the splicing boundary, providing structurally complete point cloud data for subsequent tilt detection. A hierarchical architecture with two branches serially cascaded is adopted, consisting of a missing region generation and N2P attention refinement branch, a label encoding splicing transition unit, and an FRN displacement field fusion refinement branch connected in series.

[0031] The missing region generation and N2P attention refinement branch includes a multi-scale point cloud encoder unit, a multi-scale feature stitching and transformation unit, a reconstruction decoder unit, and an N2P neighborhood point attention refinement unit. The multi-scale point cloud encoder unit downsamples the original point cloud to three spatial scales through two-stage iterative downsampling, and then performs point-by-point feature extraction via a cascaded multilayer perceptron, simultaneously capturing multi-scale geometric information of the overall tower outline and local components such as crossarms and braces. The multi-scale feature stitching and transformation unit first stitches three sets of depth features at different scales along the feature channel dimension, and then performs feature dimension regularization and adaptation via a multilayer perceptron, integrating global structural features and local detail features into a unified multi-scale feature tensor. The reconstruction decoder unit adopts an architecture of linear layers, fully connected layers, and one-dimensional convolutions to perform feature upsampling and three-dimensional coordinate regression, generating a coarse-grained missing region point cloud with local jagged distortion. The N2P neighborhood point attention refinement unit selects 32 spatial neighborhood points for each center point using the K-nearest neighbor algorithm, leveraging Q, K, and V... Three sets of linear projection layers calculate local correlation and attention weights, adaptively weighted aggregate neighborhood geometric features, effectively suppress jagged and hole distortions at sparse components, and output a refined missing point cloud with smooth details.

[0032] The label encoding splicing transition unit is a bridge connecting two branches. It assigns a unified label 0 to the original observation point and a unified label 1 to the refined missing point cloud. It uses the one-dimensional label as the fourth-dimensional channel to splice and fuse with the three-dimensional coordinates of the point cloud to generate a four-dimensional combined point cloud with point source identifiers, providing a basis for the determination of differential constraints of the downstream displacement field.

[0033] The FRN displacement field fusion refinement branch includes an encoder feature extraction unit, a residual block feature enhancement unit, a decoder displacement regression unit, and a displacement constraint and point cloud fusion unit. The encoder feature extraction unit consists of four concatenated convolutional layers, progressively expanding the network's receptive field and deeply extracting geometric features at the splicing boundaries, accurately capturing coordinate deviations and density jumps at the intersection of original and generated points. The residual block feature enhancement unit fuses shallow contour features and deep boundary features through internal skip connections, alleviating the gradient vanishing problem in deep networks and further enhancing the network's ability to capture minute displacement deviations. The decoder displacement regression unit consists of four convolutional layers; after the first two convolutional layers, a Dropout regularization strategy is applied to avoid overfitting, gradually mapping high-dimensional features back to three-dimensional coordinate space, regressing to obtain the three-dimensional displacement field corresponding to each point. The displacement constraint and point cloud fusion unit applies hard displacement constraints based on the label channels of the four-dimensional point cloud, forcing the displacement of original observation points with a label of 0 to be zero, and only applying constraints to points with a label of 1. The generated missing points are fine-tuned with three-dimensional coordinates to correct geometric cracks in the splicing boundary. Finally, the fine-tuned missing point cloud is merged with the original observation point cloud to output a geometrically continuous and crack-free complete tower point cloud. In the training phase of this branch, a parameter isolation strategy is adopted, fixing all network weights of the generated branch above and only updating its own parameters. The symmetric chamfer distance is used as the loss function to decouple the tasks of generating missing regions and optimizing splicing boundaries.

[0034] The K-center robust fitting tilt calculation module extracts the tower's central axis and calculates the tilt ratio from the complete point cloud. It suppresses interference from auxiliary structures through clustering and resists the influence of outliers through robust fitting, outputting stable and reliable tilt detection results. This module consists of an elevation slice discretization unit, a KMeans cluster center point extraction unit, and a RANSAC robust linear fitting and tilt calculation unit connected in series.

