## 3 Proposed Algorithmic Procedure
### Image Processing for the Laser-Box Image  
#### 3.3.1 Detecting Structured Edge Map  
The structured silhouette edges of the captured image should be obtained to compute the image 2D coordinates of the intersections and the vertices crossed by the laser plane and the edge of the box. The VGG16 [25] network is modified. This section presents an automated and effective method for detecting structured edge map and extracting straight lines from them with deep learning. In this section, we propose a novel trimmed-HED network. This structure has the best edge prediction results in our repeated tests. Our trimmed-HED model is improved from three aspects: (1) the laser-box image data set we built, and (2) the first two side-output layers of the HED cut to ignore the detail feature in the image, and (3) the loss function slightly simplified by calculating the fusion layer outputs only that can improve the edge map prediction coarse-to-fine structure progressively. (1) Laser-box image dataset  
The problems of structured edge map detection is solved by learning from diverse samples. In building the data set, the best-fitted rectangle is marked by manual manipulation. We labeled images with nine 2D coordinates on the laser-box image containing the four intersections (intersection of the edge of box face and laser line) and other four points (on the box face edge), and the ground truth is obtained by drawing the straight line of these 2D coordinates. Figure 8 shows the sample images and the ground-truth structured edge maps of our developed dataset. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameters** & **Minimal Value** & **Maximal Value** & **True Value** \\ \hline \(\alpha\) & 2345.064 & 2363.778 & 2353.85 \\ \(\beta\) & 2358.273 & 2377.399 & 2367.13 \\ \(u_{0}\) & 1244.827 & 1262.702 & 1254.69 \\ \(v_{0}\) & 1007.973 & 1026.720 & 1018.36 \\ \(k_{1}\) & \(-\)0.0241551 & \(-\)0.008247 & \(-\)0.016697 \\ \(k_{2}\) & 0.155643 & 0.3567460 & 0.232305 \\ \(a_{1}\) & 0.00905 & 0.106500 & 0.01021 \\ \(b_{1}\) & \(-\)0.013303 & \(-\)0.009352 & \(-\)0.010614 \\ \(c_{1}\) & 0.0019727 & 0.002677 & 0.002166 \\ \(a_{2}\) & 0.0095584 & 0.013372 & 0.010326 \\ \(b_{2}\) & 0.009839 & 0.016606 & 0.010347 \\ \(c_{2}\) & 0.0018325 & 0.0025490 & 0.002031 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calibration parameters of the visual sensor. Figure 8: Two example images and the ground-truth edge results for our dataset: (**a**,**c**) Input images; (**b**,**d**) are the ground-truth by human annotation of (**a**,**c**), respectively. Data augmentation is an effective method to generate sufficient training data for learning a robust deep network. We rotate the images to seven different angles (45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\), 225\({}^{\circ}\), 270\({}^{\circ}\), and 315\({}^{\circ}\)). In total, our dataset comprises 96,000 training images and 500 testing images. (2) Trimmed-HED network  
Figure 9 shows an overview of the proposed trimmed-HED network structured edge detection. The original HED network was designed with five side-output layers and one fuse-output, and the final output was obtained through the weighted-fusion and average layer. HED and RCF indicate that the side-output layers in front of the network (low-level network) are focused on extracting the detail edges of the image, and the high-level network is focused on the extraction of the target contour. However, the overall structured edge of the box face and the laser straight line are the main concerns in the present work. Therefore, the trimmed-HED cut the first two side-output layers of HED.