A point cloud segmentation method for power lines and towers based on a combination of multiscale density features and point-based deep learning

ABSTRACT The point segmentation of power lines and towers aims to use unmanned aerial vehicles (UAVs) for the inspection of power facilities, risk detection and modelling. Because of the unclear spatial relationship between the point clouds, the point segmentation of power lines and towers is challenging. In this paper, the power line and tower point datasets are constructed using Light Detection and Ranging (LiDAR) and a point segmentation method is proposed based on multiscale density features and a point-based deep learning network. First, the data are blocked and the neighbourhood is constructed. Second, the point clouds are downsampled to produce sparse point clouds. The point clouds before and after sampling are rotated, and their density is calculated. Next, a direct mapping method is selected to fuse the density information; a lightweight network is built to learn the features. Finally, the point clouds are segmented by concatenating the local features provided by PointCNN. The algorithm performs effectively on different types of power lines and towers. The mean interaction over union is 82.73%, and the overall accuracy can reach 91.76%. This approach can achieve the end-to-end integration of segmentation and provide theoretical support for the segmentation of large scenic point clouds.


Introduction
Transmission facilities are crucial for the power system and are the lifelines of electric energy transportation required for national production and life.Power lines and towers undergo long-term exposure to the natural environment, with air as the insulator.These equipment are always affected by environmental factors such as sunlight, pollution and strong winds.To ensure the safe and continuous long-distance transmission of electric energy, the power operation department has invested a lot of workforce and material resources for the periodic inspections of transmission facilities (Zhou, Zhai, and Jiang 2018;Lou et al. 2019;Lai et al. 2014;Chen, Chang, and Zhao 2022).The traditional approach mainly encompasses manual ground inspection, which is time-consuming and laborious.Assessing 'blind areas', such as canyons and swamps, presents inconveniences and challenges for personnel in meeting the needs for the rapid construction and development of power facilities (Mills et al. 2010).The advancement of sensors has driven the rapid expansion of high-resolution remote sensing technology.Power inspection methods based on satellite remote sensing images (Kobayashi et al. 2009;Xu et al. 2016), synthetic-aperture radar images (Deng et al. 2012;Yang et al. 2006), aerial images (Zhao, Lei, and Wang 2019;Jóźków, Vander Jagt, and Toth 2015), thermal infrared images (Zhang et al. 2014;Jadin, Ghazali, and Taib 2013), light detection and ranging (LiDAR), and other remote sensing technologies have emerged with time (Lin et al. 2016;Liu, Zheng, and Xu 2017).The unmanned airborne LiDAR technology can collect high-precision and high-density three-dimension spatial information of the transmission facilities after one flight without switching off the power supply (B.Yang, Liang, and Huang 2017).Point clouds offer distinct advantages over other remote sensing methods because they can directly retrieve the 3D information of ground objects (Liu, Zheng, and Xu 2017;Matikainen et al. 2016).They have become a prominent hotspot in the research of the intelligent inspection of transmission facilities and digital power grid management.
However, the use of point clouds is problematic.Point clouds are embedded in continuous space, unlike the images arranged on a regular pixel grid.This occurrence makes point clouds structurally different from the images, making it difficult to migrate them and directly apply standard computer vision methods.To address this concern, several types of deep learning methods using point clouds, such as voxel space for the application of discrete convolution, have emerged (Maturana et al. 2015;Song et al. 2017).However, this pursuit causes huge computing and memory costs and the underutilisation of point sparsity.Sparse convolution networks ease these limitations by operating only on non-empty voxels (Graham et al. 2018;Choy et al. 2019).Some networks work directly at point clouds and propagate information via pooling operators (Qi et al. 2017;Qi et al. 2017) or continuous convolutions (Wang et al. 2018;Thomas et al. 2019); they can also implement point transformers using self-attention networks (Zhao et al. 2021).Another series of methods connect point clouds to the diagram for passing messages (Wang et al. 2019;Li et al. 2019).These deep learning methods have produced unique results in point cloud classification and segmentation (Tang et al. 2022;Lai et al. 2022).
Extracting point clouds in power lines and towers is the foundation of intelligent power inspection.Power lines and towers are prominent and special structures of surface objects.Investigating the extraction methods of these objects can significantly enrich the fields of point cloud utilisation and inspire the extraction of many similar objects, such as roads, communication towers, among others.For the power lines, some studies apply elevation histograms for calculating the elevation distribution information of local point clouds based on the elevation characteristics of power line point clouds.Power line point clouds are classified as point clouds whose elevation difference from the corresponding local terrain point clouds exceeds the segmentation threshold (Liu, Zheng, and Xu 2017;Wang et al. 2017).Chen et al. proposed extracting power line point clouds using a line detection algorithm while projecting the roughly extracted candidate power line point clouds to the XY plane.They then used the twodimensional Hough transform to obtain the power line point cloud corresponding to the line (Chen et al. 2015;Liu et al. 2009).These methods based on 2D line detection are vulnerable to the effects of linear objects, such as buildings and roads, and have poor adaptability