# Growing Neural Gas with Different Topologies for 3D Space Perception
## 3 Experimental Results
### RGB-D Data
#### 3.2.2 Experimental Result

Table 2: Experimental results of quantization error of position in simulation experiment, where GNG, GNG-W and GNG-DT indicate growing neural gas, GNG with weighted distance measurement, and GNG with different topologies, respectively. \(scl\) indicates scale factor. Figure 10: Experimental results of quantization errors (\(r^{pos}\)) divided by scale vales (\(scl\)). (**a**) Data1, (**b**) Data2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data1** & **GNG** & **GNG-W** & **GNG-DT** \\ \hline \(scl\) = 1.0 & 25.152 \(\pm\) 0.499 & \(\mathbf{22.583\pm 0.567}\) & 26.178 \(\pm\) 0.425 \\ \(scl\) = 10.0 & \(\mathbf{21.094\pm 0.554}\) & 23.081 \(\pm\) 0.623 & 26.168 \(\pm\) 0.509 \\ \(scl\) = 0.1 & 28.619 \(\pm\) 0.682 & 27.623 \(\pm\) 0.650 & \(\mathbf{26.072\pm 0.534}\) \\ \(scl\) = 0.01 & 33.693 \(\pm\) 1.891 & 30.425 \(\pm\) 1.005 & \(\mathbf{26.094\pm 0.475}\) \\ \hline Data2 & GNG & GNG-W & GNG-DT \\ \hline \(scl\) = 1.0 & 46.740 \(\pm\) 0.290 & 45.396 \(\pm\) 0.233 & \(\mathbf{33.925\pm 0.034}\) \\ \(scl\) = 10.0 & 34.099 \(\pm\) 0.055 & 33.933 \(\pm\) 0.028 & \(\mathbf{33.919\pm 0.032}\) \\ \(scl\) = 0.1 & 48.084 \(\pm\) 0.496 & 47.841 \(\pm\) 0.419 & \(\mathbf{33.915\pm 0.031}\) \\ \(scl\) = 0.01 & 49.462 \(\pm\) 1.301 & 48.056 \(\pm\) 0.766 & \(\mathbf{33.915\pm 0.034}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results of quantization error of color in simulation experiment, where GNG, GNG-W and GNG-DT indicate growing neural gas, GNG with weighted distance measurement, and GNG with different topologies, respectively. \(scl\) indicates scale factor. In addition, the color distribution of the nodes is the same as the point cloud, except the boundary nodes from Figure 8. From these results, GNG-DT can robustly generate the topological structure from the point cloud with color information in the scale differences. In the result of clustering, the GNG and GNG-W could not cluster four rectangles from the 2D simulation data, while only GNG-DT could cluster four rectangles in all of the scales. Specifically, as the scale factor is 10.0, GNG and GNG-W could not preserve the space structure of the point cloud. This shows that the edges between the same color were not deleted since the color information is a predominant factor in the input vector. On the other hand, the topological structure of GNG-DT (\(C^{col}\)) could cluster the four rectangles in all of the scale factors. Table 4 shows the experimental result of the error \(e_{i}\) between the center of cluster and true value in each rectangle in the topological structure \(C^{col}\). The results of error had constant values in all of the scales. In Figure 8, the topological structures of color information had isolated nodes in the vicinity of the boundary. As a result of the isolated nodes, the centers of clusters shifted from the true value of each center. Next, Figure 11 shows an example of the learning result using GNG-DT in Data2. In the topological structure of the position information \(C^{pos}\) (Figure 11a), the number of clusters is 1 since the point cloud of Data2 is composed of two objects on the surface plane. In the topological structure of the color information \(C^{col}\) (Figure 11b), the number of clusters is 3. The surface point cloud and the part of quadratic prism is clustered as the same cluster since the color is almost the same value. In the topological structure of the normal vector information \(C^{nor}\) (Figure 11c), the number of clusters is 4 according to the surface direction. In the topological structure of the color and normal vector information \(C^{col}\cdot C^{nor}\) (Figure 11d), the number of clusters is 5 with segmented red and brown planes in the prism by combining the multiple topological structures of the color and normal vector information. In this way, GNG-DT can generate the multiple clustering results according to each property within the framework of the online learning method, preserving the geometric feature of the point cloud.