Traditional methods primarily employ either unsupervised or supervised machine learning techniques, relying heavily on handcrafted features and predefined physical constraints.

Unsupervised methods, such as Principal Component Analysis (PCA), are widely used to identify linear structures such as power lines by computing dominant eigenvectors. These approaches offer high computational efficiency; however, they are sensitive to outliers and exhibit limited capacity in modeling complex spatial configurations, resulting in suboptimal performance for large-scale semantic segmentation tasks (Rejichi and Chaabane, 2015; Hui et al., 2021; Nurunnabi et al., 2012; Cao et al., 2025).

Supervised classification methods, including Random Forest (RF) (Jiang et al., 2022; Liao et al., 2022; Ni et al., 2017; Tang et al., 2023) and Support Vector Machines (SVM) (Chen et al., 2019; Zhang et al., 2013), utilize manually crafted feature vectors to perform object classification at the scene level. RF enhances robustness through ensemble learning, but suffers from limited interpretability and difficulty in distinguishing geometrically similar objects. SVM seeks an optimal hyperplane in high-dimensional feature space; however, its performance often deteriorates in multi-class segmentation scenarios due to challenges in defining consistent decision boundaries across diverse object classes (Zafar et al., 2018).

Overall, these traditional approaches are inherently constrained by their reliance on domain-specific rules and limited generalization capabilities, rendering them inadequate for modern large-scale, fine-grained monitoring of power transmission systems (Mirzaei et al., 2022; Grothum et al., 2023; Shen et al., 2024).

With the rapid advancement of 3D deep learning, point cloud semantic segmentation has achieved significant progress across a wide range of domains, including autonomous driving, digital twins, and smart grids. Deep learning-based methods can generally be categorized into point-based methods, convolution-based methods, and hybrid approaches.

Our work focuses on three-dimensional point cloud data from high-voltage transmission corridors scenario. We employ a convolutional architecture that integrates kernel point convolutions and graph-based modeling to extract point-wise semantic features. The KPConv block is implemented following the variational convolutional framework proposed in Thomas et al. (2019), and its structure is illustrated in Figure 1.

Our work focuses on three-dimensional point cloud data in high-voltage transmission corridor scenarios. We employ a convolutional architecture that integrates kernel point convolutions with graph-based modeling to extract point-wise semantic features. The KPConv block is implemented based on the variational convolutional framework proposed in Thomas et al. (2019), and its architecture is illustrated in Figure 1.

In KPConv, each convolutional kernel is composed of a set of kernel points with predefined coordinates in 3D Euclidean space. For a given input point, convolution is performed by computing weights based on its relative position to these kernel points. The input to the KPConv layer consists of both spatial coordinates and associated feature vectors. The spatial coordinates, typically represented as ( x , y , z ) , encode the geometric structure and spatial relationships among points in the cloud. Formally, a KPConv kernel is defined by a set of kernel points { p i } i = 1 I , where each p i denotes a kernel point in 3D space. These kernel points serve as learnable positions analogous to filter weights in conventional image convolution, but are distributed irregularly to adapt to the unstructured nature of point clouds. During training, the positions of the kernel points are optimized to improve feature extraction capability, allowing KPConv to capture local geometric variations more effectively than grid-based methods.

Given an input point cloud P ∈ R N × 3 and its associated features F ∈ R N × D , the kernel g convolution for a point x i can be defined as follows (Equation 1): F ∗ g x = ∑ x i ∈ N x g x i − x f i (1)

Further, it can be explained that for each input point x i , the network searches for a set of neighboring points N ( x i ) . This is typically accomplished using a nearest neighbors search, where neighbors are determined by calculating the Euclidean distance ‖ x j − x i ‖ between points and selecting the nearest n points (or within a spherical neighborhood). KPConv performs a distance-weighted convolution operation. The output feature f i ′ for each input point x i is computed as follows (Equation 2): f i ′ = ∑ j ∈ N x i ∑ k = 1 K h ‖ x j − x i − p k ‖ ⋅ f j (2)

Here, h ( ⋅ ) is a weighting function, such as a Gaussian kernel, that calculates the weight based on the distances between neighboring points x j and kernel points p k . The convolution kernel defined by the kernel points aggregates features from the neighboring points through weighted summation to produce a new feature vector. This new feature effectively captures local geometric and attribute information, representing the characteristics of the point cloud.