in complex environments.Yu et al. first performed point cloud filtering using a triangulation encryption filtering algorithm.Next, they removed vegetation point clouds by applying point cloud echo information and elevation distribution characteristics, ultimately completing the power line extraction (Yu et al. 2011).This 3D line feature extraction method requires previous knowledge, such as the number of lines.The extraction efficiency and accuracy are easily affected by point cloud noise and integrity.Liang, Ma, and Cai (2019) proposed a power line extraction algorithm based on a support vector machine (SVM), which combines the advantages of statistical analysis and supervised classification (Liang, Ma, and Cai 2019).This supervised method can better tackle the problem of missing line point clouds and poor accuracy of overlapping extraction in the vertical direction.However, this method does not have a high degree of automation, and the extraction results must be further processed via singleline point segmentation.Yang et al. suggested extracting the dimensional features of point clouds for power tower extraction to recognise similar cylindrical features (B.Yang and Dong 2013).Guan et al. proposed using an onboard laser radar measurement system to collect data and ground point clouds via filtering and then divide them into blocks before using voxel model detection to classify buildings and rods (Guan et al. 2016).Lai et al. presented an algorithm based on the density characteristics of point clouds to extract power towers but ignored the impact of vegetation on the algorithm (Lai, Qin, and Lu 2016).Ye et al. first processed the point clouds via the open operation in image processing and then applied k-means clustering to locate and extract the power tower (Ye, Liu, and Hu 2010).Zhang et al. used statistical methods to create a spatial hash matrix to store the point clouds following noise removal.Then they identified the power tower point clouds by calculating the local distribution characteristics of point clouds in each hash matrix and analysing the grid characteristics in the horizontal and vertical directions (Zhang et al. 2019).Zhao et al. extracted tower point clouds, including density, elevation histograms, terrain elevation distribution and characteristic elevation distribution, by statistically determining the spatial distribution of point clouds in the transmission corridor (Zhao et al. 2019).Tan et al. applied the k-dimensional tree (KD-Tree) segmentation method, a regiongrowing algorithm, and random sample consensus (RANSAC) for the coarse and fine extraction of power tower point clouds (Tan et al. 2021).Wang et al. utilised the spatial, topological and geometric distribution features of point clouds to extract communication towers (Wang et al. 2022).These methods generally adopt the practice of establishing artificial features.Even with high extraction accuracy, the applicability and accuracy of these methods are significantly reduced when objects are inconsistent with previous knowledge and insignificant features in the data.
The abovementioned studies show that these methods are often aimed at one specific object, some evident features of which are used to construct the extraction models with a good segmentation effect for objects with prominent features.However, they are relatively independent.Every time a power facility needs to be extracted, a new algorithm must be investigated, significantly reducing the method's applicability and increasing redundancy.Moreover, the algorithms often concentrate on independent objects with complete and clear structures as the research objects to achieve excellent performance.There are limitations in extracting objects: poor data quality, complex background environments, and/or missing structures in production.Deep learning is an excellent tool for solving the problems defined above.This method is not limited to the specific characteristics of the object and can achieve the end-to-end segmentation of multiple classes.It offers excellent advantages in extracting power lines and towers, which are strongly associated with one another.Among all kinds of deep learning methods for processing point clouds, the point-based model has lower computational complexity, less noise error and can directly achieve feature information from point clouds.In addition, CNNs are derived from image algorithms, and their principle is intuitive and easy to understand and construct.Thus, this method is one of the cornerstones of automatic point classification and segmentation research.
This paper takes power lines and power towers as the core research objects.It should be noted that the power lines described in the subsequent sections constitute the collections of various types of bundled lines and other devices on the lines.The power tower includes the tower body and the different types of equipment on it.The premise for this definition is that this paper focusses on multiple classes of segmentation in a large scene to develop end-to-end power lines and towers to be extracted simultaneously.Small structures are not the primary objects, and the possibility of precise extraction is limited for poor-quality data.This study proposes a deep learning method based on multiscale density features: first, the point clouds were blocked, and the neighbourhood system was constructed.Then, the point clouds were downsampled in every neighbourhood and were rotated before and after sampling.Moreover, the density was calculated, the density information was fused from sampling and rotation, and the algorithm was trained with a lightweight network to attain the multiscale density features and, finally, the local features provided by PointCNN were combined to segment the point clouds of the power lines and towers.This paper primarily aims to achieve the simultaneous extraction of these two objects from data of limited quality in complex environments under their common structural density characteristics and relatively ideal results.The proposed model is intuitive and lightweight.It provides a methodological basis for broad applications in practical production.

