## 5 Experiments
### Cost Map of Terrain Traversability from Aerial Image with DCNN Experiment  
In this experiment, a CNN is used to determine from aerial images of a terrain a traversability cost map, which can be the basis for trajectory planning in an autonomous navigation task. In a previous experiment, in Section 5.2 of this article, it was realized that with FDEKF, the highest accuracy is achieved in a problem including scenic images outdoors or in unstructured environments. In the present experiment, this capacity is used for an outdoor terrain recognition problem. A CNN of three convolutional layers is trained with RGB images of 40 \(\times\) 40 pixels, corresponding to a captured square area of five meters per side. The images for training and testing are included in the global image of Figure 7, a 1 km\({}^{2}\) aerial capture of a region of Estonia, the same used in [41], with a resolution of 1/64 m\({}^{2}\)/pixel and available at [[https://geoportaal.maaamet.ee/eng/](https://geoportaal.maaamet.ee/eng/)]([https://geoportaal.maaamet.ee/eng/](https://geoportaal.maaamet.ee/eng/)), accessed on 26 July 2023. We have divided the image into 25 regions of 200 m \(\times\) 200 m each, then we have subdivided them into squares of 5 m \(\times\) 5 m, that is to say, 40 \(\times\) 40 pixels. For the training set, we have selected three of the 25 regions, so we have 4800 images, each labeled with a cost value between 0 and 1. Once the CNN is trained, the 40,000 images (40 \(\times\) 40 pixels) in the 25 sectors of the global image are presented to the CNN to generate the terrain cost map. Other authors have used the EKF to address this problem but in a different way. In [42], they use EKF in combination with particle filtering to trace roads in satellite images, starting from a specific point and direction. This method tends to recognize real roads due to the use of the gray level of the images to identify road profiles. In our article, we train a CNN with the FDEKF to generate a terrain traversability cost map, enabling the recognition of real paths and the planning of trajectories in other accessible areas based on the labels of the training data set. First, the task has been faced as a regression problem; therefore, the output of the network is scalar. After has been approached as a classification problem, for which the output dimension of the network corresponds to the number of classes and the training set is relabeled by distributing the classes in equal intervals between 0 and 1. Figure 6: MNIST with DCNN experiment—loss. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Mean Accuracy** & **Standard Deviation** \\ \hline Adam & 0.8900 & \(1.51\times 10^{-3}\) \\ sKAdam & 0.9873 & \(8.91\times 10^{-4}\) \\ REKF & 0.9187 & \(6.82\times 10^{-3}\) \\ FDEKF & 0.9864 & \(1.43\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of Accuracy and SD for MNIST Test Set after Ten Training Process. The result of the regression problem is interpreted through Figure 8, a grayscale image as a cost map. The traversability cost in the range [0, 1] of each 5 m \(\times\) 5 m cell is directly represented by the pixel brightness. Therefore, the areas that are difficult to navigate are light, and the easier ones are dark. It is important to note that the simple grayscale image of the original image does not itself provide a cost map, making the objects reflect almost like easily traversable surfaces. The neural network learns features that determine the cost using different receptive fields, beyond the intensity of the individual pixel. The cost map resulting from the CNN in the classification problem is shown in Figure 9. Compared to the image in the previous figure, this one has a higher contrast because the cost value is in a discrete range due to the choice of 20 classes in this experiment. Both the continuous and discrete cost maps clearly show the surfaces that are easiest to navigate, and obviously, the roads of the urbanization are the darkest, then the small parking areas.