[0035] The elevation slice discretization unit discretizes the input point cloud into multiple overlapping horizontal slices along the elevation direction. The slice thickness is set greater than the step size to ensure overlap between adjacent slices, avoiding sampling blind spots in the elevation direction. Simultaneously, a point count threshold is used to filter out sparse and invalid slices, decomposing the 3D tower centerline fitting problem into a multi-layered 2D center estimation problem, reducing overall computational complexity. The KMeans clustering center point extraction unit performs KMeans clustering operations on the XY plane coordinates of each valid slice. The number of clusters is set and a fixed random seed ensures reproducibility. Utilizing the geometric characteristics of the four cluster centers corresponding to the four corners of the tower, the geometric mean of the four cluster centers is taken as the tower center point of the current slice, effectively suppressing interference from external auxiliary structures such as crossarms, ladders, and foot spikes on the center calculation. After traversing all valid slices, a sequence of tower center points arranged in elevation order is obtained. RANSAC The robust linear fitting and tilt calculation unit uses a random sampling consensus algorithm to perform spatial linear fitting on the center point sequence, automatically eliminating local outlier center points to avoid deviations caused by local defects or auxiliary structures. After fitting the direction vector of the tower's central axis, the horizontal offset and vertical tower height are calculated based on two points on the central axis, and finally the tower tilt ratio and tilt percentage are derived.

[0036] The threshold-triggered weighted fusion output module integrates the tilt detection results of the original incomplete point cloud and the completed point cloud, controls the error spread caused by the completion distortion, and further improves the robustness of the detection results. This module is composed of a dual-path tilt percentage calculation unit, a difference calculation unit, and a three-segment rule output unit connected in sequence.

[0037] The dual-path tilt percentage calculation unit simultaneously calculates the tilt percentage based on the original residual point cloud and the tilt percentage based on the completed point cloud, providing two independent detection bases for fusion decision-making. The difference calculation unit calculates the absolute difference between the two tilt percentages as the trigger judgment index for fusion rules. The three-stage rule output unit executes the corresponding output strategy according to the three threshold intervals of the difference. When the difference is less than or equal to 0.1%, the completed tilt percentage is output directly. When the difference is between 0.1% and 0.5%, the original result with a weight of 0.3 and the completed result with a weight of 0.7 are weighted and fused before output. When the difference is greater than 0.5%, the smaller value of the two results is taken as the conservative output, and finally the final tilt percentage result of the system is obtained.

[0038] Unlike the compact, continuous, and uniformly distributed point clouds in general completion datasets, transmission tower point clouds have unique characteristics such as sparse and elongated structures and splicing boundary artifacts. For the asymmetric defects in transmission tower point clouds, an ideal completion strategy should preserve the original observed point cloud and only generate the missing regions. PFNet, which predicts only the missing parts, can preserve the original input point cloud and is suitable as a base network; however, its local geometric modeling capabilities are limited, and the boundary fusion between the missing regions and the original point cloud is insufficient. Therefore, the PFAR Net proposed in this invention introduces Neighborhood-Point Attention (N2P) to enhance the local geometric refinement of sparse structures and adds Displacement Field Fusion Refinement (FRN) to eliminate splicing boundary artifacts.

[0039] In one embodiment of the present invention, the specific structural parameters of the trained PFAR Net are as follows: the input is an incomplete point cloud of a tower sampled and fixed to 2048 points from the farthest point; In the missing region generation and N2P refinement branch, the samples are downsampled to 512 and 256 points using two levels of IFPS. The three scales are respectively achieved through cascaded Conv1d (1-Dimensional Convolution) (3, 64, 1), Conv1d (64, 128, 1), Conv1d (128, 512, 1) (Scale 1), Conv1d (3, 64, 1), Conv1d (64, 256, 1), Conv1d (256, 1024, 1) (Scale 2), and Conv1d (3, 64, 1), Conv1d (64, 128, 1), Conv1d (128, 512, 1) (Scale 3). Each layer is followed by batch normalization and ReLU (Rectified Linear Array). Unit (corrected linear unit), after max pooling to obtain 512, 1024, 512-dimensional global features, concatenated into a 2048-dimensional vector, then transformed by fully connected layers (2048→1024, ReLU) and (1024→1024, ReLU), then through linear layers (1024→256) and fully connected layers (256→1920) and reshaped into (640, 3), and then smoothed by Conv1d (3, 3, 1) to generate a coarse missing point cloud; The N2P refinement module first embeds features using Conv1d(3, 128, 1), performs a K=32 nearest neighbor search on each center point, and calculates scaled dot product attention using 4-head attention (Q, K, and V projections are all Linear(128, 128), with each head having a dimension of 32) and performs softmax normalization. After residual connection, it regresses using Conv1d(128, 3, 1) to obtain a refined missing point cloud of 640 points. The original 2048 points are labeled 0, and the refined 640 points are labeled 1. The four-dimensional composite point cloud is stitched together as (2688, 4); the FRN displacement field branch encoder consists of Conv1d(4, 64, 1), Conv1d(64, 128, 1), Conv1d(128, 256, 1), and Conv1d(256, 512, 1) in series, all with batch normalization and ReLU. The residual block contains Conv1d(512, 512, 1) + BN + ReLU and Conv1d(512, 512, 1) + BN (Batch Normalization (batch normalization) and jump addition are performed. The decoder is successively Conv1d(512, 256, 1) + ReLU + Dropout(0.2), Conv1d(256, 128, 1) + ReLU + Dropout(0.2), Conv1d(128, 64, 1) + ReLU and Conv1d(64, 3, 1) with no activation, and outputs a displacement field of (2688, 3). Hard constraints are applied to make the displacement of points with label 0 zero, and only the coordinates of points with label 1 are finely adjusted and merged with the original point cloud to obtain the complete tower point cloud. During training, the missing generated branches are frozen, and only the AdamW optimizer (learning rate 0.001, batch size 4) is used to update the FRN branches with symmetric chamfer distance loss until convergence, which is the trained PFAR Net.