Additionally, to enhance the learning capability for varying object sizes, the convolution can incorporate deformable kernels. While some scholars argue that deformability has negligible effects on ALS data (Lin et al., 2021; Wen et al., 2021; Wen et al., 2020), we believe that in the context of high-voltage transmission line scenes, deformable KPConv can adapt to local geometric shapes, thus enhancing the representation of detailed features. This is particularly beneficial for capturing the significant geometric variations of objects such as power towers and buildings. Therefore, in our work, we still adopt a mixed approach as suggested by Thomas et al. (2019), Thomas et al. (2024), incorporating both rigid and deformable kernels within the overall semantic segmentation structure. The calculations and definitions for the deformable kernel features are expressed in Equations 3, 4: F ∗ g x = ∑ x i ∈ N x g deform x i − x , Δ x f i (3) g deform y i , Δ x = ∑ k < K h y i , x ̃ k + Δ k x W k (4)

Here, Δ k ( x ) represents the offsets generated by the rigid KPConv, mapping the dimension of input features to 3 K values. During training, the network simultaneously learns to generate shifts for the rigid kernel and output features for the deformable kernel, with the learning rate for the former set to 0.1 times that of the global network learning rate. After the convolution operation, nonlinear activation functions, specifically ReLU, along with batch normalization, are applied to enhance the model’s nonlinear capacity and stability.

Although KPConv can learn local features of points through direct point convolution, its neighborhood learning limitations prevent it from obtaining a broader receptive field, particularly for capturing global information. Additionally, point-wise features fail to encode relationships between objects within a scene, resulting in challenges when exploring interactions among objects. This limitation affects our task by hindering the accurate segmentation of transmission lines and other linear targets, as well as distinguishing between poles and buildings that may be obscured by vegetation. Previous work has demonstrated that incorporating global contextual information can enhance model performance for large-scale semantic segmentation tasks (Thomas et al., 2019; Huang et al., 2024). To address this issue, we introduce a Graph Edge-Conditioned Convolution (GECC) block to encode and extract features based on dependencies between global objects. Inspired by SPG and DGCNN, we designed the GECC block, illustrated in Figure 2. We construct graphs from geometric homogeneous points along line segments to capture relationships between objects. By combining segment features with point features, the network can adaptively encode local and global features, thereby achieving improved semantic predictions on the ALS dataset.

For the definition of the graph structure and embedding encoding, our process is as follows. First, for edge-conditioned convolution, we consider it as a directed or undirected graph G = ( V , E ) , where V is a finite set of vertex geometries with | V | = n and E ∈ V × V is a set of edges with | E | = m . Let I ∈ { 0 , … , I max } be the layer index in the feedforward neural network. There exists a function X l : V → R l d that assigns labels to each vertex, and L : E → R s that assigns labels to each edge. We utilize the concept of the Superpoint graph from SPG and apply an unsupervised L 0 -cut pursuit algorithm (Landrieu and Obozinski, 2017) to partition the point cloud into individual clusters. This step involves pre-computing semantic labels and predefined geometric features before training. As a result, the graph structure remains fixed, eliminating the need to update segment labels repeatedly during training, thereby avoiding unnecessary computational overhead.

Next, we construct the graph structure based on the input. Given a point cloud P with its geometric features X p (such as linearity or normal vectors), we build a directed graph G = ( V , E ) and set its labels X 0 and L as follows. We create a vertex i ∈ V for every point p ∈ P and assign the respective signal to it by X 0 ( i ) = X p ( p ) (or 0 if there are no features X p ( p ) ). Then, we connect each vertex i to all vertices j in its spatial neighborhood via a directed edge ( j , i ) . The edge-conditioned convolution can dynamically produce filtering weights Φ ( j , i ) l ∈ R d l × d l − 1 based on the edge ( j , i ) and flexibly handle varying neighborhood sizes to capture contextual information between different segments. Algorithm 1 presents the pseudocode for constructing the graph structure and computing the features using the Graph Edge-Conditioned Convolution (GECC) module. The computation of ECC is as follows (Equation 5): X l i = 1 | N i | ∑ j ∈ N i Φ j , i l X l − 1 j + b l (5)

We learn the parameters Φ ( j , i ) l from a multilayer perceptron. The edge features ( j , i ) are processed by Φ ( j , i ) l to generate a weight matrix, which is then used to perform matrix-vector multiplication with the features of neighboring nodes. Finally, the updated node features are directly backpropagated to each point, resulting in F gecc ∈ R N × C as the output of this block. Physically, this formulation enables each point to aggregate and filter geometric features from its spatial neighbors, allowing the model to learn contextual relationships based on local geometry.

