# A Quantitative Detection Method for Surface Cracks on Slab Track Based on Infrared Thermography
## 2 Infrared-Thermogram Processing
### Edge Detection of Infrared Thermogram
Multiply the phase congruency values of all pixels by 255, i.e., convert the phase\(-\)congruency values of each pixel into the corresponding grayscales, and obtain the phase\(-\)congruency image, as shown in Figure 5b. Step 3. Use [PERSON]'s method to solve the segmentation threshold of the phase\(-\)congruency image of the slab-surface crack, obtain the area with a large gray value (i.e., phase\(-\)congruency value), and convert the segmented phase\(-\)congruency image into a binary image, as shown in Figure 5c. Step 4. Use the morphological filter to solve the over-segmentation and under-segmentation problems caused by [PERSON]'s method. In the morphological filter, the dilation  
Figure 5: Crack-edge-detection process of infrared image of track-slab-surface crack: (**a**) Infrared image of slab surface crack; (**b**) phase congruency image; (**c**) binary image after segmentation; (**d**) processed binary image; (**e**) crack area (before refining); (**f**) refined crack area. operation is used to connect the fracture points in the crack area and the open operation is used to eliminate the isolated noise points and maximumly preserve the structure of the crack area. Furthermore, it should be noted that the track-slab surface is not smooth and features deficient, and there are temperature-distortion points in the collected infrared images, which can generate blocky pseudo-edge areas in the segmented images. By comparing the distribution of the pseudo-edge area and the crack area in the segmented images, it is found that the number of pixels occupied by the pseudo-edge area due to the defiement and temperature distortion is lower than the number of pixels in the crack area. Furthermore, the crack appears as a long and narrow strip area in the segmented image, while the pseudo-edge area appears as a block area, which means the length-width ratio of the crack area is greater than that of the pseudo-edge area. In this regard, in this paper, the crack area and pseudo-edge area are marked in the binary image after morphological processing as connected domain \(\{bw_{1},bw_{2},\cdots,bw_{sum}\}\), where \(sum\) is the total number of crack areas and pseudo-edge areas. Next, the total number of pixels, and the lengths of the major axis and the minor axis of all connected domains are calculated. The major axis and the minor axis refer to the major and minor axis of the ellipse with the same standard second-order central moment as the area. Next, the total number of pixels, as well as the ratio of the length of the major axis to the minor axis of all connected domains, are sorted, and two sets \(V_{1}\), \(V_{2}\) are formed, accordingly, by thresholding the number of pixels. The threshold value of \(V_{1}\) is set to \(thv_{1}\), i.e., the pseudo-edge area can be defined as the connected domain with the number of pixels less than \(thv_{1}\); the threshold value of \(V_{2}\) is set to \(thv_{2}\) and \(thv_{2}=\alpha*max\{V_{2}\}\), where \(\alpha\) is an empirical parameter and \(\alpha\)\(\in\)\([0.4,\ 0.7]\), i.e., the pseudo-edge area can be defined as the connected domain with a ratio of the length of the major axis to that of minor axis less than \(thv_{2}\). After morphological processing and elimination of pseudo-edge areas, a full image of the crack area can be extracted from the segmented binary image, as shown in Figure 5d. Step 5. Refine the crack area. It can be seen from Figure 5e that the crack area obtained in Step 4 is larger than the actual crack area in the infrared thermography, and the redundant part is the slab concrete near the crack edge, so the crack area obtained in the previous step needs to be refined. Because the thermal conductivity of the air in the surface cracks is quite different from that of the concrete material, heat accumulates more easily inside the cracks, and the speed of heat dissipation is also slower than that in the non-crack areas, resulting in differences in temperature values and temperature gradients between the cracks and non-cracks on the slab surface.