UAV point cloud data
The point cloud data used in this paper relied on the QLiDAR-H200H1C unmanned airborne point cloud and image-integrated data acquisition system.This system was mounted on a DJ M600 multirotor UAV operating at a wavelength laser of 905 mm at frequencies of 10 and 20 Hz.The data acquisition area was mainly distributed in the rural regions of Yongchuan and Fuling Districts, Chongqing, China, in July 2020 and October 2021.The effective acquisition length was about 200 km, and the acquisition objects were transmission corridors operating at 220 and 550 KV.Six datasets were used in this study based on the collected point cloud data after screening and framing (Figure 1).Table 1 presents the specific parameters of the data.The point clouds in these sections primarily include power lines, power towers (it should be noted that some data also include 220-V telegraph poles (Figure 1(g2)), which also appear with the power lines but are not the segmentation objects of this paper), and other surrounding objects (primarily vegetation, buildings and roads), and take the power transmission corridor as the data's centre line.Clear topographic relief can be observed because of the large relative height difference among the data collected in the mountainous rural areas; moreover, these areas have lush vegetation and few buildings.In contrast, the point clouds collected in cities and towns are relatively flat and open, with concentrated artificial objects (e.g.buildings and roads) and dense power transmission facilities.

Characteristics of power line point clouds
(1) The power lines are natural hanging lines with a linear distribution of point clouds, which usually run through the whole data area and have strong extensibility.(2) The power lines have straight and parallel projections between two adjacent towers in the horizontal direction.The power lines in the same corridor will not intersect, but power lines are crossing between different corridors.The elevations of power line point clouds are effectively the same in a small, local area.(3) Generally, the area above the power lines is not covered by other ground objects, and the power line information is primarily concentrated in the first echo of point clouds.

Characteristics of power tower point clouds
(1) Various types of power towers, primarily made of metal, are dominated by four prisms and use tripod network structures with a particular plane area inside.(2) There is a sizeable local elevation difference in the elevation direction, which is significantly higher than the vegetation and buildings below the power towers.It has continuous and regular distribution in the elevation direction.
(3) The internal structure is relatively complex, with more echo signals.

Density characteristics
Point density is a crucial feature of point cloud data.Making full use of density features is a common objective of point cloud object extraction.The point density can be defined as the number of point clouds in an area sampled divided by the ground surface (Heideman 2014).The point cloud density used in this paper is the number of point clouds per square meter (pts/m 2 ).In general, the denser the point cloud, the more specific the object's shape.In contrast, the thinner the point cloud, the more blurred the object's shape.However, the fuzziness of the shape and structure is different for some specific objects.Figure 2 shows that the same power tower point clouds were sampled four times.The characteristics of the tripod nets inside the power tower quickly disappear with the continuous reduction in the point density.However, the main structure of the tower and the basic structure of the tower's shoulder still exist.The objects can still be quickly identified through these structures.The power line has a simple structure.There are no more point clouds to describe the detailed characteristics, and the point cloud has a uniform density.With the gradual thinning of the point clouds, the shape of the power line effectively does not change, and the primary structure is still visible.These features were defined whose shape varies a little with the decrease in the point density as structural features.In contrast, other characteristics used to describe the details of objects are defined as unstructured features.However, the standard deep learning point cloud model has a relatively strong ability to mine the local correlation between point clouds.It is more inclined to mine their local non-structural features for dense point clouds; moreover, utilising the overall structural features becomes relatively complex (Tatebe et al. 2017;Tatebe et al. 2018).Conversely, sparse point clouds have many advantages in this regard: a high degree of retention of their structural features, a low density of point clouds, the filtering of detailed information and greater ease of extracting their structural features.
The point density variation characteristics of an object can be determined by rotating it; for example, the rotation of a block from the power tower point cloud (Figure 3) along the distribution direction of structural points.The variation range of point density is small because the direction of the main structure is compatible with the direction of the rotation axis, with a relatively uniform distribution of these points.However, the distribution of other points during rotation depicts significant variability; therefore, the density of these point clouds changes more dramatically, which is more evident in the sparse point clouds (Yan et al. 2020).These structural and unstructured features can be divided using the difference in the point cloud densities before and after rotation.

Data preprocessing
Due to the large area of the point cloud scene where the power transmission facilities are located, if the entire point cloud is directly input into the extraction model, it will cause severe computational burden and disrupt network training.Therefore, the primary purpose of data preprocessing is to restrict the large area of point clouds so that the model can operate normally and enhance its operational efficiency.The convolution layer can obtain high-dimensional information in the sampling process.The preprocessing includes two steps: dividing the large-scale point clouds into blocks with regular size and no overlapping area, and establishing neighbourhood systems in every block.The subsequent operations are conducted based on these neighbourhoods.