[0040] like Figure 4 As shown, in one embodiment of the present invention, the PFAR Net adopts a hierarchical architecture with two branches serially cascaded. It is composed of the upper missing region generation and N2P refinement branches and the lower FRN branches connected in series. The network sequentially completes missing region prediction, local detail refinement and splicing boundary smoothing, and finally outputs a complete tower point cloud with high geometric accuracy and natural boundary transition. The multi-scale point cloud encoder is the feature extraction entry point of the network. The input is the original tower point cloud that is determined to be incomplete by the integrity pre-detection. The encoder first downsamples the original point cloud to three spatial scales with the number of points N, N / k, and N / k² through two-level IFPS iteration downsampling of the farthest point. Then, the point clouds of the three scales are fed into the corresponding CMLP cascaded multilayer perceptron to complete point-by-point feature extraction. Simultaneously, it captures the overall outline of the tower, crossarms, diagonal braces and other geometric information at different levels, and outputs three sets of high-dimensional depth features corresponding to different scales.

[0041] The CONCAT multi-scale feature splicing layer takes three sets of CMLP output features at different scales and splices and fuses the three sets of features along the feature channel dimension. It integrates the global structural features and local detail features under different receptive fields into a unified multi-scale feature tensor, providing richer geometric representation input for the subsequent decoding and generation process, and avoiding the loss of structural information caused by single-scale features.

[0042] The MLP feature transformation layer receives the concatenated multi-scale feature tensors and performs nonlinear transformation and channel dimension regularization on the features through a multilayer perceptron. This maps the multi-source heterogeneous fused features into deep features of a unified dimension, completing the dimensional adaptation transition from the encoder to the decoder and ensuring that the input specifications of the subsequent decoding module match.

[0043] The reconstruction decoder is one of the core improvements of PFAR Net over the baseline PFNet. It replaces the original point pyramid decoder and adopts a decoding architecture consisting of linear layers, fully connected layers, and one-dimensional convolutions. Features are first mapped to the initial dimensions by linear layers, then upscaled to a 1920-dimensional feature space by FC1920 fully connected layers, and finally upsampled and regressed to three-dimensional coordinates by one-dimensional convolutional layers. This architecture effectively expands the local receptive field of the network, is more suitable for the slender and sparse structural characteristics of towers, and strictly follows the rule of predicting only missing regions, outputting a coarse-grained point cloud of missing regions with local jagged distortion.

[0044] The N2P neighborhood point attention refinement module takes over the coarse-grained missing point cloud and is the core module for improving the details of local completion. The module first uses the KNN nearest neighbor search algorithm to select K=32 spatial neighbor points for each center point in the missing point cloud to build local geometric neighborhood relationships. Then, the Multi-Head Attention mechanism is used to calculate the attention weights between the center point and each neighbor point, and adaptively weighted aggregates the geometric feature information of the neighborhood, focusing on optimizing the local morphology of sparse components such as crossarms and diagonal braces, and suppressing the jagged distortion of the coarsely generated point cloud. At the end of the module, a Residual connection is set to fuse the input coarse point cloud features with the attention-refined features to avoid the degradation problem of deep networks. Finally, the refined missing point cloud with complete details and smooth morphology is output.

[0045] The label encoding splicing transition unit is a bridge connecting the upper and lower branches. It synchronously receives the original incomplete tower point cloud and the refined missing point cloud output from the upper branch. It assigns a unified label 0 to the original observation points and a unified label 1 to the missing points generated by the network. Then, it splices the one-dimensional label as the fourth-dimensional channel with the three-dimensional spatial coordinates of the point to form a four-dimensional combined point cloud containing the source identifier of the point, providing a clear basis for determining the displacement constraints of the lower FRN branch.

