# Fast Planar Detection System Using a GPU-Based 3D Hough Transform for LiDAR Point Clouds
## 4 Experiments and Analysis
### Three-Dimensional Hough Space and Flag Map Performance  
The generated 3D Hough space buffer is shown in Figure 7, where theta \(\theta\), radius \(r\), and phi \(\varphi\) are three coordinate axes. The cross sections perpendicular to the \(\varphi\) axis are displayed sequentially as the value \(\varphi\) increases.  
Figure 8a,b show the Hough space generated by all point clouds and a fraction of point clouds, respectively. Figure 8a illustrates images of \(\theta\)-\(r\) cross sections under different \(\varphi\) values in the Hough space generated by all point clouds. The entire point clouds are massive and inhomogeneous, causing a distribution with high complexity in the Hough space, as shown in Figure 8a. The peak values generated in the Hough space buffer therefore are difficult to be extracted, meaning that the accuracy of planar reduces. Figure 8b shows the Hough space generated by a fraction of points after being  
Figure 6: Unmanned vehicle platform with light detection and ranging (LiDAR).  
divided. As presented in the figure, when the number of points after division is rather small and the coverage area is also relatively small, the generated Hough space is clear and efficient, where the peak values can be easily extracted and precisely represent the planar surfaces in a fraction area. In the Hough space, the ranges of the variables \(\theta\), \(\varphi\), and \(r\) was between 0\({}^{\circ}\) to 360\({}^{\circ}\), 0\({}^{\circ}\) to 180\({}^{\circ}\), and 0 to 100 m, respectively. Accordingly, the resolutions were 1\({}^{\circ}\), 5 dm, and 5\({}^{\circ}\), respectively. The coordinates (\(\theta\), \(\varphi\), \(r\)) of cells with peak values were recorded as planar slide parameters in the Hough space. Because of the limited memory of GPU devices, the resolution of variable \(\theta\) was set higher than that of axis \(\varphi\) to ensure that the detection of planes in the vertical direction shows a higher accuracy.  
Figure 8: Hough space and flag maps generated by all point clouds and a fraction of point clouds. **(a)** The Hough space generated by all point clouds in a frame. **(b)** The Hough space generated by a fraction of the point clouds in a frame. **(c)** The flag map generated by all point clouds using a connected component labelling algorithm. **(d)** The flag map generated by a fraction point cloud using a connected component labelling algorithm.  
Figure 7: Display order of a 3D Hough space buffer.  
Figure 8c,d illustrates the 3D flag map generated from the Hough space buffer in Figure 8a,b, where different cell clusters are rendered in different colors. As shown in Figure 8c, due to the horizontal linear distribution of LiDAR point clouds, a large number of valid cells are clustered into a cluster with a strip shape in the middle of the flag map. The peak searching in such cluster was against our purpose of performing clustering before peak searching, for its undiminished complexity and unincreased accuracy. The clusters in the flag map generated by a fraction of points, however, were concentrated in several separated parts. The peak of each cluster is searched with a higher accuracy, as shown in Figure 8d. Therefore, the Hough space generated by a fraction of points was more applicable for subsequent peak extraction than that generated by all points.