## 3 Methods
### Sampling Module with Adaptive Radius  
The Pointnet++ [14] network uses an iterative farthest point sampling (FPS) method to select the centroids of a subset. However, in the process of using ball sampling, the number of all points in the ball radius is counted first, from which n points are selected as sampling points, and other points are discarded for processing; when the points in the ball radius do not reach n, the point with the largest value is copied to fill in. In indoor dense point clouds data, such processing can meet the requirements of feature learning. However, in the inhomogeneous sparse road extensive field point clouds data, it is easy to cause the loss of local information and the reduction of point clouds segmentation accuracy.  
Considering the characteristics of the road point clouds data collected by MLS using line scan, we design a new sampling method as in Figure 3. Calculate the Euclidean distance between the sampling center point and all the selected points. All the points greater than \(r^{2}\) are assigned the value N, where N is null, and the rest keep the original value. The points in the sampling radius are arranged in ascending order, and n points are taken out of the remaining points as sampling points, where n is a parameter. In the MLS road point clouds environment, n is set to 36 or 48. Considering that there may be points containing N values among the n points, i.e., less than n points are in the ball sampling radius, then judge whether there are points containing N values in the sampling points. If so, the ball sampling radius is expanded by b(0.1)m. Then, judge whether the points in the ball sampling satisfy the condition again. If not, the radius is expanded again until the condition of n numbers is satisfied and ensuring that enough points to learn the features to enhance the high-dimensional features from the sampled points.  
This deep learning model extracts local features by sampling and delimiting a range in the whole point clouds. The points inside as local features for one feature extraction, and the extracted local features capture the fine geometric structure from the small neighborhood. A multilayer perceptron (MLP) operation is performed for each point in the local area, and finally, a maximum local pooling is performed to obtain the local global features.  
Figure 2: (**a**) Backbone network structure of MLS road point clouds data processing, the left side is the input MLS road point clouds data, the right side is the output segmentation results, the orange part represents the addition of adaptive sampling radius module and channel attention module. (**b**) The specific structure of the orange section.  
After multiple sampling operations, although the original number of point clouds becomes smaller, the existing points all contain local features extracted from the points in the previous cycle, and each point contains more information. These local features are further grouped into larger units and processed to produce features on a larger scale. This process is repeated until features are obtained for the entire point clouds data.  
Up-sampling is performed by linear difference, and for the point to be recovered, the closest points in the same scale space are determined, and the inverse of the distance weights the features to obtain the features of the points after up-sampling. Then, the up-sampled point features are stitched with those obtained from the previous part of the encoder through a jump connection. Then, feature extraction is performed and repeated until the point clouds resolution is consistent with the original point clouds resolution.