[0046] The encoding segment of the FRN network consists of five layers, L1 to L5. The L1 layer is composed of three concatenated Conv one-dimensional convolutions, BN batch normalization, and ReLU activation functions. It performs preliminary feature extraction on the input four-dimensional combined point cloud, mapping the spatial coordinates and source label information to a high-dimensional feature space. L2, L3, and L4 are three consecutive convolutional encoding layers that expand the receptive field of the network layer by layer, deeply extract the geometric features at the splicing boundary, and accurately capture the coordinate deviation and density jump at the intersection of the original point and the generated point. L5 is a residual block structure that fuses shallow contour features and deep boundary features through internal skip connections, alleviating the gradient vanishing problem of deep networks and further enhancing the network's ability to capture small displacement deviations.

[0047] The decoding section of the FRN network consists of four layers, L6 to L9. The L6 layer is composed of a cascaded Conv one-dimensional convolution, BN batch normalization, and ReLU activation function. It receives the deep features output from the residual block and initiates the decoding upsampling process. L7, L8, and L9 are three consecutive convolutional decoding layers that gradually map the high-dimensional features back to the three-dimensional coordinate space and regress to obtain the corresponding three-dimensional displacement field point by point. The first two convolutional layers of the decoding section apply a Dropout regularization strategy to avoid overfitting the network on small-scale tower datasets. The last layer does not set an activation function to output continuous three-dimensional displacement offsets.

[0048] The network ultimately completes the output by merging displacement constraints and point clouds. The three-dimensional displacement field output by FRN applies hard constraints based on the label channel of the four-dimensional point cloud, forcing the displacement of the original observation point with label 0 to be zero. The actual lidar observation data is not modified throughout the process. Only the generated missing points with label 1 are fine-tuned in three dimensions to correct the geometric cracks and density jumps at the splicing boundary. Finally, the fine-tuned missing point cloud is merged with the original observation point cloud to obtain the final complete tower point cloud.

[0049] During the training phase, the network adopts a parameter isolation training strategy, fixing all network weights of the upper missing generation branch and only updating the parameters of the lower FRN branch through backpropagation. The symmetrical chamfer distance is used as the loss function to optimize the fitting effect of the displacement field, thereby decoupling the tasks of missing region generation and splicing boundary optimization, and improving the overall training stability and completion accuracy of the network.

[0050] Figure 4 The meanings of each character in the table are shown in Table 1. Table 1 Figure 4 Chinese definitions of each character

[0051] This invention first uses a structural integrity pre-detection module based on slice symmetry analysis to determine if there are structural defects in the tower point cloud. If no defects are found, the process directly proceeds to the tilt ratio estimation stage. If defects are found, the data is fed into a completion network. The completion network only predicts the point cloud of the missing region and splices it with the original input to generate a complete point cloud with restored geometry. Subsequently, the K-center robust fitting method is used to fit the central axis of the completed point cloud, and a threshold-triggered weighted fusion strategy is combined to integrate the tilt ratio estimation results before and after completion. This invention preserves the true observation of the original point cloud while restoring the missing region with high quality and eliminating splicing boundary artifacts. It robustly extracts the central axis and fuses the information before and after completion in defect scenarios, thereby reducing tilt detection errors.

[0052] In one embodiment of the present invention, a joint simulation and experimental dataset was constructed, wherein the simulation data comes from 24 pole point clouds converted from 3D models; the experimental data comes from 11 pole point clouds collected by the UAV LiDAR system, of which 3 poles have real defects and 8 poles have complete structures.

[0053] For each base original point cloud, two independent data augmentation methods were performed. The first was random augmentation, which involved random scaling, random rotation around each coordinate axis, random translation within the plane, random mirroring, adding Gaussian noise, voxel downsampling, and random deletion of some points, generating 70 distinct variants per base. The second was viewpoint missing simulation, using a spherical viewpoint model to generate 21 viewpoints on a unit sphere. Under each viewpoint, the points farthest from the viewpoint were deleted at missing rates of 10%, 20%, and 30%, respectively. The retained points were used as incomplete inputs, and the deleted points were used as ground truth, generating 63 incomplete sample pairs per base. The specific composition of the dataset is shown in Table 2.

[0054] Table 2. Dataset Composition and Function

[0055] Experimental Setup: The experiment was conducted on Ubuntu 22.04, using Python version 3.8.19 and CUDA version 11.7. Training and testing were performed using the PyTorch 2.0.0 deep learning framework in a virtual environment. The hardware configuration included an Intel Core i7-12700 F processor, an NVIDIA GeForce RTX 3090 GPU, and 32GB of RAM. The AdamW optimizer was used, with an initial learning rate of 0.001 and a batch size of 4.

