# Fast Planar Detection System Using a GPU-Based 3D Hough Transform for LiDAR Point Clouds
## 4 Experiments and Analysis
### Parallel 3 DHT Performance  
As illustrated in Section 3.2, the Hough space is generated by computing each radius \(r\) according to each parameter pair (\(\theta\), \(\varphi\)). In a traditional 3 DHT algorithm, the computational complexity of generating a Hough space with number \(N\) points reaching \(O\left(I\times J\times N\right)\), where \(I\) and \(J\) represent the count of \(\theta\) and \(\varphi\) values. The time consumption for the generation process increases with the resolutions.  
In estimating the operating efficiency of our proposed system, we utilized the frame per second (fps) as the evaluation method to compare the Hough space generating time using the entire point clouds and fractions of point clouds in approximately 90 different frames shown in Figure 10. Figure 10 illustrates the recorded fps of the generated Hough space in different resolutions when all of the point clouds and fractions are used.  
Figure 10: Speed performance and time consumption in generating Hough space. (**a**) The Hough space generating time using all of the point clouds. (**b**) The Hough space generating time using multiple fractions.  
As shown in Figure 10a,b, a higher resolution corresponds to a lower fps. As the resolution value increases, the fluctuation of the fps curves becomes more evident. Figure 10a illustrates the recorded fps in generating the Hough space with all of the point clouds in different resolutions at approximately 100 different frames. When the resolution reaches 4.0, the overall values of fps are the highest among the compared datasets, fluctuating between 80 and 100. Before the 45 th frame, the fps values in resolution 4.0, whose changing trade remains steady, fluctuate at approximately 80. After the 45 th frame, the changing trade becomes relatively volatile, where several recorded values reach or exceed 100 fps. Figure 10b shows the condition when generating Hough space with multiple fractions. When the resolution is 10.0, the fps values, fluctuating smoothly between 25 and 30 fps, are higher than the fps values whose resolution is lower than 10.0. By comparing Figure 10a,b, the fps curve when using all of the points to generate Hough space is much lower and unstable than that which uses the proposed fraction-to-fraction method when the resolution values are equal.  
Table 1 presents the fps of the plane detection that uses the RANSAC and Hough transform based on CPU and GPU computing. As presented on the table, the efficiency of RANSAC based on parallel computing is remarkably improved compared with the traditional RANSAC. In our proposed parallel 3 DHT algorithm, when the resolution value is approximately 10.0, the multi-frame average fps exceeds that of the RANSAC algorithm. When the resolution is higher, the fps of a single frame also remarkably surpasses RANSAC, as shown in resolutions 2.0 and 3.0. Therefore, unlike the GPU-based RANSAC, our proposed method can significantly improve the computing speed in plane detection when an appropriate resolution value is adopted.  
The speed efficiency of the plane surface detection that uses our developed parallel 3 DHT algorithm has a noticeable improvement when compared with our previous work through the RANSAC algorithm [27] and CUDA-based RANSAC [29].