Data blocking
Data blocking lowers the computational load and is necessary for the subsequent construction of neighbourhood systems.This neighbourhood system uses the KNN algorithm (Coomans and Massart 1982), which sets a search radius r to traverse point clouds at a particular range.The range was set for each block.When there is no point less than r in the block, the next block is entered for the next round of traversal.However, if the point cloud in some areas is sparse, or if the density of the point cloud is reduced after downsampling and there is no data block, KNN may only search in a local area.It can no longer search when the point spacing exceeds r (Figure 5).
The blocks were set as cuboids, and the S-shape was used to traverse the point cloud space for blocks (Figure 6a).The size of the blocks should be adapted to the point space's size (i.e. the minimum circumscribed cube of all point clouds) and the shape of the segmentation objects.Because of the large length and small height of the point cloud space in question, the power lines are treated as objects with strong horizontal extensibility.Therefore, the length and width of the blocks are defined as one-hundredth of the point space boundary.The block height is one-30th of the point height boundary in the point space with a significant height difference.In contrast, in the point cloud space with a slight height difference, the block height is one-tenth of the height of the point clouds, which can ensure a relatively uniform block size.For example, for the data of No. 2 and No. 3 in Table 1, the sizes of the point clouds were 1020.1 m × 481.9 m × 197.8 and 1020.5 m × 450.5 m × 73.5 m, respectively.On the contrary, the block sizes were 10.2 m × 4.8 m × 6.6 and 10.2 m × 4.5 m × 7.4 m, respectively.Following division, the blocks without point clouds are deleted directly.Via blocking, the data of different sections can be divided into multiple fixed areas for the subsequent construction of neighbourhoods.

Construction of the neighbourhood system
The KNN clustering algorithm combined with KD-Trees (Kanungo et al. 2002) could effectively build a neighbourhood system.First, the first point is taken in one block as the starting point,  and the nearest k-point clouds are searched around this point.The first k−1 point and the starting point are combined into one neighbourhood (KD-Tree block).Next, the k-th point is used as the starting point of the following combination until the number of point clouds in the block is less than the threshold k (Figure 6b).All objects in the point cloud space are divided into multiple neighbourhoods.Each neighbourhood has equal number of point clouds, but has different sizes.The structure is simple and clear with a uniform point density of the structural features, and the neighbourhood size is large and uniformly distributed.The density of point clouds on the unstructured features changes considerably, which have complex structures and small and dense neighbourhoods (Figure 6c).

Extraction of density features
Based on previous knowledge, such as the change law of density features provided in Section 2.3, the basic idea of extracting density features is to determine the density of sparse point clouds after downsampling (with obvious structural features) and the density of the original dense point clouds (with rich unstructured features) to build multiscale density information.Then, the proposed method aims to use a lightweight network to extract features, followed by combining structured and unstructured characteristics to enhance the local spatial correlation of point clouds.This process mostly includes downsampling, data rotation, density calculation and feature fusion (Figure 7).

Data downsampling and rotation
The power tower and power line point clouds in the origin cloud are relatively dense; hence, it is not easy to define their structural information.Therefore, the original data must be downsampled to reduce their density.In this study, the random downsampling method was selected.After downsampling, two parts of point clouds P and P', with different densities, can be determined, representing the dense point clouds and sparse point clouds, respectively.To facilitate the subsequent feature fusion, it is also necessary to record the position (i.e.index) of each sampling point in these two parts, which are recorded as Index and Index', respectively.It is noteworthy that the neighbourhood system before and after sampling will no longer change, although the density of the point clouds has changed.The sparse point clouds fully inherit the blocks and neighbourhoods of the original clouds so that the subsequent density calculation standards are unified.The rotation operation takes the z-axis of the point clouds as the rotation axis at any angle.It rotates P and P' counterclockwise around the rotation axis to obtain R P and R P , respectively.The specific calculation method is shown in Formulae (1) and (2): where z (u) represents the counterclockwise rotation around the z-axis along the angle θ, P is the origin cloud, R P is the origin cloud after rotation, and the point clouds after downsampling are the same.

Density calculation
The external shape features and internal structural features of an object are relatively independent (Lecun, Bengio, and Hinton 2015), and density information can be used to categorise these features.
Several methods can be used to calculate the point cloud density.This paper defines the number of point clouds per unit area as point density.First, the three-dimensional space plane equation of each neighbourhood is constructed, and the calculation method is expressed as follows: where A,B, C, and D represent the constants describing the space.x, y and z are the coordinate values of a point.Any three point clouds a (x1, y1, z1), b (x2, y2, z2), and c (x3, y3, z3) in the neighbourhood can be selected for elimination to determine the constant.Then, for other point clouds in the neighbourhood that are not on the plane, the projection of these point clouds can be calculated on the plane (through the intersection of the vertical line of the point and the plane).The minimum circumscribed rectangle of these coplanar point clouds is constructed as the range of density calculation (Figure 8), and the point density is calculated using the following formula: where D P i represents the density of a neighbourhood, n i is the number of point clouds in the neighbourhood, and s i represents the area of the minimum circumscribed rectangle of a plane point and projection point in the neighbourhood.This density calculation method is intuitive in principle and simple in operation.It directly uses the results of neighbourhoods, enabling it to effectively reduce redundancy and increase the efficiency of the entire model.The point clouds in the same neighbourhood share the same density value.The area of the circumscribed rectangle can vary; however, there is an equal number of point clouds in the neighbourhood of the same region.A circumscribed rectangle created by densely distributed point clouds is small, whereas one formed by alienated point clouds is large.Using this density calculation method, point clouds with similar structural characteristics can be separated from other point clouds with different structures.The area of the circumscribed rectangle of the neighbourhood is only calculated in the origin clouds-the point clouds following downsampling use the same rectangle, which is convenient for subsequent fusion and can increase the intensity of density variations.If there are no point clouds in a neighbourhood of sparse point clouds, the neighbourhood's density is recorded as 0.

