# Feature-Preserved Point Cloud Simplification Based on Natural Quadric Shape Models
## 3 Experiments and Discussions
### Comparison of the Simplification Effect with Other Algorithms
#### 3.3.1 Point Cloud Simplification for Natural Data Sets  
The experiment used two classic data sets, bunny and dragon, which were provided by Stanford University. The size of the bunny data set was 35,947 points. From the first experiment, we knew that the experiment parameters could be set as \(c=35\ 000\), \(k=70\), and \(\sigma=500\) to provide satisfactory simplification results. By running the FPPS algorithm, the simplification data were obtained and are shown in Figure 11. The simplification ratio was 15.6%. In order to compare the simplification effect of the two reconstructed surfaces, which were reconstructed by \(S\) and \(R\), this experiment was implemented, the results of which are shown in Figure 12. When we estimated the deviation value between the two surfaces, the experimental results show that using the four simplification algorithms, the deviation value range is [\(-0.008\), \(+0.008\)]. For the different areas of the bunny's surface, we compared the simplification effects by four simplification algorithms. The simplification ratios of FPPS, uniform-based and curvature-based are set to the identical value, 15.6%. For the grid-based simplification algorithm, the point cloud simplification is implemented as the grid resolution. Therefore, the biggest interval distance of points in S equals the biggest interval distance by grid-based simplification. Subsequently, the simplification algorithm of grid-based simplification is 15.1%, which is close to 15.6%. For the ears area indicated by the red circle in Figure 12, the uniform-based and grid-based simplification algorithms produced large surface deviations. For the top of the ears, the gray areas show that all the points on one side are absent in the simplification result. The curvature-based simplification's deviation value was less than 0.03, and just one ear has an obvious gray area in Figure 12c. Compared with the other algorithms, the FPPS produced a complete simplification effect in the ear area without a gray area, as shown in Figure 12d, and there was no large hole in the reconstructed surface. For the eye area, the uniform simplification produced an ambiguous reconstructed surface, and the eye area was difficult to recognize from other areas. The grid-based algorithm showed a more refined effect around the eyes than uniform-based simplification. The curvature-based and FPPS algorithms showed the best effects around the eye position. Relative to the ears and eyes, the body surface of the bunny was smoother. For the body area,  
Figure 11: The simplification point cloud at a simplification ratio of 15.6%. the uniform-based algorithm was similar to the original surface, and the curvature-based, grid-based, and FPPS algorithms produced more deviation areas. According to the experimental results mentioned above, for the FPPS algorithm, the simplified data loses surface precision, although the error is small and acceptable. Especially for the feature-rich area, surface holes and large deviations are less frequent occurrences. For the relatively smooth area, FPPS performs better than the grid-based and curvature-based algorithms, but the uniform-based algorithm shows the best effect. In addition, FPPS can protect the boundary data well with no large surface deviation, e.g., in the ear and tail areas. In order to analyze the stability of FPPS, we applied the four simplification algorithms to the \"bunny\" and implemented 20 groups of tests. After the execution of the 20 groups of tests, the deviation of the experimental results is recorded with the decrease in the simplification ratio, as shown in Figure 13. From Figure 13, we can see that the FPPS is a stable simplification algorithm. However, when the ratio is decreasing, the data volume is too small to present a satisfactory effect caused by the curvature-based algorithm. In Figure 13, the curve of uniform-based simplification is masked by the curve of FPPS, because for the \"bunny\" the stability of the uniform-based algorithm is similar to that of FPPS.