[0056] The evaluation metric used in this invention is the chamfer distance of the missing region, which is used to evaluate the point cloud completion quality and is defined as the average nearest distance between the generated point cloud and the actual missing region point cloud. Pre-detection performance evaluation: To verify the effectiveness of the integrity pre-detection method based on slice symmetry analysis proposed in this invention, tests were conducted on the entire dataset. The pre-detection output was either complete or incomplete, with real complete samples being the positive class. The performance metrics obtained from the tests are summarized in Table 3.

[0057] The pre-detection method achieved zero false negatives for complete samples on the simulation dataset, correctly identifying all 1680 real complete point clouds; on the experimental dataset, the number of false negatives for complete samples was 2. Regarding false positives, 97 incomplete samples were misclassified in the simulation dataset, and 50 incomplete samples were misclassified in the experimental dataset. Analysis shows that the main reason for false positives is that points within certain slices may be completely deleted during the creation of incomplete point clouds, leading to misclassification.

[0058] In terms of overall performance, the proposed method achieves an accuracy exceeding 96% and an F1 score exceeding 95% on both datasets, with a recall rate close to 100% for complete samples. This indicates that the pre-detection method can reliably distinguish between complete and incomplete point clouds, and almost never mistakenly feeds complete point clouds into the subsequent completion network. In summary, the proposed pre-detection method has high practical value and can be used as a pre-screening module for completion networks.

[0059] Table 3 Integrity Pre-detection Performance Indicators

[0060] Correlation verification was conducted to examine the relationship between point cloud completion quality and tower tilt detection accuracy. Pearson correlation analysis and Spearman rank correlation analysis were performed on the chamfer distance (CD) of the missing region obtained by different methods at different missing rates in comparative and ablation experiments, and the corresponding absolute deviation of tilt measurement. The Pearson correlation coefficient was 0.67144, with a p-value of 0.00613; the Spearman rank correlation coefficient was 0.69286, with a p-value of 0.00419. Both correlation coefficients reached a moderately strong level, and the p-values ​​were both less than 0.01, indicating that the positive correlation between CD and tilt error is statistically significant. The scatter plot shows that as the CD value decreases, the tilt error generally shows a decreasing trend, and approximately 45% of the error variation can be explained by changes in completion quality. These results empirically demonstrate that point cloud completion quality directly affects the accuracy of tilt detection: the more accurate the recovery of the missing region, the lower the tilt measurement error. This verifies the rationality of the detection framework after completion in this invention.

[0061] Comparative Experiments: To evaluate the performance of PFAR-Net in the pole point cloud completion task, three representative deep learning point cloud completion methods were selected for comparison: PMP-Net (Point Moving Paths Network), GRNet (Gridding Residual Network), and FoldingNet (Folding Network). All methods used the same dataset partitioning and training parameters, and were uniformly evaluated on the test set. To ensure fairness, all completed point clouds were subjected to tilt ratio detection using the KCR method (K-Center Robust Fitting Method) without employing a weighted fusion strategy. The experimental results are shown in Table 4. Direct detection of tilt errors at 10%, 20%, and 30% missing values ​​resulted in errors of 1.1203%, 1.2877%, and 1.5275%, respectively. The more severe the missing value, the larger the error, indicating that directly using the residual point cloud significantly affects detection accuracy. PMP-Net completes the incomplete function by predicting the movement path of points. It performs moderately well across different levels of missing data, with a tilt error of 1.2741% at 30% missing data. However, the ends of the crossarms in its completed result are still incomplete. GRNet uses voxelized meshes and 3D convolutions. The low-pass smoothing effect leads to severely blurred edges in the output point cloud, with a CD value as high as 17.113 at 30% missing data. Although the tilt error is as low as 0.8645%, it is due to a coincidence of the central axis and does not reflect the quality of the incomplete function. FoldingNet is based on 2D mesh folding, resulting in a ring-shaped pseudo-structure in the output, which completely fails to represent the sparse and slender characteristics of the tower. At 30% missing data, the tilt error is as high as 3.7359%, indicating that this method is ineffective. PF-Net only predicts the missing parts and retains the original point cloud, making it suitable as the base network for this invention. However, its local geometric modeling ability is limited, and there are obvious geometric cracks at the splicing interface. The improved PFAR-Net significantly outperforms the baseline in detail recovery and boundary smoothing, verifying the superiority of the network structure and the effectiveness of incomplete function in improving tilt detection accuracy.

[0062] Table 4. CD and skew detection errors of various completion networks under different missing rates.