Feature fusion
Using the above operations of downsampling, rotation and density calculation, four density features are obtained: the origin density D P , origin density after rotation D RP , sparse point density D P and sparse point cloud density after rotation D RP .All these features are one-dimensional.To further combine them with the local features of point clouds provided by PointCNN, the density features must be fused to achieve multiscale information.D P with D P can be connected to obtain the multiscale density, and D RP can be fused with D RP' to determine the multiscale density after rotation.
Many methods can be applied to fuse the features of point clouds with different densities, such as descriptor interpolation based on the distance between adjacent point clouds (Figure 9a).In this method, the information of a point is incorporated with its adjacent point clouds and weighted according to the distance.However, applying this method may aggregate two point cloud belonging to different classes, resulting in unstable segmentation.A direct mapping method was selected for feature fusion (Figure 9b).The fusion process is divided into two steps: first, the point clouds not in Index' from D P according to Index' are deleted so that D P and D P retain the same point clouds.Meanwhile, the indices of D P and D P ' are both Index', but their densities are different.The second step is feature fusion through the consistency of the point index.By merging the point features with the same index in D P and D P , a set of two-dimensional density features with different scales can be obtained, which are recorded as F PP .Because the point index correlation is maintained in the downsampling process, feature fusion through direct mapping will not result in redundant calculations.This process can be expressed by the following formula: (5) where Index is an index set of point clouds in D P ; Index' is an index set of point clouds in D P ; D P'new is the original cloud density information deleted from Index'; and F PP' represents the multiscale point cloud density information after fusion.In the same way, the rotated point clouds' fusion information F RPRP' can be obtained.Finally, the lightweight convolution layers are applied to train the multiscale density information, as shown below: where F d represents the high-dimensional density information after training; Conv represents the convolution layers; g represents the symmetric function of the maximum pooling layer; and D Fin represents the high-dimensional density information after the pooling layer.

Point segmentation
The extracted density information is combined with PointCNN for semantic analysis.
PointCNN is an end-to-end network that directly analyses the point clouds based on coordinates and converts coordinate information into local features via X-Convs (Li et al. 2018) (Figure 10).Density extraction and PointCNN can be used to obtain two different features: local features (n = 256) and density features (n = 1,024).Local features are present on a small scale and represent the shape of the local region of the neighbourhood.The density features come from the aforementioned density extraction, and the density extraction network is present on a large scale to analyse the topological relationship of the whole sample's blocks.A total of N instances of the density features were selected to create a matrix with the same shape (n = 1024).Then, they were stacked together as input data (n = 1280) using the concatenation layer (Formula ( 9)).In point segmentation, it is necessary to predict the category of each point in the neighbourhood.Through the convolution layer and multilayer perceptron (MLP), the output is an (N, C) matrix, where C is the category of every point (Figure 10).
where F represents the features after concatenation; Conc represents the concatenation layer; and Loc represents the local features provided by PointCNN.

Experimental setup
In this study, the data presented in Section 2.  The data of each section were recorded in the form of an n-dimensional one-hot vector (where n is the number of point clouds, [1, 0, 0,.… , 0] represents power lines, [0, 1, 0,. … , 0] represents power towers, and [0, 0, 1,.… , 0] represents other classes in turn).Data blocking and neighbourhood construction were conducted as described in Section 3.1.Table 2 shows the division details, and Figure 11 depicts the schematic diagram of these blocks and neighbourhoods.
The Ubuntu 16.04 operating system and the TensorFlow 1.6.0GPU were selected for this study.The activation function of the hidden layer uses rectified linear unit, the activation function of the output layer uses softmax, and the training process uses an Adam optimiser with an initial learning rate of 0.005.The learning parameters were optimised by dropout, batch normalisation and an exponentially decaying learning rate.All the experiments were designed and implemented using a PC with the following specifications: i9-10850k CPU at 3.6 GHz, a 10 GB RTX3080 GPU, and 128 GB memory.

