# Fast 3D Transmission Tower Detection Based on Virtual Views
## 3 Methodology
### Virtual View Generation Based on 2D Splatting  
Point cloud data are typically sparse and irregularly distributed, posing challenges for direct 3D object detection, especially for airborne LiDAR point clouds comprising tens of millions of points. Projecting the point cloud onto a plane to create a denser representation is a more effective method to alleviate these challenges. This approach also allows the leveraging of established 2D object detection techniques [23,24], thereby ensuring a robust detection rate. The conventional projection strategies commonly used for airborne LiDAR data include the BEVs and side views. The BEV provides a top-down perspective, with the generated virtual view being an orthogonal projection onto the XY plane. This virtual view can directly show the TTs and the surrounding environment on a global scale. However, since the key features of the TTs are primarily distributed in the elevation direction, their projection onto the XY plane results in a small coverage area and less prominent features (as shown in Figure 2a), which can make object detection difficult. Therefore, this paper adopts a side-view projection model, which is more conducive to the detection of TTs. Specifically, a parallel projection matrix, \(P\), is used to project the point cloud onto a vertical plane formed by the flight direction and the elevation direction (as shown in Figure 2b). This approach helps to better capture the relevant features of the TTs, enhancing the overall detection performance. Figure 1: Overall pipeline of the proposed method. The detected TTs are highlighted in red rectangles in the virtual image and are rendered in red within the 3D point cloud. It is worth noting that because 3D points lack inherent spatial dimensions, their direct projection onto a 2D plane leads to the creation of numerous empty spaces and allows distant backgrounds to seep through nearby objects. This process, consequently, compromises the original spatial scale and occlusion relationships inherent in the 3D point cloud. As shown in Figure 2b, the projections of the TT are heavily mixed with those penetrating projections of distant trees. To address this issue, traditional methods typically assign a fixed size to each 3D point based on empirical experience. However, the predefined point size commonly falls short of meeting the demands of practical applications. A size that is too small is inadequate for effectively addressing the spacing and penetrating challenges associated with distant objects. Conversely, if the size is excessively large, it may lead to overlapping and occupation of 3D points in densely populated areas within the point cloud. Given the inherent sparsity and uneven distribution of 3D point clouds, it is necessary to increase the point size in areas with sparse point density and reduce the point size in areas with high point density. Therefore, an adaptive point size setting strategy is required. To solve this problem, this paper builds upon the surface splatting technique [25] and incorporates the latest 2D splatting techniques [26] to automatically set the point size based on local point cloud density. Specifically, each 3D point is treated as a 3D Gaussian distribution, where the spatial probability distribution follows a Gaussian distribution. Its mathematical expression is as follows:  
\[G(X)=e^{-\frac{1}{2}(X-\mu)^{T}\sum^{-1}(X-\mu)} \tag{1}\]  
where \(\mu\) denotes the center of the 3D Gaussian point, and \(\sum\) is the 3D covariance matrix, which could be calculated by averaging the distances to the top three nearest neighbors, respectively, in the X, Y, and Z directions.