# Color Structured Light Stripe Edge Detection Method Based on Generative Adversarial Networks
## 4 Experimental Results and Discussion
### Pixel Location Accuracy  
Figure 12 shows a comparison of the location accuracy of the color stripe edges detected with the proposed method and two other methods, including a modified Canny edge detector [16] and a modified Sobel edge detector [43]. Notice that the green lines indicate the edges in the ground-truth image, and the red lines indicate the edges detected by the three methods. The experimental results show that the methods in [16; 43] could detect almost all color stripe edges in the images. There were, however, some edges that were wrongly detected (Figure 12b,c). The cause of this occurrence is that these methods \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Method** & **TP** & **FP** & **FN** & **TN** & **Acc (\%)** & **Pre (\%)** & **Re (\%)** & **F1 (\%)** \\ \hline Pix2 pix & 289,185 & 99,553 & 88,510 & 4,110,272 & 95.90 & 74.39 & 76.57 & 75.46 \\ RU-GAN & 291,195 & 72,268 & 66,500 & 4,157,557 & 96.98 & 80.12 & 81.41 & 80.76 \\ URCA-GAN & 378,496 & 48,021 & 39,199 & 4,121,804 & 98.10 & 88.74 & 90.62 & 89.67 \\ Proposed w/o AG & 383,662 & 59,401 & 24,033 & 4,120,424 & 98.18 & 86.59 & 94.11 & 90.19 \\ Proposed & 388,841 & 20,373 & 28,854 & 4,149,452 & 98.93 & 95.02 & 93.09 & 94.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative comparison of segmentation performance of different methods (Unit Pixels). Figure 11: Segmentation results of the image of a colored textured carton box with different methods. cannot reduce the effect of surface characteristics such as colored texture, inter-reflection (porcelain dish), and rust stains (metal sheet). Meanwhile, the above problems are well-handled with the proposed method (Figure 12d). To evaluate the pixel location accuracy of the edges detected with different methods, the images, including the edge images obtained with the three methods and the corresponding ground-truth images, were cropped into small images with a size of 1000 \(\times\) 1000 pixels in the experiments. Notice that the edges of the color stripes in the ground-truth images are 1 pixel wide. As observed in Figure 12, the edges detected by different methods do not  
Figure 12: Comparison of pixel location accuracy of color stripe edge detection methods: (**a**) part of the original image; (**b**) results with modified Canny in [16], (**c**) with modified Sobel in [43], and (**d**) with the proposed method. coincide with the edges in the ground-truth image due to the influence of the characteristics of the object's surface. This means the number of correctly detected pixels corresponding to TPs in the above metrics may be very small, even zero. Therefore, the above metrics cannot be used to evaluate the local pixel accuracy of the different methods. Thus, the experiments were conducted using the mean square error (\(MSE\)), which is defined in Equation (5), as the evaluation metric:  
\[MSE=\frac{\sum_{i=1}^{N}\left(C_{d}-C_{g}\right)^{2}}{N} \tag{5}\]  
where \(C_{d}\) is the coordinates of the points on the edges detected with different methods, \(C_{g}\) is the coordinates of the points on the edges in the ground-truth image, and \(N\) is the number of points in each ground-truth image. In order to confidently conclude that the color structure light stripe edge detection method proposed in this paper is better than the methods in [16; 43], we performed a statistical significance test with a comparison of MSE, which was achieved with these methods, as shown in Table 3.  
Using the data in Table 3, a 90% confidence interval for the true mean differences can be obtained. The approximate \(100\%(1-\alpha)\) confidence interval for \(\tau\) is defined as Equation (6):  
\[\overline{\tau}-g_{\frac{\pi}{2},(n-1)}\Omega(\overline{\tau})\leq\tau\leq \overline{\tau}+g_{\frac{\pi}{2},(n-1)}\Omega(\overline{\tau}) \tag{6}\]  
where \(\overline{\tau}\) denotes a sample mean of \(\tau\) based on a sample of size \(n\). In this case \(n=5\).