## 3 Method
### Feature Encoding Network  
The role of the FEN is to first encode the point clouds into multi-scale pillars and then convert them into pseudo images so that they can be extracted by the 2D CNN backbone of the Detection Neck for feature extraction. Our work is mainly focused on ASP and CPA in the FEN, as shown in Figure 2.  
The closer an object is, the larger the point cluster it will form. Consequently, the closer the object is, the larger the pillar used to abstract larger-scale features. Conversely, a smaller pillar is used for distant objects to provide a more focused abstract to reduce the spatial information loss caused by distant objects. Below are the details of the ASP module. Figure 1: The architecture of ASCA-PointPillars. Within this framework, FEN serves to generate a pseudo image from point clouds, while the Detection Neck is responsible for extracting and fusing the features of the pseudo image. Finally, the Detection Head produces classification results and regresses the bounding boxes, enabling accurate object detection. 1. ASP module  
In this module, the input point clouds are first divided into pillars, whose sizes are \(V_{x}\times V_{y}\) on the \(X\)-\(Y\) plane (the \(Z\)-axis is ignored). Here, \(V_{x}\) and \(V_{y}\) are the sizes of the pillars along the \(X\) and \(Y\)-axis, respectively, and the value of \(V_{y}\) is 0.16 m. The \(V_{x}\) value for the pillars nearest to the LiDAR along the \(X\)-axis is 0.32 m, which is the biggest among all pillars, and \(V_{x}\) is adaptively decreased with the increasing size of \(X\). Therefore, the ASP module forms bigger pillars near the LiDAR and smaller pillars in distant areas. Figure 3 shows the schematic diagram of the ASP module. In Figure 3, \(d_{min}\) is defined as the shortest distance along the \(X\)-axis between the pillars and the LiDAR, while \(d_{max}\) is the longest. \(D_{max}\) stands for the greatest distance between any two pillars along the \(X\)-axis, as determined by Equation (4). \(d\) refers to the distance from a specific row of pillars to the LiDAR, and \(D\) denotes the distance from a specific row of pillars to the first row of pillars, which is the row closest to the LiDAR. The relationship between \(d\) and \(D\) is depicted in Equation (3). In the coordinate system, \(V_{x}\) decreases as \(D\) increases. \(V_{max}\) is the value of \(V_{x}\) for the first row of pillars. The value \(V_{x}\) for the \(n\)th size of the pillar can be derived from Equation  
Figure 3: Schematic diagram of ASP module. The horizontal axis \(D\) represents the distance from a specific row of pillars to the first row of pillars, which is the row closest to the LiDAR, and the vertical axis \(V_{x}\) represents the size of the pillars along the \(X\)-axis. It indicates that the size of the pillars along the \(X\)-axis, denoted as \(V_{x}\), decreases as the distance \(D\) increases. Figure 2: Feature Encoding Network of ASCA-PointPillars. This section begins with the utilization of ASP to encode point clouds into multi-scale pillars, generating tensor data. Subsequently, a simplified version of PointNet is employed to extract high-dimensional features. Then, CPA is applied to enhance these features. Finally, the enhanced features are projected as a pseudo image, facilitating accurate object detection. (1). Equation (2) provides the value of \(n\), which is associated with the distance ratio \(a\). Equation (5) reveals that \(a\) is the ratio of \(D\) to \(D_{max}\). According to Equation (2), there can be at most \(K\) different sizes of pillars. \[V_{x}=\frac{1}{2^{(n-1)}}V_{max} \tag{1}\]  
\[n=\left\{ \begin{array}{l}1,a\in\left[0,\frac{1}{K}\right)\\ 2,a\in\left[\frac{1}{K},\frac{2}{K}\right)\\ \ldots\\ K,a\in\left[\frac{K-1}{K},1\right]\end{array} \right.,\;K\in N^{+} \tag{2}\]  
\[D=d-d_{min} \tag{3}\]  
\[D_{max}=d_{max}-d_{min} \tag{4}\]  
\[a=\frac{D}{D_{max}} \tag{5}\]  
Upon encoding the point clouds into pillars, the data are converted into tensors of size (\(B\), \(P\), \(N\)).