## 3 Results and Discussion
### Determination of the Position of the Transverse Crack within the Concrete Slab  
Once the coordinates of all the slabs within the orthomosaic were computed, 224 \(\times\) 224 image blocks were assigned to the specific concrete slab; however, when a joint was across the 224 \(\times\) 224 image block, the correct assignment could not be accomplished. For this reason, it was necessary to recalculate the transverse crack bounding box(es) coordinates from the 224 \(\times\) 224 image block to coordinates within the orthomosaic. Furthermore, the transverse crack bounding boxes were labeled with a serial number during the recalculation. Although using an Adam optimizer in the YOLOv2 detector considerably reduced the number of multiple detections in a transverse crack, they still occasionally occurred. In these cases, the overlapping bounding boxes were reduced to one bounding box with coordinates covering the maximal values of all participating bounding boxes.  
The effect of the bounding box reduction is illustrated in Figure 11. Blues squares represent 224 \(\times\) 224 image blocks in the square grid with their serial number. Green rectangles are predicted bounding boxes with their serial number (red), and the black lines are the boundary between the concrete slabs; i.e., the joint.  
The knowledge of the coordinates of each concrete slab and the coordinates of the transverse crack bounding box(es) within the orthomosaic allows for the correct assigning of the transverse crack to a particular concrete slab. Furthermore, each concrete slab is conceptually divided into four quadrants, two longitudinal and two transverse edges, and four corners. The size of each quadrant is half the width of the concrete slab and  
Figure 11: The predicted bounding box reduction: (**a**) Multiple detections in one transverse crack obtained from the YOLOv2 detector; (**b**) The effect of the reduction of multiple object detections.  
Figure 10: (**a**) Example of a concrete slab cutout from the orthomosaic as an RGB image; (**b**) The result of image segmentation and morphological operations to determine the boundary and coordinates of the concrete slab.  
half its height. The corners have the size of a square with side dimensions of 0.6 m. The longitudinal and transverse edges are between corners, and their width corresponds with the size of the corner.  
In order to determine the location of the transverse crack within the concrete slab, it was necessary to calculate the coordinates of the quadrants, edges, and corners using the known dimensions (concrete slab width and height, side length of the squares) and GSD value. Further, it was essential to recalculate the transverse crack bounding box(es) coordinates within each concrete slab. The whole coordinates recalculation process is summarized in Figure 12.  
Similar to the YOLOv2 detector performance assessment, the _IoU_ method was used to measure the overlapping area between the transverse crack bounding box \(B_{TC}\) and the rectangle bounding box of the concrete slab \(B_{CS}\) or its parts (quadrants, edges, and corners) \(B_{QEC}\) within the slab, respectively. An overlap ratio greater than zero signified that the transverse crack was located within the given object, and a logical value of 1 was assigned. If the overlap ratio was equal to zero, the transverse crack was not found within the object, and a logical value of 0 was assigned (Equation (15)). The transverse cracks were assigned to specific concrete slabs in this way, and their positions within the concrete slabs were determined.  
\[\begin{array}{c}IoU(B_{CS},\;B_{TC})\\ IoU\big{(}B_{QEC},\;B_{TC}\big{)}\end{array}\bigg{\{}\begin{array}{c}>\;0, \;\text{true}\;(1)\\ =0,\;\text{false}\;(0)\end{array} \tag{15}\]