# A Vision-Based Two-Stage Framework for Inferring Physical Properties of the Terrain
## 2 Proposed Method
### Second Stage: From the Terrain Type to Physical Properties
Taking land as an example, we can see that it has four different states in the dataset, namely, ordinary land, deciduous or hay-covered land, loose land and muddy land. It is these different states that lead to different friction and stiffness properties of the same type of terrain. For the sake of description, we name the land in different states land 1, land 2, land 3 and land 4 in order. We extracted the brightness features of the land 1 images, and then gathered statistics. The details are as follows. First, we selected 50 RGB images containing land 1 from the FITI dataset and cropped the corresponding parts of land 1 into many image patches with a resolution of 100 \(\times\) 100. Then, a large number of image patches (ours is 300) were randomly selected to extract the brightness features, and the same number of brightness patches were generated. After that, we calculated the average brightness in each brightness patch. Finally, by fitting all the averages using Equation (6), we obtained a normal distribution that can describe the optical characteristics of land 1. In addition, land 2, land 3 and land 4 were treated the same. \[p=\frac{1}{\sqrt{2\pi\sigma}}e^{-\frac{(\sigma-\mu)^{2}}{2\sigma^{2}}} \tag{6}\]  
where \(v\) is the average value, \(\mu\) is the mean and \(\sigma^{2}\) the variance. In the same way, we extracted the brightness features of ices, rocks and asphalt roads in different states and gathered statistics. Of course, we treated the surface structure characteristics equally. After the above steps, we got the Gaussian distributions of optical characteristics and surface structure characteristics of land, ice, rock and asphalt road in different states. Their respective means \(\mu\) and variances \(\sigma^{2}\) are shown in Tables 1 and 2, and their respective curves are shown in Figure 11. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Terrain in Different States** & \(\mu\) & \(\sigma\) \\ \hline land 1 & 202.2 & 15.9 \\ land 2 & 169.1 & 14.6 \\ land 3 & 125.2 & 20.0 \\ land 4 & 88.1 & 8.6 \\ rock 1 & 228.6 & 10.5 \\ rock 2 & 123.7 & 22.8 \\ rock 3 & 154.3 & 21.9 \\ ice 1 & 190.4 & 12.7 \\ ice 2 & 161.2 & 22.8 \\ asphalt road 1 & 158.4 & 17.8 \\ asphalt road 2 & 113.3 & 5.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Means and variances of optical characteristics. Figure 11: The Gaussian distributions of optical characteristics and surface structure characteristics of land, rock, ice and asphalt road in different states. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Terrain in Different States** & \(\mu\) & \(\sigma\) \\ \hline land 1 & 15.7 & 5.6 \\ land 2 & 108.6 & 15.9 \\ land 3 & 40.3 & 8.9 \\ land 4 & 57.9 & 11.4 \\ rock 1 & 19.0 & 4.8 \\ rock 2 & 47.1 & 10.9 \\ rock 3 & 79.8 & 22.6 \\ ice 1 & 8.3 & 3.6 \\ ice 2 & 33.1 & 7.9 \\ asphalt road 1 & 61.8 & 9.3 \\ asphalt road 2 & 84.1 & 12.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Means and variances of surface structure characteristics. In the subgraphs of Figure 11, each curve represents the corresponding terrain in a certain state. The position on the horizontal axis and shape of the curve reflect the distribution regularity of the feature of the terrain in this state. We can see that the waves of different curves in the same subgraph can be staggered significantly, which means terrain in different states has good distinguishability. Therefore, it is reasonable to use the above feature extraction methods to extract the optical characteristics and surface structure characteristics of the terrain image. To reduce the impact of the instability of a single feature during inference, we established a decision mechanism to achieve the mapping from terrain types to physical properties with both feature extraction methods. We obtained 3300 data points of optical characteristics and 3300 data points of surface structure characteristics through the previous steps. To better quantify these two kinds of features, we used \(k\)-means algorithm to cluster the data corresponding to each feature separately.