# Vision-Based Concrete-Crack Detection on Railway Sleepers Using Dense U-Net Model
## 4 Results and Discussions
### Crack Measurement Results  
In the previous section, we provided the visualization of the segmented cracks by both of the models. We found that the Dense U-net model can detect cracks in more detail. So, we consider the output of the Dense U-net model for finding the number of cracks and the morphological features of the individual cracks in an image. Figure 5 shows a few images in which the individual crack boundaries are designated with different colors; the locations of the cracks that contain the maximum widths are highlighted by a green line, and the cracks are labeled by one specific number. Figure 4: Comparison of original U-net and Dense U-net crack segmentation result. (**a**) Original Image (**b**) Ground Truth (**c**) U-net (**d**) Dense U-net. Figure 5 displays the first image containing only one crack; each of the second, third, and fourth images contain two different cracks; and finally, the fifth picture contains three different cracks. After finding the number of cracks, we have also calculated the length, maximum width, and area of the individual cracks by following the approach presented in Section 3.4.2. We have also determined the entire area of the cracks and the crack density so that we can have a better idea about the severity of cracks in a particular image. Furthermore, we have counted the number of white image pixels to justify the determined area by the method. Table 2 Summarizes the measurement results for all the pictures in Figure 5.  
From Table 2, it is evident that in the first image, the crack is the least severe. Only 1.77% of the image contains the cracks. In the second image, there are two separate cracks. One of the cracks is more prominent (208.24 pixels in length), and the other is smaller (17.20 pixels). The maximum width of the two cracks is 9 and 6 pixels, respectively, in this image. We can see that the crack area in the second image is 1288.82 pixels, and it has about 2.56% of crack density. The second, third, and fourth images also contain two separate cracks. Still, the crack density of the third image is higher (3.33%) than the other images, which contain one and two individual cracks. The maximum width of the major crack is also relatively thicker (15 pixels) in this image. In the case of the fifth image, we can see that there is a total of three individual cracks. If we notice carefully, it can be seen that there is a vast difference between the estimated total area and the sum of white pixels for this picture. The main reason behind this is the third crack of this image has a non-crack portion inside the crack boundary. As the other crack portions are continuous, our model counted it as a single crack. Still, for having a non-crack portion, the area calculated by our method has become much greater than the total number of pixels. Furthermore, the maximum width of the first and third cracks is overestimated and not estimated in the correct location. We have used the boundary positions of the cracks to calculate the maximum width. So, if a \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Image** & **Cracks** & **Length** & \begin{tabular}{c} **Maximum** \\ **Width** \\ \end{tabular} & **Area** & **Total Area** & \
\begin{tabular}{c} **Sum of White** \\ **Pixels** \\ \end{tabular} &
\begin{tabular}{c} **Density** \\ **(\%)** \\ \end{tabular} \\ \hline
1 & 1 & 213.47 & 7 & 892.82 & 892.82 & 873 & 1.77 \\ \hline
2 & 1 & 208.24 & 9 & 1227.40 & 1288.82 & 1247 & 2.56 \\  & 2 & 17.20 & 6 & 61.41 & 1674.28 & 1645 & 3.33 \\ \hline
3 & 1 & 185.04 & 15 & 1560.91 & 1674.28 & 1645 & 3.33 \\  & 2 & 27.51 & 5 & 113.36 & 1044.72 & 1000 & 2.08 \\ \hline
4 & 1 & 96.84 & 5 & 406.74 & 1044.72 & 1000 & 2.08 \\  & 2 & 132.00 & 9 & 637.97 & 1044.72 & 1000 & 2.08 \\ \hline
5 & 1 & 194.25 & 60 & 1292.92 & & & \\  & 2 & 32.20 & 12 & 254.74 & 5960.44 & 5123 & 11.87 \\  & 3 & 224.96 & 40 & 4413.46 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Morphological features of the cracks (unit: pixels). Figure 5: Counting and denoting the individual cracks.