## 2 Materials and Methods
### The Functions Required by the Visually Impaired People
#### 2.2.2 Depth Map and the Openness Values  
Although the FAST-SCNN can recognize the above six street environments in front of visually impaired users, it cannot give the environment distance ahead of the user. Therefore, ZED 2 provides the depth map for the image ahead to reinforce this deficiency. Let the color image captured from ZED 2 be on the left of Figure 4. The corresponding depth map is the middle one which was the output from ZED SDK. Take Figure 4 as an example, in which the images (a) and (b) represent the original color image and the depth map corresponding to (a), respectively. Suppose \(M_{d}(i,j)\) is the value corresponding to the pixel \((i,j)\), where \((i,j)\) is the position of the pixel in the depth map and is defined as  
\[M_{d}(i,j)=\left\{\begin{array}{l}-\infty,\text{ if }d<1.6\text{ m}\\ d,\text{ if }1.6\leq d\leq 20\\ 20,\text{ if }d>20\end{array}\right. \tag{1}\]  
where \(d\) is the distance of the pixel \((i,j)\) in the depth map away from the user, since the ZED 2 is mounted on the cap of the user, the front ground within 1.6 m is invisible, but if an object located within 1.6 m and is high enough to be seen by ZED 2, therefore, the pixel \((i,j)\) on the object with distance \(d<1.6\text{ m}\) will have \(M_{d}(i,j)=-\infty\). If the pixel on the image with distance \(1.6\leq d\leq 20\), then let the value of \(M_{d}(i,j)\) be the distance; if the pixel on the image with a distance of more than 20 m, then the value of \(M_{d}(i,j)\) is set 20.  
Next, we consider an entirely open area as the image Figure 4c, in which there is no object except the ground within the image. Let us define \(M_{o}(i,j)\) be the value calculated from (1) in the entirely open area (such as image (c)). The darker the image's color (c) means, the closer it is to the user. Hence, the bottom pixels of the image are close to the user, and the white color of the upper part denotes the pixels are more than 20 m away from the user. Suppose we define the openness value of pixel \((i,j)\) as (2).  
\[Open(i,j)=\frac{M_{d}(i,j)}{M_{o}(i,j)} \tag{2}\]  
It is seen that \(\sum\limits_{i}\sum\limits_{j}Open(i,\ j)=-\infty\text{ }or\ \in(0,\ N]\) for any outdoor image, where \(N\) is the total number of pixels in the image. In other words, if \(\sum\limits_{i}\sum\limits_{j}Open(i,\ j)=-\infty\) which means there is a close obstacle (within 1.6 m) in front of the visually impaired user, but  
Figure 4: (**a**) The original image; (**b**) the real depth map corresponding to the image in (**a**); (**c**) the depth map of a completely open area.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **IoU** \\ \hline Sidewalk & 84.53\% \\ Crosswalk & 84.08\% \\ Stairs & 76.15\% \\ Road & 82.50\% \\ Mean & 81.81\% \\ Pixel Accuracy & 95.10\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: The performance of FAST-SCNN.  
\(\sum\limits_{i}\sum\limits_{j}Open(i,\ j)\in(0,\ N]\) means the depth map image is not entirely open. In other words, there are some objects except the ground in the image. If \(\sum\limits_{i}\sum\limits_{j}Open(i,\ j)=N\) which means the depth map is an entirely open area.