[0063] Ablation Experiments: To verify the effectiveness of each improved module in PFAR-Net, using PF-Net as the baseline, N2P, FRN, and combinations thereof were introduced into the joint dataset for training. The CD values ​​of the baseline PF-Net at 10%, 20%, and 30% missing rates were 5.166, 4.640, and 5.156, respectively. After introducing the N2P module alone, the CD values ​​decreased to 4.584, 4.192, and 4.642, respectively. N2P effectively improved the jagged distortion in the skeleton region by enhancing local geometric modeling, resulting in a more reasonable layout of the coarse missing point cloud. After introducing the FRN module alone, the CD values ​​decreased to 3.842, 3.768, and 4.477, respectively. FRN significantly reduced the geometric gaps between the original and generated point clouds by smoothing the stitching boundaries through displacement fields, resulting in a natural transition in the stitched region. When N2P and FRN are introduced simultaneously, CD further decreases to 3.692, 3.744, and 4.328, representing reductions of 28.5%, 19.3%, and 16.1% compared to the baseline, respectively. This achieves the best balance between sparse detail restoration and smooth boundary fusion. These results demonstrate that N2P and FRN have a synergistic effect: N2P provides FRN with higher-quality coarse missing point clouds, while FRN further eliminates stitching artifacts. The combined use of both achieves optimal completion accuracy in high-impact scenarios.

Claims

1. A method for detecting the tilt of transmission towers based on point cloud completion and robust fitting, characterized in that, include: Step 1: Pre-inspection of the integrity of the tower point cloud; Step 2: Restore the missing regions of the point cloud that is determined to be incomplete; Step 3: Calculate the tilt ratio using the K-center robust fitting method on the complete point cloud; Step 4: Output the final tilt percentage based on the tilt percentage difference of the point cloud.

2. The method for detecting the tilt of transmission towers based on point cloud completion and robust fitting according to claim 1, characterized in that, Step 1 includes: Step 1.1: Align the main axis and normalize the height of the input tower point cloud, and construct a symmetrical reference plane with the direction of the second principal component as the normal vector; Step 1.2: Slice the point cloud along the elevation direction with a fixed step size to obtain several slice point sets; Step 1.3: Calculate the signed vertical distance of each point in each slice point set relative to the reference plane, count the number of points on both sides of the plane, and calculate the symmetry ratio; Step 1.4: Determine the integrity of the tower point cloud; If the cumulative height of the longest consecutive slice interval satisfying the elevation slice symmetry ratio <0.6 exceeds 0.9m, the cumulative height of all slices with an elevation slice symmetry ratio <0.6 accounts for more than 20%, or the proportion of extremely asymmetrical slices satisfying the elevation slice symmetry ratio <0.3 exceeds 8% and the average symmetry ratio of the entire tower is less than 0.85, then the point cloud is determined to be an incomplete tower point cloud and step 2 is executed; otherwise, the tower point cloud is considered complete and step 3 is executed.

3. The method for detecting the tilt of transmission towers based on point cloud completion and robust fitting according to claim 1, characterized in that, Step 2 includes: Step 2.1: Perform multi-level iterative downsampling of the farthest point and point-by-point feature extraction on the original tower point cloud that is determined to be incomplete by the integrity pre-detection. Transform the geometric information of the overall outline of the tower and the local components of the crossarm and diagonal brace into multi-scale high-dimensional depth feature vectors to complete the encoding of the geometric information of the original point cloud. Step 2.2: First, perform dimensionality compression on the multi-scale high-dimensional depth feature vector, then complete feature upsampling and three-dimensional coordinate regression to generate a coarse missing point cloud with jagged distortion and uneven spatial distribution. Step 2.3: After processing the coarse missing point cloud, a refined missing point cloud is generated; Step 2.4: Assign differentiated labels to the original tower point cloud and the refined missing point cloud. The original tower point cloud is uniformly labeled with label 0, and the refined missing point cloud is uniformly labeled with label 1. The one-dimensional label is used as the fourth-dimensional channel and spliced ​​and fused with the three-dimensional coordinates of the point cloud to generate a four-dimensional combined point cloud that simultaneously contains spatial coordinates and point source identifiers. Step 2.5: Apply hard displacement constraints to the four-dimensional combined point cloud, forcing all original observation points with a label value of 0 to have their displacements reduced to zero, and only applying coordinate fine-tuning to the generated missing points with a label value of 1, finally outputting the three-dimensional displacement field of each point in the corresponding combined point cloud. Step 2.6: Apply the displacement offset to the refined missing point cloud to obtain the set of missing points after coordinate fine-tuning and smoothing. Keep the original tower point cloud coordinate values ​​unchanged, and perform a set union operation on the original observation point cloud and the fine-tuned missing point cloud to obtain the final complete tower point cloud.

