## 3 Image Feature-Based Extraction of Damage Indicators
### Through-Lane Inspection  
For the role of the bridge deck sub-goal function, the bridge deck provides a vehicle path if there is a path on the bridge deck that has a certain width and the paths across the bridge ends are always continuous so that vehicles can safely pass through the bridge (such a path can be called a vehicle path). For the traffic function sub-goal for bridge decks, the bridge deck provides multiple lanes for transit vehicles to run parallel to each other, with the number of parallel lanes varying for different widths of bridges, with the number of lanes being proportional to the width of the bridge deck and each lane being the same size in width. According to the AASHTO Green Book, the recommended lane width for general use is 12 feet (3.6 m) [40]. The existence of through-paths on the bridge deck and the number of lanes that can be parallel are intuitive parameters reflecting the capacity of the bridge deck. The through-lane detection algorithm is proposed, which simplifies the bridge deck as a rectangle and the crater as a circle, establishes a coordinate system, determines the bridge and crater locations and dimensions through image processing technology, merges craters that do not have through-paths between craters, and then detects the number of transverse lanes according to the relationship between the crater locations, dimensions, and spacing. The algorithm flow is as follows:  
1. Take one side corner of the bridge deck as the coordinate origin; the width of the bridge is \(W\) and the length is \(L\). Set the width direction of the bridge as the x-axis, the length direction as the y-axis, and the width of the vehicle is set as \(W^{\prime}\), as shown in Figure 5. 2. Combine the bridge deck change detection results to generate the crater location matrix \(P=[(x_{1},y_{1}),(x_{2},y_{2}),\ldots,(x_{M},y_{M})]\) and the diameter matrix \(d=[d_{1},d_{2},\ldots,d_{M}]\) of the crater, where the order in the sample crater location matrix is sorted from smallest to largest according to the size of the x-coordinate; \(x_{i}\) is the x-coordinate, \(y_{i}\) is the y-coordinate, \(M\) is the number of craters, and \(d_{i}\) is the diameter of the ith crater. Calculate the distance \(D_{jk}(j,k=1,2,\ldots,M)\) between the centers of any two craters and form the distance square matrix \(D\), where the elements of the square matrix can be calculated by the following equation: \[D_{jk}=\sqrt{(x_{j}-x_{k})^{2}+(y_{j}-y_{k})^{2}},\] (6)  
Figure 5: Simplified diagram of bridge deck. 3. If square \(D\) does not exist, i.e., there is only one crater, skip to step 5.; if square \(D\) exists, compute the rows and columns of all elements in the lower triangular portion of square \(D\) (excluding the diagonal) that are smaller than \(\frac{d_{i}}{2}+\frac{d_{i}}{2}+W^{\prime}\), i.e., the numbering of the non-existing through-paths between the two craters, and form the matrix \(\zeta\), in which each row contains the row numbering and the column numbering of the conforming elements, with the element on the left-hand side being the smaller numbered value, and the element on the right-hand side of the column being the numbering of the larger values; the different rows are sorted from smallest to largest according to the size of the elements on the left: \[\zeta=\left[ \begin{array}{cc}\xi_{11}&\xi_{12}\\ \xi_{21}&\xi_{22}\\ \ldots&\ldots\\ \xi_{n1}&\xi_{n2}\end{array} \right],\] (7) where \(n\) is the number of elements less than \(\frac{d_{i}}{2}+\frac{d_{k}}{2}+W^{\prime}\) in the lower triangular part of the \(D\)-square matrix. ;
4. Combination of non-adjacent craters. Two craters with a distance between them of less than the width of the through-lane are referred to as immediate neighboring craters, and such craters are merged.