Comparison of different methods
Figure 12 demonstrates the segmentation results of the power line and tower point clouds, combined with multiscale density information and local feature information from PointCNN.All objects in the test data are effectively segmented.The segmented power lines and power towers have a complete structure and a clear shape.However, some segmentations were missing for power lines with very sparse point clouds.Some false results were present at the boundaries between roads and the roofs of buildings.
PointNet was selected for comparison to verify the method's effectiveness.This model is also a commonly used point analysis method based on spatial coordinates (Qi et al. 2017).Because the maximum pooling layer is used at the end of feature extraction, the extracted features are more inclined to become the global features of point clouds.In addition, a simple comparison was also made with Point Transformer, and a point cloud extraction model of the self-attention mechanism was proposed.This algorithm designs self-attention layers for point clouds and uses these layers to create self-attention networks for scene segmentation.This method excels in general large-scale point cloud scene segmentation (Zhao et al. 2021).The effects of multiscale density features on the accuracy of object point segmentation can be further analysed by combining density features (D), local features (L), and global features (G)-that is, using PointNet (G) and PointCNN (L), concatenated density and PointNet (D + G) or concatenated density and PointCNN (D + L) and applying to the results of Point Transformer.The intersection over union (IoU) and accuracy can be used as indicators to measure the segmentation effect.The specific calculation methods are defined as follows: where TP is true positive, indicating that the ground truth (gt) is the object and the segmentation result is also the object; TN is true negative, suggesting that the gt is another class and the segmentation result is also another class; FP is false positive, demonstrating that the gt is another class, but the segmentation result is the object; and FN is false negative, showing that the gt is the object, but the segmentation result is another class.
Figure 13 shows the parts of the segmentation results.The D + L results are the most consistent with the ground truth, where the mean IoU and overall accuracy can reach 82.73% and 90.76%, respectively (Figure 14 and Table 3).Due to the mining of structural information from density features and the extraction of object details from local features, it is suitable for segmentation with  prominent structures and rich details, such as power lines and power towers (Figure 13a4, b4, c4, d4).However, missing segmentation occurs in the power lines with few point clouds because the information of the adjacent point clouds is too weak.The base point clouds are falsely segmented because the base of the power tower is seriously blocked by vegetation.Using G alone has the worst segmentation effect.Due to the limited ability of global features to describe the object-especially in the segmentation of large scenic point clouds-a lot of false segmentation (the false results of the roof and road edge under the power line are evident because maximum pooling exerts a 'compression' effect on the extracted features.Hence, the objects under the object are seriously affected) are present.Moreover, the global features do not adequately describe the details when the point clouds are sparse; therefore, it is essentially impossible to extract the complete shape of the object (Figure 13c1).Adding density features can make up for this lack of description of the relationship between point clouds to a certain extent (Figure 13c3).As a new point cloud deep learning model, the Point Transformer exhibits high segmentation accuracy, but it is not as good as D + L in terms of detail segmentation and anti-background interference (Figure 13b5).It is worth noting that all deep learning methods separate low power towers and power lines (Figure 13d1-d4) because the combination of small towers and lines is consistent with the goal, and their structures are similar.These objects are not the primary focus of the segmentation in this paper; thus, they are not taken as the ground truth (Figure 13d), but this finding also proves that the deep learning point cloud segmentation method can mine potential information.

Analysis of downsampling degree
The proposed method must downsample the original point clouds to determine the structural features of the point clouds and the density information of different scales.Choosing different degrees of downsampling will affect the final segmentation results (D + L mode).1/5th, 1/10th and 1/20th of the original data as different downsampling levels (Figure 15) and conducted model training and testing under different downsampling.Figure 16 shows relevant results, and the detailed accuracy is presented in Table 4.The segmentation results of the 1/10th downsampling scale are better   because this sampling level can effectively dilute the data without destroying the adjacency relationship between point clouds.Structural features can be determined from sparse point clouds, whereas detailed features can be obtained from dense point clouds.However, the 1/5th sampling level cannot dilute the data-the object point clouds are still dense and the density changes a little after rotation; hence, the structural features cannot be extracted.The 1/20th sampling level is too sparse for the data; consequently, the relationship between point clouds is seriously damaged, and the structural features are not prominent.Therefore, there are more false and missed segmentations, and the results are similar to those obtained using only local features.