4. The method for detecting the tilt of transmission towers based on point cloud completion and robust fitting according to claim 3, characterized in that, Step 2.3 includes: Step 2.3.1: First, use adaptive convolution to map the 3D coordinates of the coarse missing point cloud to a high-dimensional feature space to generate a deep feature tensor; Step 2.3.2: For each center point, the K-nearest neighbor algorithm is used to filter spatial neighbor points. The local correlation between the center point and the neighbor points is calculated with the help of two sets of learnable linear projection layers, Q and K. Then, the attention weights corresponding to each neighbor point are obtained through normalization. Step 2.3.3: Use the V linear projection layer to perform weighted aggregation of neighborhood features to obtain refined features of the center point; Step 2.3.4: Map the refined features back to the three-dimensional coordinate space, eliminate jagged edges and hole distortions at sparse components of the tower, and output the refined missing point cloud with improved detail accuracy.

5. The method for detecting the tilt of transmission towers based on point cloud completion and robust fitting according to claim 1, characterized in that, Step 3 includes: Step 3.1, Discretization of tower point cloud elevation direction slices: Discretize the input point cloud into multiple overlapping horizontal slices along the elevation direction, and filter the valid slices by the number of points threshold; Step 3.1.1: Set the slice thickness and step size according to the tower pitch and point cloud density; Step 3.1.2: Generate several horizontal slices sequentially along the elevation direction. Perform point count verification on the point set of each slice. If the number of points in a slice is less than a preset threshold, it is determined to be an invalid slice and is skipped. The point set data of all valid slices are retained. Step 3.2, Extraction of the center point of the slice tower body based on KMeans clustering: Perform clustering operation on the planar coordinates of each valid slice, calculate the center of the slice tower body by the geometric mean of the cluster centers, and obtain the sequence of center points in the elevation direction; Step 3.2.1: Read the point set of each valid slice in sequence, extract the XY plane coordinates of all points, perform KMeans clustering operation on the two-dimensional coordinate set, set the number of clusters and fix the random seed, and obtain the cluster center after the operation; Step 3.2.2: Take the geometric mean of the cluster centers as the tower center point of the current slice. After traversing all valid slices, obtain the tower center point sequence arranged in order of elevation. Step 3.3, RANSAC robust linear fitting and slope ratio calculation: Step 3.3.1: Receive the sequence of tower center points sorted by elevation, and use the RANSAC random sampling consensus algorithm to perform spatial straight line fitting on the sequence to obtain the direction vector of the central axis, and select two points A and B on the fitted line; Step 3.3.2: Calculate the horizontal offset and tower height based on the coordinates of the two points respectively; The horizontal offset is the projection length of vector AB on the horizontal plane, and the tower height is the projection length of vector AB in the vertical direction. Step 3.3.3: Calculate the tower tilt ratio and tilt percentage.

6. The method for detecting the tilt of transmission towers based on point cloud completion and robust fitting according to claim 1, characterized in that, Step 4 includes: outputting the final tilt percentage q based on the tilt percentage difference Δq of the point cloud using a three-segment rule. final : If Δq≤0.1%, then q final =q comp ; If 0.1% < Δq ≤ 0.5%, then q final =0.3×q orig +0.7×q comp ; If Δq > 0.5%, then q final =min(q) orig q comp ); The percentage difference in tilt of the point cloud is Δq = |q comp -q orig |; Where, q orig q is the tilt percentage based on the original residual cloud. comp This represents the tilt percentage based on the completed point cloud.

7. A transmission tower tilt detection system based on point cloud completion and robust fitting, characterized in that, The method for detecting the tilt of a transmission tower based on point cloud completion and robust fitting as described in any one of claims 1 to 6 includes a tower point cloud integrity pre-detection module, a PFAR Net point cloud completion module, a K-center robust fitting tilt calculation module, and a threshold-triggered weighted fusion output module connected in sequence. The tower point cloud integrity pre-detection module is connected to the K-center robust fitting tilt calculation module.

8. The transmission tower tilt detection system based on point cloud completion and robust fitting according to claim 7, characterized in that, The tower point cloud integrity pre-detection module consists of a main axis alignment and height normalization unit, an elevation slice division unit, a slice symmetry ratio calculation unit, and an integrity judgment unit connected in series. The main axis alignment and height normalization unit first performs main axis alignment and height normalization processing on the input tower point cloud, and constructs a symmetry reference plane with the direction of the second principal component as the normal vector. The elevation slice division unit divides the point cloud into several slice point sets along the elevation direction with a fixed step size, and decomposes the three-dimensional tower structure into multiple horizontal slices. The slice symmetry ratio calculation unit sequentially calculates the signed vertical distance of each point in each slice relative to the symmetry reference plane, counts the number of point clouds on both sides of the reference plane and calculates the symmetry ratio, and quantifies the degree of symmetry of the point clouds at each height layer. The integrity determination unit outputs the final determination result based on three types of preset determination rules. If the point cloud is determined to be incomplete, it is sent to the PFAR Net point cloud completion module; otherwise, it is determined to be complete and directly sent to the K-center robust fitting tilt calculation module.

