## 3 Results and Discussion
### Transverse Crack Size Determination  
Once the location of the transverse crack was determined, the next step was the measurement of its dimensions; i.e., the width and length. Image segmentation followed by morphological operation was similarly used for the determination of the edges of the concrete slabs with several improvements applied. Bounding boxes containing the transverse crack were cropped from the orthomosaic (Figure 7) based on their coordinates, and thus the images obtained were further processed. First, the images were converted to grayscale, and their features were enhanced using the unsharp masking method with a Gaussian low-pass filter, which resulted in a sharper image. Unlike the previous case, where the dark character of the asphalt grout was used to determine the threshold, [PERSON]'s method was implemented for the global image threshold calculation. This method effectively distinguishes two types of homogenous objects in case the histogram lacks a deep and sharp  
Figure 12: The coordinates recalculation leading to a determination of the transverse crack position within the concrete slab. valley between two peaks representing objects and background [37], which is ordinary for a crack occurring on the concrete surface (Figure 13). [PERSON]'s thresholding method involves iterating through all the possible threshold values and calculating a measure of spread for the pixel levels on each side of the threshold, namely the pixels that fall into one of the classes: foreground or background [38]. There are two options to find the threshold. The first option searches the threshold that minimizes the within-class variance, defined as a weighted sum of variances of the two classes:  
\[\sigma_{W}^{2}(t)=\omega_{0}(t)\sigma_{0}^{2}(t)+\omega_{1}(t)\sigma_{1}^{2}(t) \tag{16}\]  
where weights \(\omega_{0}\) and \(\omega_{1}\) are the probabilities of the two classes separated by a threshold \(t\), and \(\sigma_{0}^{2}\) and \(\sigma_{1}^{2}\) are variances of these two classes. The second option is to maximize the between-class variance equivalent to the within-class variance. Due to its simplicity, the second variant is considered a faster approach for the optimal threshold determination according to the following formula:  
\[\sigma_{B}^{2}(t)=\omega_{0}(t)\omega_{1}(t)\sigma_{1}^{2}\big{[}\mu_{0}(t)- \mu_{1}(t)\big{]}^{2} \tag{17}\]  
where \(\mu_{0}\) and \(\mu_{1}\) are the class means. The obtained threshold was then used for grayscale image binarization. Each predicted bounding box from the YOLOv2 detector contained just one transverse crack; i.e., a dominant object in the foreground representing the largest connected component in the binary image. The transverse crack was further extracted from the binary image; if it contained some holes, they were filed by foreground pixels. The whole process of preparing the transverse crack for the measurement is depicted in Figure 14.  
The dimensions of the transverse crack were measured by combining calculations of its surface area by counting the number of individual pixels and using some features of the Feret diameter. The Feret diameter, sometimes called the caliper diameter (refers to measuring the object size with a caliper), is usually applied in the analysis of particle sizes in microscopy, such as biology or geology, and is defined as the distance between two parallel tangents of the particle at an arbitrary angle. Based on the endpoints (boundary points) coordinates of the object in the foreground, the maximal (minimal) Feret diameter \(\mathrm{d}_{\mathrm{Fmax}}\) (\(\mathrm{d}_{\mathrm{Fmin}}\)) and maximal (minimal) Feret angle with respect to the horizontal axis of the image can be measured. Although the Feret diameter allows measuring in one stroke, due to the shape of the cracks, which is generally jagged and curvy, only the maximum boundary points were used as a part of the process to determine the end of the transverse crack.