Algorithm 1

GECC Block Feature Generation Algorithm.

Require: Point features F in ∈ R N × C in , segment labels S ∈ { 1 , … , N s } N

Contextual information is essential for capturing global relationships within a scene. In point cloud semantic segmentation, local features typically focus on the geometric properties of points within a local neighborhood, but points belonging to the same category can share similar characteristics despite being spatially distant. Identifying the correlations among points in feature space can significantly improve the model’s predictive accuracy. The Channel-Spatial Attention Module (CSAM) is frequently used in remote sensing to model the global contextual information of targets in images, enhancing the global feature representation. Similarly, we employ a CSAM to compute the attention of features processed by the graph-point convolution, allowing for the modeling of similarities between distant targets and improving the global understanding of the scene.

As shown in Figure 3, the input features are projected into different feature subspaces through various learnable fully connected layers, which are then used to construct queries, keys, and values for the attention function. The output of the attention function serves to enhance the features by encoding global contextual information. Our channel attention mechanism focuses on selecting and amplifying the features that are most beneficial for the network. In Figure 3, the weights for different features are computed by analyzing the relationships between them. These computed weights are then multiplied with the features to emphasize those that are crucial for network classification. During this weight computation, we reduce the spatial dimensions of the input features to improve computational efficiency. For multi-feature aggregation, unlike PointNet, which directly applies max pooling, we use average pooling to better capture the extent of target categories. Thus, before summation, we perform feature aggregation using both max pooling and average pooling. The specific operations of the channel attention mechanism are outlined as follows.

First, we aggregate spatial dimension information between different feature channels using both average pooling and max pooling to obtain the average pooled feature F x ( i , j ) avg and the max pooled feature F x ( i , j ) max . Then, these two distinct features are input into a multi-layer perceptron (MLP) network to generate an important feature mapping function M c ∈ R 1 × D . This MLP network consists of two fully connected layers, an activation function, and a dropout mechanism applied after the second fully connected layer to enhance the network’s generalization capability. Finally, the results from the MLP processing of the two different features are summed element-wise, which can be expressed as follows (Equations 6, 7): M c = σ φ F x i , j   avg ⊕ φ F x i , j max (6) F x i , j ′ = M c F x i , j ⊙ F x i , j (7) where ⊕ and ⊙ represent element-wise addition and matrix multiplication, respectively, σ denotes the activation function, and φ represents the MLP network.

The spatial attention module is specifically designed to select neighborhoods that are more beneficial for expressing point cloud shape information, as illustrated in the flowchart below in Figure 3. For the input features, we first apply average pooling and max pooling operations to enhance the focus on the relationships between different object categories. Notably, the features here are the aggregated feature matrics from GECC and KPConv, representing a point-object level feature aggregator. Next, we concatenate the resulting features M k ∈ R K × 1 and perform convolution operations to generate different attention coefficients: M k = σ φ θ max F x i , j ′ ‖ θ avg F x i , j ′ (8) in Equation 8,where σ stands for the activation function, φ stands for the MLP network, ‖ represents the concatenation operation, and θ max and θ avg represent the max pooling and average pooling operations, respectively.

Finally, we combine the channel attention and spatial attention, passing them through a fully connected network to obtain point-wise attention scores. Through this spatial-channel attention module, point features are updated from a global perspective, enabling comprehensive learning of interactions between complex points. This process enhances the model’s ability to capture dependencies across spatially distant points, thereby improving prediction accuracy.

We propose the graph kernel convolution attention-based encoder (GKCAE) for local-global feature encoding of airborne LiDAR point cloud data in high-voltage transmission corridor scenes. Inspired by previous work, we use a U-Net architecture as the overall framework, and the designed semantic segmentation model is illustrated in Figure 4. The model employs a five-layer network for encoding, with the structures of graph edge-conditioned convolution (GECC), kernel point convolution (KPConv) and channel spatial attention module (CSAM) in each layer depicted in Figure 5.

To capture local geometric information at multiple scales, we applied downsampling to gradually expand the convolutional receptive field. In the decoder, nearest-neighbor upsampling is employed to obtain the final point-wise features. Throughout the encoding layers, we extract local-global features and incorporate CSAM in the first, third, and fifth layers to capture contextual information. In addition, skip connections are used to transfer intermediate features from the encoder to the decoder, where they are combined with the upsampled features and passed through a fully connected layer to produce the final semantic predictions.

