# Growing Neural Gas with Different Topologies for 3D Space Perception
## 3 Experimental Results
### RGB-D Data
#### 3.3.2 Experimental Result  
Tables 5 and 6 show the experimental results of the quantization error. In Table 5, GNG-DT outperformed the other methods in all quantization errors of the position information. Next, GNG-W outperformed the other methods in most quantization errors of the color information since the weight of the color information has a positive effect on decreasing the error values. However, the GNG-DT's quantization errors of the color information were smaller than those of GNG-W in (a) and (c). Therefore, the weighted distance based method needs to design suitable weight parameters according to the 3D point cloud measured by an RGB-D camera. On the other hand, GNG-DT preserved the geometric space of the 3D point cloud data accurately, which can be utilized to extract features related to the shape of the point cloud. From the above, the distance using only the position information in GNG-DT is a suitable strategy in the 3D space perception.  
Figure 11: Clustering examples in 3D point cloud data (Data2). Each color of the node and edge represents each cluster. (**a**) Position \(C^{pos}\), (**b**) color \(C^{col}\), (**c**) normal vector \(C^{nor}\), (**d**) color \(C^{col}\) and normal vector \(C^{nor}\).  
Next, Figure 12 shows examples of the learning and clustering results of GNG-DT. GNG-DT could learn the geometric feature and color information simultaneously. In addition, GNG-DT could provide the different clustering results from the point cloud by using topological structures of each property. In particular, in Figure 12, the topological structure of segment 4 comprises surface planes of white and brown boxes by combining the topological structures of color and normal vector information from the real environmental data. In this way, GNG-DT can be applied to the unknown 3D point cloud measured in the real environment and cluster the point cloud from the viewpoint of multiple properties with online learning.  
Figure 12: Experimental dataset and results of GNG-DT. The first column is the 3D point cloud measured by an RGB-D camera, the second column is the learning results of GNG-DT, the third column is the clustering results using the topological structure of position information \(C^{pos}\), the fourth column is the clustering results using the topological structure of color information \(C^{col}\), the fifth column is the clustering results using the topological structure of normal vector information \(C^{nor}\), and the sixth column is the clustering results using the topological structure of color and normal vector information \(C^{col}\) and \(C^{nor}\).  
\begin{table}
\begin{tabular}{c c c c} \hline  & **GNG** & **GNG-W** & **GNG-DT** \\ \hline Figure 12a & 12.796 \(\pm\) 0.0011 & 12.341 \(\pm\) 0.0018 & \(\textbf{11.976\pm 0.0005}\) \\ Figure 12b & 12.754 \(\pm\) 0.191 & 12.914 \(\pm\) 0.015 & \(\textbf{12.754\pm 0.0004}\) \\ Figure 12c & 11.428 \(\pm\) 0.001 & 10.857 \(\pm\) 0.001 & \(\textbf{10.014\pm 0.0005}\) \\ Figure 12d & 8.908 \(\pm\) 0.090 & 8.526 \(\pm\) 0.088 & \(\textbf{8.309\pm 0.109}\) \\ Figure 12e & 10.151 \(\pm\) 0.016 & 9.849 \(\pm\) 0.023 & \(\textbf{9.725\pm 0.043}\) \\ Figure 12f & 9.492 \(\pm\) 0.0006 & 9.200 \(\pm\) 0.0008 & \(\textbf{8.998\pm 0.0005}\) \\ \hline \end{tabular}
\end{table}
Table 5: Experimental results of quantization error of position in real environment, where GNG, GNG-W and GNG-DT indicate growing neural gas, GNG with weighted distance measurement, and GNG with different topologies, respectively.