Analysis of point intensity
The echo intensity is an essential aspect of point clouds.The echo intensity can describe the ability of objects in different media to reflect the laser.The stronger the reflection ability, the greater the intensity and vice versa.The LiDAR sensor used in this paper records the positional information of the point clouds and also determines the echo intensity (Figure 17) of each point.By adding the intensity information to the training and testing of the model, objects with similar structural characteristics but significant material differences can be distinguished.Figure 18 shows that the low poles (where the primary material of the columns is cement) are not the detection object of the power towers (where the primary material is metal); therefore, the ground truth is not labelled.The low poles are completely segmented before the intensity information is added.Still, after adding the intensity, these pole point clouds are effectively avoided, and the point clouds on the small number of poles are mainly concentrated on the metal parts at the top.The specific evaluation indicators  are shown in Table 5, demonstrating that the intensity information can effectively distinguish objects with similar structures but different materials.However, using intensity means adding one-dimensional information to the input data, which will prolong the training and testing times of the model (Figure 19), and may not apply to some tasks requiring rapid segmentation.5. Discussion and conclusions

Discussion
(1) Density is a critical feature of point clouds.In addition to reflecting the denseness of point distribution, density can also describe the structural characteristics of objects.The point clouds are downsampled step by step, and the number of point clouds providing detailed information keeps decreasing.However, the point clouds describing the essential structure can maintain a relatively complete shape; hence, the features whose shape changes little with the decrease in the point density can be defined as structural features.The degree of change in the density of these structural feature point clouds during rotation is small, and this phenomenon is more evident in sparse point clouds.Therefore, the density features of structural information can be obtained using the combination of density changes before and after rotation and different scales of point clouds.A lightweight convolution network can be selected to train and learn this feature, and applying it to point segmentation can significantly improve the accuracyespecially for objects with prominent structural and detailed features such as power towers.(3) The method combining multiscale density features with a deep learning network achieved satisfactory accuracy in segmenting power lines and power tower point clouds, but there are still some shortcomings.For example, many manual thresholds, such as how to set the size of the blocks and decide on the downsampling level, are present in the whole method.These thresholds must be determined by testing in combination with experimental data.They have certain peculiarity that hinders the application of this method in different regions and on various data from LiDAR sensors.Future works should adjust the optimal thresholds obtained by these artificial experiments to be adaptive to ensure timely adjustment for further data.

Conclusions
In this study, training and testing datasets for power lines and towers were constructed using UAV LiDAR point data (with a total of six sections), and the density characteristics of these data were analysed.The density of the point clouds located on the basic structure of the object changed slightly after rotating at different angles.In contrast, the density of the point clouds in the details changed significantly, providing a theoretical foundation for the point segmentation of the power lines and towers.
In terms of methods, a model combining multiscale density features and deep learning was proposed in this study.First, the point data are blocked, and the neighbourhood system is constructed.The subsequent operations are based on these neighbourhoods.Next, the point clouds are downsampled once to obtain the sparse point clouds.The point clouds before and after sampling are rotated, and their density is calculated.A direct mapping method is used to fuse the density information, and a lightweight network is constructed to train the features.Finally, the density information is concatenated with the local features provided by PointCNN, and the joint features are used to segment the point clouds.This method has two advantages: (1) The power lines and towers have apparent structures and rich details, making them suitable for feature mining using density.Multiscale density features can effectively distinguish the object point clouds.(2) Combined with the point-based deep learning network, the spatial relationship between point clouds can be fully described, the point classes can be further accurately segmented, and the impact of interrupted objects and noise point clouds can be well-controlled.The experiments on the test data illustrate that the proposed method has good segmentation accuracy for the objects, and this end-to-end method can achieve the synchronous acquisition of power lines and power towers with poor-quality data in complex environments.The IoU and accuracy for the power lines are 84.93% and 90.15%, respectively, whereas the IoU and accuracy for the power towers can reach 82.40% and 92.24%, respectively.The mean IoU is 82.73%, and the overall accuracy can reach 91.76%.In general, this method can fulfil the requirements of point segmentation of power lines and towers with limited data quality in actual production, achieve integrated segmentation of objects, and provide a data basis for subsequent works on topics such as dangerous point detection, 3D modelling, and point completion.However, due to data conditions and considerable difficulties in the end-to-end segmentation of multiple classes, the method has not yet reached the level of refined extraction.In the future, it will be necessary to optimise the data and the methodology further to improve the accuracy.

Figure 1 .
Figure 1.Point data: (a1-f1) Top views of the point clouds in sections 1-6.(a2-f2) The side view of point clouds in sections 1-6.(g1) Different types of power towers.(g2) Telegraph poles.(h) Different types of power lines (cross-section of bundled lines in the red box).

Figure 2 .
Figure2.Different densities of point clouds: The average densities of (a-d) are 45.8, 21.5, 9.4 and 4.5 pts/m 2 , respectively.The average densities of (e-h) are 30.6,13.1, 5.8 and 1.9 pts/m 2 , respectively (the red lines show the basic shape and structure of the objects).
3. The segmentation of power tower and power line point cloudsA point cloud segmentation strategy based on the combination of multiscale density and local features was used in this research, which can be divided into three main steps: (1) The data must be preprocessed, including blocking, using k-nearest neighbours (KNN) and k-dimensional trees (KD-Trees) to construct neighbourhoods to improve the efficiency.The subsequent operations take neighbourhoods as the basic units.(2) The sparse point cloud is obtained by downsampling the data.The point clouds are then rotated before and after sampling, and their density is calculated.The density features of the origin point clouds and the sparse point clouds before and after rotation are fused, and the multiscale density features are obtained by training a lightweight network.(3) The local features provided by PointCNN are concatenated to segment and acquire the point clouds of the power towers and lines.Figure 4 shows the detailed flow of the methodology.