To train the network, we use a weighted cross-entropy loss, as shown in Equation 10: w c = N c ∑ c = 1 C N c (9) Loss = ∑ i = 1 N ∑ c = 1 C w c A i c ′ ⁡ log ρ i c + 1 − A i c ′ log 1 − ρ i c (10)

The weight w c for each class is calculated based on its proportion in the total number of points, as shown in Equation 9, where N c denotes the number of points in class c . In Equation 10, A i c ′ indicates whether the true label of the i − t h sample belongs to class c , while ρ i c represents the corresponding predicted probability.

In order to verify the effectiveness of our method, we manually annotated three regions collected by airborne LiDAR. The data was collected in Anhui, China, using a DJI M600 drone equipped with a Riegl VUX-LR laser scanner. The point density of this data reaches 40–50 points per square meter. To validate the model, we employed the CloudCompare software for manual annotation. As shown in Figure 6, the three datasets used in this experiment and their annotation results are presented. It can be observed that, in addition to the conventional categories such as ground, vegetation, buildings, poles and frames, and wires, we further classified the wires into a total of 9 categories, including crossing lines, ground wires, insulators, jumper wires, etc. For each dataset, we manually divided it into blocks, and then partitioned them into training, validation, and test sets at a ratio of 7:1.5:1.5 respectively, for the training and validation of the proposed method. Table 1 shows the number and proportion of points for each category in the test dataset. It can be observed that there is a pronounced class imbalance in high-voltage transmission line scenarios. Large-scale objects such as vegetation, buildings, and ground account for more than 97% of the points, while power facility categories represent less than 3%. In particular, the proportions of classes like insulator and drainage thread are even lower.

Specifically, the block division was carried out by cropping 50 m on each side along the direction perpendicular to the transmission line corridor. Meanwhile, along the direction of the transmission line corridor, the data was cropped into blocks every 300 m, and a 10-meter overlapping buffer zone was reserved between adjacent blocks to avoid the fragmentation of ground objects during cropping.

To quantitatively evaluate our method, we follow the protocol adopted in previous studies (Zhou et al., 2024; Wang et al., 2023; Jiang et al., 2022), use Overall Accuracy (OA) and Mean Intersection over Union (mIoU) as assessment metrics. OA measures the percentage of correctly predicted points relative to the total number of test points, while mIoU evaluates the semantic segmentation performance across various categories. The calculation formulas are as follows (Equations 11, 12): OA = TP all TP all + FP all (11) mIoU = 1 C ∑ c = 1 C TP TP + FP + FN (12) where T P , F N , and F P represent true positives, false negatives, and false positives, respectively, in a confusion matrix.

In terms of implementation details, we adopt the Adam optimizer to train the network, which is developed and implemented using the PyTorch framework. A warm-up learning rate strategy is employed to gradually adjust the learning rate during the initial training phase. Prior to training, additional grid-based downsampling is applied to the input data to ensure uniform point spacing. Specifically, the grid size is set to 0.2, and a hash mapping between the downsampled points and the original point cloud is maintained. During inference, a voting-based strategy is used to map the predicted labels back to the original point cloud based on this mapping. For the kernel point convolution layers, the spherical neighborhood radius is set to 25 m, and the initial kernel radius is set to 0.5 m. The receptive field gradually expands with increasing network depth. To improve the model’s generalization and robustness, we apply random data augmentations, including rotation, translation, and noise injection. During training, ground-truth semantic labels are utilized to construct and optimize the Graph Embedding and Coordinate Conversion (GECC) graph. However, during validation, semantic labels are excluded, and the graph is constructed solely based on the learned features and geometric coordinates. All experiments are conducted on a single NVIDIA GeForce RTX 4090 24 GB GPU.

In this section, to validate the effectiveness and performance of the proposed method, we conduct an analysis from both quantitative and qualitative perspectives. Additionally, we select several state-of-the-art (SOTA) methods of the same type for comparison. These include the point-based MLP method, PointNet++ (Charles et al., 2017; Qi et al., 2017), the point convolution-based method KPConv (Thomas et al., 2019), and the Transformer-based PointTransformer (PT) (Wu et al., 2024b; Wu et al., 2024a; Wu et al., 2022). In the comparative experiments, the data sample partitioning follows the strategy described in Section 4.1. For KPConv, we set the input radius to 25 m and the initial kernel radius to 0.5 m, consistent with the settings used in our model’s KPConv block. For the other methods, the hyperparameters are set to the empirical values reported in their respective original papers.