9. The transmission tower tilt detection system based on point cloud completion and robust fitting according to claim 7, characterized in that, The PFAR Net point cloud completion module is composed of missing region generation and N2P refinement branch, label encoding splicing transition unit, and FRN branch connected in series. The missing region generation and N2P refinement branch includes a multi-scale point cloud encoder unit, a multi-scale feature stitching and transformation unit, a reconstruction decoder unit, and an N2P neighborhood point attention refinement unit. The multi-scale point cloud encoder unit downsamples the original point cloud to three spatial scales through two-level iterative point downsampling, and then performs point-by-point feature extraction through a cascaded multilayer perceptron, simultaneously capturing multi-scale geometric information of the overall outline of the tower and local components. The multi-scale feature stitching and transformation unit first stitches three sets of depth features at different scales along the feature channel dimension, and then performs feature dimension regularization and adaptation through a multilayer perceptron, integrating global structural features and local detail features into a unified multi-scale feature tensor. The reconstruction decoder unit adopts an architecture of linear layers, fully connected layers and one-dimensional convolutions in series to complete feature upsampling and three-dimensional coordinate regression, generating a coarse-grained point cloud of missing regions with local jagged distortion. The N2P neighborhood point attention refinement unit selects spatial neighborhood points for each center point through the K nearest neighbor algorithm, calculates local correlation and attention weights with three sets of linear projection layers (Q, K, V), adaptively weights and aggregates neighborhood geometric features, and outputs a refined missing point cloud with smooth details. The label encoding and splicing transition unit splices and merges the one-dimensional label as the fourth-dimensional channel with the three-dimensional coordinates of the point cloud to generate a four-dimensional combined point cloud with point source identifiers; The FRN displacement field fusion refinement branch includes an encoder feature extraction unit, a residual block feature enhancement unit, a decoder displacement regression unit, and a displacement constraint and point cloud fusion unit; The encoder feature extraction unit consists of four convolutional layers connected in series, which expand the network's receptive field layer by layer, deeply extract the geometric features at the splicing boundary, and capture the coordinate deviation and density jump at the junction of the original point and the generated point. The residual block feature enhancement unit fuses shallow contour features and deep boundary features through internal skip connections; The decoder displacement regression unit consists of four convolutional layers. After the first two convolutional layers, a Dropout regularization strategy is applied to gradually map the high-dimensional features back to the three-dimensional coordinate space, and the regression yields the three-dimensional displacement field corresponding to each point. The displacement constraint and point cloud fusion unit applies hard displacement constraints based on the label channel of the four-dimensional point cloud, forcing the displacement of the original observation point with label 0 to be zero. Only the generated missing points with label 1 are subjected to three-dimensional coordinate fine-tuning to correct the geometric cracks at the splicing boundary. Finally, the fine-tuned missing point cloud is merged with the original observation point cloud to output a geometrically continuous and crack-free complete tower point cloud.

10. The transmission tower tilt detection system based on point cloud completion and robust fitting according to claim 7, characterized in that, The K-center robust fitting tilt calculation module consists of an elevation slice discretization unit, a KMeans cluster center point extraction unit, and a RANSAC robust linear fitting and tilt calculation unit connected in series. The elevation slice discretization unit discretizes the input point cloud into multiple overlapping horizontal slices along the elevation direction, setting the slice thickness to be greater than the step size, and filtering out sparse and invalid slices through a point count threshold; the KMeans clustering center point extraction unit performs KMeans clustering operation on the XY plane coordinates of each valid slice, sets the number of clusters and fixes the random seed, takes the geometric mean of the four cluster centers as the tower center point of the current slice, and obtains the tower center point sequence arranged in elevation order after traversing all valid slices; the RANSAC robust linear fitting and tilt calculation unit uses the random sampling consensus algorithm to perform spatial linear fitting on the center point sequence, automatically removes local outlier center points, and after fitting the direction vector of the tower's central axis, calculates the horizontal offset and vertical tower height based on two points on the central axis, and finally derives the tower tilt ratio and tilt percentage; The threshold-triggered weighted fusion output module includes a dual-path tilt percentage calculation unit, a difference calculation unit, and a three-segment rule output unit connected in sequence. The dual-path tilt percentage calculation unit simultaneously calculates the tilt percentage based on the original incomplete point cloud and the tilt percentage based on the completed point cloud; the difference calculation unit calculates the absolute difference between the two tilt percentages; the three-segment rule output unit executes the corresponding output strategy according to the three threshold intervals of the difference to obtain the final tilt percentage result.

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