Figure 3 .
Figure 3.The density characteristics of point clouds (rotating a block of the point clouds along the direction of the structural points).

Figure 4 .
Figure 4.The flowchart of the segmentation method.

Figure 5 .
Figure 5.The limitations of the KNN algorithm in the local area.

Figure 6 .
Figure 6.The flow of data preprocessing: (a) Data blocking.(b) Construction of the neighbourhood system.(c) Neighbourhoods in structural and unstructured point clouds.

Figure 7 .
Figure 7. Extraction process of density features.

Figure 8 .
Figure 8. Density calculation method: (a) Build a 3D plane and project the point clouds.(b) The area of the minimum circumscribed rectangle between the plane point clouds and the projection point clouds is the range of density calculation.

Figure 9 .
Figure 9. Two feature fusion methods: (a) Feature interpolation based on the distance between adjacent point clouds.(b) Direct mapping method for feature fusion.
Figure 10.The flow of point segmentation.
terrain.No. 5 has a sizeable relative height difference with sparse objects, and there is an interruption of the power line point clouds.No. 6 has almost no height difference with dense objects and has diverse types of power towers.Each sample point is labelled into one of nine classes (i.e.power lines, power towers, buildings, high vegetation, low vegetation, ground, roads, structures and others).Because power lines and power towers are small classes (i.e.their numbers of point clouds are far lower than the others) in the large scene, they can cause substantial sample imbalance problems, preventing the normal training of the model to train normally.Therefore, it is essential to label the sample carefully.With power lines and towers as core objects, multiple classes can be trained and predicted, and other classes can be integrated following prediction.

Figure 12 .
Figure 12.The segmentation results of the power line and power tower point clouds: (a) Ground truth of No.5's point clouds.(b) The results of No.5's point clouds.(c) Ground truth of No.6's point clouds.(d) The results of No.6's point clouds.Green point clouds are power lines, blue point clouds are power towers and grey point clouds are other classes.

Figure 13 .
Figure 13.The segmentation details of power line and power tower point clouds: (a-d) Ground truth.(a1-d1) The results of G mode. (a2-d2) The results of L mode.(a3-d3) The results of D + G mode. (a4-d4) The results of the D+L mode.(a5-d5) The results of Point Transformer.Green point clouds are power lines, blue point clouds are power towers, and the red boxes highlight the obvious false and miss segmentation.

Figure 13
Figure 13 Continued

Figure 15 .
Figure 15.The point clouds at different densities: (a) the original density; (b) 1/5th of the original density; (c) 1/10th of the original density; (d) 1/20th of the original density.Green point clouds are power lines, and blue point clouds are power towers.

Figure 14 .
Figure 14.The trends of indicators for evaluating segmentation: (a) The trend of the mean IoU.(a2) The trend of the overall accuracy.

Figure 16 .
Figure 16.The segmentation results at different densities (using the D + L mode): (a,e) the ground truth; (b,f) 1/5th of the original density; (c,g) 1/10th of the original density; (d,h) 1/20th of the original density.Green point clouds are power lines, and blue point clouds are power towers.

Figure 17 .
Figure 17.The echo intensity of point clouds.

Figure 18 .
Figure 18.The influence of echo intensity on the segmentation results (using D + L mode): (a,d) the ground truth; (b,e) model without echo intensity; (c,f) model with echo intensity.Green point clouds are power lines, and blue point clouds are power towers.
(2) The method of deep learning offer tremendous advantages in the task of point segmentation.The point-based model can particularly grasp the global and local features of point clouds and apply these features to ascertain the class of every point.It can solve the unclear spatial relationships of point clouds that affect information extraction to a certain extent.In this study, the density features identified by training were combined with the classical point-based deep learning point cloud segmentation model.Excellent results were obtained in the experiments on power lines and towers.This result provides a new approach for the point segmentation of such objects and broadens the inspection methods of power towers and lines.Compared with other conventional methods of extracting object point clouds based on artificial features, the proposed method can achieve end-to-end simultaneous extraction of multiple objects, avoid the redundancy of developing independent algorithms for characteristics, and have better adaptability to data with poor quality.This highly integrated model will be the focus of long-term research in the future.

Figure 19 .
Figure 19.The effect of echo intensity on model training time (using the D + L mode).

Table 2 .
Blocking details.Figure 11.The schematic diagram of blocks and neighbourhoods.

Table 3 .
Segmentation evaluation of different methods.

Table 4 .
Segmentation evaluation of different downsampling degrees (using D+L mode).

Table 5 .
Evaluation of the influence of echo intensity on segmentation (using the D + L mode).