# Regressed Terrain Traversability Cost for Autonomous Navigation Based on Image Textures
## 4 Experiment and Results
### Results and Discussion  
As a result of TNUD discrimination, training process for homogeneous and non-homogeneous terrains was achieved using 1956 and 368 observations, respectively. The predictions of the motion information for homogeneous and non-homogeneous terrains were generated using 220 and 38 image texture samples, respectively. To facilitate the interpretation of the regression results, we summarize the results in Table 2 and plot the results of the predicted vibrations for both homogeneous and non-homogeneous terrains in Figures 13 and 14. The error of the prediction for both homogeneous and non-homogeneous terrains is far lower than the prediction error of the regressor proposed in [24]. Moreover, the failed prediction error is also lower than the method proposed in [24]. The results are shown in Table 3.  
The current framework sometimes fails to predict the vibrations in the terrain samples judged by the multiscale analysis to be either uniform or non-uniform. In the case of non-uniform terrains, as shown in Figure 14, the Gaussian process outputs negative predictions for vibration since we are not imposing any restrictions in this regard. Such negative vibration prediction is not consistent with the nature of the feature used in this study, which is always positive, as described by Equation (10). The only computations that are performed on the image are the global contrast measurement and contrast distance maps for scales 1, 2, and 3. The purpose of doing so was to understand and evaluate the behavior of the contrast distance feature toward non-uniformity. Multiscale analysis for scales 1, 2, and 3 suffers a slightly high computation time, as shown in Table 4. A scale 1 contrast distance map was generated with an image of size 1080 \(\times\) 1920, a scale 2 contrast distance map was generated with an image of size 540 \(\times\) 960, and a scale 3 contrast distance map was generated with an image of size 270 \(\times\) 480. Since we could confirm that non-uniform regions have a higher contrast distance feature value than uniform regions, we propose in future work to accelerate this process by focusing only on the ROI and not the whole image. The ROI is approximately 10% of the whole image; thus, the computational time will decrease drastically.  
Compared with [36], where motion prediction with varying speed based on the 3D reconstruction problem setting was investigated, our platform run at a constant speed of 0.2 m/s. We propose to study the effect of speed variations on the prediction of vibrations in future works.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Process** & **Computation Time** \\ \hline Multiscale analysis–contrast distance scale 1 & 880 ms \\ Multiscale analysis–contrast distance scale 2 & 200 ms \\ Multiscale analysis–contrast distance scale 3 & 47 ms \\ Multiscale analysis–fusion (refined contrast distance map) & 2.2 ms \\ Texture extraction & 67 ms \\ Motion feature & 47 μs \\ Prediction for non-uniform terrains & 100 ms \\ Predictor for uniform terrains & 22 ms \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computation time.  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{Application of TNUD} & Uniform terrains & 0.2373 \\ \cline{2-3}  & Non-uniform terrains & 0.268 \\ \hline Non-application of TNUD & - & 0.3567 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction error.  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{Application of TNUD} & Uniform terrains & 0.4640 \\ \cline{2-3}  & Non-uniform terrains & 0.4419 \\ \hline Non-application of TNUD & - & 0.6048 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Prediction error for failed cases.