Algorithm 2 Edge Detection and Stixel Estimation-Based Segmentation

Use $y\in Y={\mathbb{Z}}^{d\times d}$ to denote the segmentation mask, use $y^{\prime }\in Y^{\prime }={\left\{0,1\right\}}^{d\times d}$ for a binary edge map. Find the intensity gradients of the image. Generate candidate features $x\left(i,j,k\right)$. Define a mapping $\Pi :Y\to Z$. Run the structured edge detector on the original, half, and double resolution version of $I$ and average the result of the three edge maps after resizing to the original image dimensions. Track the edges by hysteresis thresholding: Finalize the detection of the edges by suppressing all the other edges that are weak and not connected to strong edges. $$\begin{array}{l}{H}_{ij}=\frac{1}{2\pi {\sigma }^2}\exp \left(-\frac{{(i-(k+1))}^2+{(j-(k+1))}^2}{2{\sigma }^2}\right);\\ 1\le i,j\le (2k+1)\end{array}$$ Generate bounding area of candidate points. $$C_{horizon}={\displaystyle \sum _i^x\frac{1}{2\pi {\sigma }^2}\exp \left(-\frac{{(i-(k+1))}^2+{(j-(k+1))}^2}{2{\sigma }^2}\right)\ast G_x};1\le i,j\le (2k+1)$$ $$C_{vertical}={\displaystyle \sum _j^y\frac{1}{2\pi {\sigma }^2}\exp \left(-\frac{{(i-(k+1))}^2+{(j-(k+1))}^2}{2{\sigma }^2}\right)\ast G_y};1\le i,j\le (2k+1)$$ where $x,y$ are the coordinates of pixel, $\sigma$ is the standard deviation of the Gaussian distribution, $I$ is the matrix of the image, and $C_{horizon}$, $C_{vertical}$ are the horizontal and vertical direction values of the histograms in Figure 2.