## 2 Developed Methodology
### Constructing Edge Maps
The second derivatives are computed by the second derivatives of the local intensity. The second derivatives are computed by the second derivatives of the local intensity. The third derivatives are computed by the second derivatives of the local intensity. derivatives of an image are calculated by the gradient vector and Laplacian Operator. The Sobel [35] edge operator provides vertical and horizontal edges defined by two horizontal and vertical masks. Like [PERSON] [35], Prewitt [38] operator performs a two-dimensional spatial gradient measurement, which consists of a pair of \(3\times 3\) convolution kernels. One kernel estimates gradient in the x-direction and the other estimates gradient in y-direction. The LoG operator [39] has been developed based on the calculation of the second derivative of the local intensities. In this operator, the sensitivity of Laplacian operator to noise has been reduced by operating Gaussian filter first. Haar transform [36] of matrices computes averages and differences of neighboring pixels in various combinations, which can be used for identifying and locating edges in an image. Haar transform [36] of an image generates a collection of sub-bands, more basic images; each of them contains different fine-scale and large-scale information of the original image. Multi-scale features of the original image can be extracted directly from the Haar decomposition coefficients, namely detail and approximation coefficients. Experimental results obtained at this stage describe the performance of the above-mentioned techniques in practical crack detection in rammed earth heritage. Figures 4 and 5 show some representative results of the edge detection analysis. As observed through this experimental study (Figure 4), the Sobel edge operator performs better in the extraction of crack pixels from the background for rammed earth images. In particular, [PERSON] predicts fewer missing pixels, although this operator may get a noisier output. Another observation confirms that the implementation of crack detection algorithms cannot achieve optimal performance by merely applying an edge detection operator on a rammed earth image. This can be attributed mainly to the fact that the detection results of the algorithms are influenced by architectural objects. Therefore, these methods are not appropriate for complex images containing architectural features. As observed in Figure 6, edge detection algorithms often join horizontal and vertical architectural lines at the corners (Figure 6a) or architectural lines and cracks at the intersections (Figure 6b,c). To circumvent this difficulty, we apply Sobel edge detection operators in the horizontal and vertical direction separately (Figure 2). Taking derivatives in this manner confirms that oriented edge maps themselves carry high-level feature information. Figure 4: Performance of edge detection operators on rammed earth images. (**a**) Sobel, (**b**) Prewitt and (**c**) Laplacian of Gaussian. Moreover, it is observed that Haar transform method can be an appropriate way to detect horizontal and vertical line objects. Figure 6 shows representative results for the Haar transform implemented on a rammed earth image containing horizontal and vertical architectural lines. It can be concluded that this method can identify horizontal and vertical joints in a rammed earth image and categorize and map them as architectural features. Although a feature classification can be obtained by representing an image through three directional edge maps at different scales and orientations, in rammed earth structures containing multiple cracks and architectural line features, this can lead to a better understanding of the relationship between the different scales and orientations. Figure 5: Sub-bands obtained by Haar transform on a rammed earth image. (**a**) Approximate edge map, (**b**) horizontal edge map, (**c**) vertical edge map and (**d**) diagonal edge map. Figure 6: Misidentification of connected components (CCs) using existing edge detection methods.