# Growing Neural Gas with Different Topologies for 3D Space Perception
## 3 Experimental Results
### RGB-D Data
#### 3.2.2 Experimental Result  
Tables 2 and 3 show the results of the quantization error, and Figures 8 and 9 show examples of the learning result. In the quantization error of position information, GNG-DT outperformed the other methods for all of the scales, except \(scl=10.0\) in Data2, and GNG-DT preserved the 2D and 3D space structures of each point cloud more accurately. In addition, GNG-DT generated almost the same topological structures of the position (\(C^{pos}\)) and color (\(C^{col}\)) properties in the different scales from Figures 8 and 9. The topological structure of color information (\(C^{col}\)) in Figure 8 was separated by the boundary of the different color, and GNG-DT clustered each rectangle in all scales. On the other hand, GNG and GNG-W generated different topological structures in the different scales. In particular, GNG and GNG-W could not preserve the space structure of the point cloud in the cases of \(scl=0.1\) and \(0.01\). This result indicates that the influence of the color information is dominant over the position information. Figure 10 shows that the position information's quantization error multiplied the inverse of the scale factor \(scl\). The results of GNG and GNG-W were affected by the scale factor, while GNG-DT did not depend on the scale factor since the error values are almost the same in Figure 10. These results also show that GNG-DT can preserve the space structure of the point cloud without affecting the input vector of the other properties by using only the position information in the distance measurement. Figure 9: Learning examples in simulation experiment using 3D point cloud (Data2). (**a**) _scl_ = 1.0. (**Upper left**: GNG, **Upper right**: GNG-W, **Lower left**: GNG-DT(C\({}^{pos}\)), **Lower right**: GNG-DT(C\({}^{col}\))), (**b**) _scl_ = 10.0 (Upper left: GNG, **Upper right**: GNG-W, **Lower left**: GNG-DT(C\({}^{pos}\)), **Lower right**: GNG-DT(C\({}^{col}\))), (**c**) _scl_ = 0.01 (**Upper left**: GNG, **Upper right**: GNG-W, **Lower left**: GNG-DT(C\({}^{pos}\)), **Lower right**: GNG-DT(C\({}^{pos}\))). In the results of the quantization error of color information (Table 3), the error values of GNG and GNG-W were lower than GNG-DT in the case of \(scl\) = 1.0 and 10.0, while GNG-DT outperformed the other methods in the other results. When the scale factor \(scl\) is 1.0, the scales of the position and color information are almost the same scale; GNG-W outperformed the other methods. On the other hand, GNG, which can be considered GNG-W whose weights are \(w^{pos}\) = 1.0, \(w^{col}\) = 1.0, outperformed the other methods in the case of \(scl=10.0\). In this way, the weighted distance approaches need to design the suitable weight according to the scale of each property for learning the point cloud effectively. On the other hand, GNG-DT, which can be considered to be GNG-W, whose weights are \(w^{pos}\) = 1.0, \(w^{col}\) = 0.0, does not depend on the scale factor, and the results are almost the same value. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data1** & **GNG** & **GNG-W** & **GNG-DT** \\ \hline \(scl\) = 1.0 & 8.687 \(\pm\) 0.062 & 7.794 \(\pm\) 0.037 & \(\mathbf{7.341\pm 0.022}\) \\ \(scl\) = 10.0 & 73.948 \(\pm\) 0.191 & 73.581 \(\pm\) 0.217 & \(\mathbf{73.434\pm 0.199}\) \\ \(scl\) = 0.1 & 1.311 \(\pm\) 0.020 & 1.144 \(\pm\) 0.015 & \(\mathbf{0.735\pm 0.002}\) \\ \(scl\) = 0.01 & 0.248 \(\pm\) 0.009 & 0.190 \(\pm\) 0.003 & \(\mathbf{0.073\pm 0.000}\) \\ \hline Data2 & GNG & GNG-W & GNG-DT \\ \hline \(scl\) = 1.0 & 11.825 \(\pm\) 0.047 & 11.133 \(\pm\) 0.038 & \(\mathbf{10.341\pm 0.021}\) \\ \(scl\) = 10.0 & **103.064 \(\pm\) 0.311** & 103.224 \(\pm\) 0.293 & 103.418\(\pm\)0.322 \\ \(scl\) = 0.1 & 1.644 \(\pm\) 0.010 & 1.456 \(\pm\) 0.008 & \(\mathbf{1.0349\pm 0.002}\) \\ \(scl\) = 0.01 & 0.279 \(\pm\) 0.003 & 0.234 \(\pm\) 0.002 & \(\mathbf{0.103\pm 0.000}\) \\ \hline \hline \end{tabular}
\end{table}