## 3 Results
#### 3.1.1 Image Similarity and Bhattacharyya Distance  
In the comparative analysis between images A-L and image 0, image A employs color-coordinated repair material, while image B acts as a control using traditional concrete repair methods. Images C through L demonstrate individual trials with various colors for repair, as depicted in Figure 16, following a single color block pattern from Figure 12. Metrics including histogram comparisons and Bhattacharyya Distance calculations assess visual similarity for each pair. These metrics are integrated into a final Similarity Score, providing a quantifiable measure of the visual coherence each technique achieves. This systematic approach allows a comprehensive evaluation of various wall repair methods, underscoring the significance of aesthetic considerations in urban environmental restoration projects.  
Comparing each of the above repair methods with VETAR, the following comparative histogram was obtained (Figure 17). The Similarity Score is presented in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Image Label** & **Bhattacharyya Distance** & **Similarity Score** \\ \hline A & 0.0414 & 95.86 \\ B & 0.2127 & 78.73 \\ C & 0.1665 & 83.35 \\ D & 0.1693 & 83.07 \\ E & 0.1807 & 81.93 \\ F & 0.1718 & 82.82 \\ G & 0.1823 & 81.77 \\ H & 0.1934 & 80.66 \\ I & 0.1847 & 81.53 \\ J & 0.1881 & 81.19 \\ K & 0.1889 & 81.11 \\ L & 0.1899 & 81.01 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Bhattacharyya Distance and Similarity Score.  
Figure 15: (**a**) VETAR method; (**b**) common ordinary cement mortar repair methods.  
Figure 16: Different cements for repairing walls. (**A**) Color-coordinated repair material; (**B**) control using traditional concrete repair methods; (**C–L**) individual trials with various colors for repair.  
Figure 17: Comparison of histograms of different repair methods. Image A (see Figure 16) is outlined in red dashed lines; other letters correspond to Figure 16.  
The horizontal axis (X-axis) represents \"Bins\". In image processing, a \"bin\" denotes a range of pixel intensities in a histogram. For grayscale images, these bins typically represent different levels of gray. In this code, as 256 is used for the number of bins, the histogram has 256 bins corresponding to gray levels from 0 to 255.  
The vertical axis (Y-axis) represents \"number of pixels\", which is the number of pixels in each bin. This value indicates how many pixels fall within that specific range of gray level in the image.  
In this code, the cv2.calcHist function is used to calculate the histogram of the image. The output of this function is an array, where each element's value represents the pixel count for the corresponding bin. These values are then used to draw the histogram, where the height of each bin corresponds to the number of pixels at that level of gray.  
In the generated histogram, the histograms of two images are overlaid for comparison:  
The red curve represents the histogram of \"image 0\".  
The blue curve represents the histogram of another image being compared, such as \"A\", \"B\", etc.  
After comparing the histograms of images B through L with the reference image 0, there are clear differences in the arrangement of peaks and troughs. These variations indicate differing degrees of visual coherence with the reference image, which can be attributed to the various repair techniques and materials utilized in each case. While image A (outlined in red dashed lines) demonstrates high consistency with the reference histogram, the other images differ, showing variations in their grayscale value distributions. These differences are apparent in the spacing and height of the histogram bars, suggesting that the color matching or texture consistency may not be as precise as that achieved with the VETAR method used for Image A.  
The remaining histograms exhibit additional peaks or different peak structures, which may indicate that the repair materials used have different textural properties compared to the original structure.