# Research on Wavelet Transform Modulus Maxima and OTSU in Edge Detection
## 5 Analysis and Discussion  
In the comparison above, the test area image was chosen with a relatively clear outline and homogeneous background in order to make the detection more effective. It is, then, worthwhile to illustrate whether the advantages of the wavelet transform modulo maxima method still exist in the case of a more complex background. Therefore, a bridge image with a more complex background is selected, as shown in Figure 11. Edge detection using wavelet transform modulo maxima is performed, and the results are shown in Figure 12. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithms** & **Information Entropy** & **SSIM** \\ \hline Wavelet transform modulus & 2.5691 & 0.0023 \\ maxima method & 2.1792 & 0.0022 \\ Canny & 2.1792 & 0.0017 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information entropy and SSIM for the three algorithms. Figure 10: Detection results: (a) [PERSON]’s algorithm. (b) [PERSON]’s algorithm. Figure 9: Edge detection results. To better illustrate the detection effect, the Canny algorithm and Laplace algorithm are still used again for edge detection, and the results are shown in Figure 13. The information entropy and SSIM of each of the three are calculated for comparison, as shown in Table 2.  
Figure 11: Original drawing of the bridge. Figure 12: Wavelet transform modulus maxima detection results. Figure 13: Detection results: (**a**) [PERSON]’s algorithm. (**b**) [PERSON]’s algorithm. As can be seen from Table 2, the edge image detected by the wavelet transform modulus maxima method has the highest information entropy and SSIM, which means that its edge image quality is optimal. In other words, the advantage of the wavelet transform modulus maxima method is still present, and even more obvious, when edge detection is performed on images with more complex backgrounds. The results in Tables 1 and 2 show the results of three algorithms (wavelet transform modulo maxima, Canny and Laplace) for Figures 2 and 11, respectively, demonstrating the effectiveness of the wavelet transform modulo maxima method. The background of Figure 2 is mainly water, which is relatively homogeneous, while the background of Figure 11 is trees, which is relatively more complex. The data from the processing results of this method for Figures 2 and 11 are now brought together again in Table 3 for full comparison. As can be seen from Table 3, the information entropy obtained by the wavelet transform modal maxima method used in this paper is roughly at the same level as SSIM, and there is even some increase in the processing index for images with complex backgrounds, with more obvious advantages. The process of edge detection is to find out grey-scale changes in an image, separate high-frequency signals from the image and accurately locate the edge position. The modulus maxima of the wavelet transform mirrors the sharply changing signals, i.e., the edges of the image. With the flexible scale, the wavelet transform has excellent local qualities in both the time and frequency domains. A small scale can distinguish between real edges and noisy signals, while a large scale can remove the influence of noise. A reasonable choice of the scale can optimize the combined performance of both and improve the overall detection effect of the method in this paper. Although this paper demonstrates some of the advantages of the combined application of wavelet transform modulus maxima and OTSU, some shortcomings were found during the processing. After edge detection, the overall outline of the image is very clear, but the detail is not yet fine enough. For example, the cars on the bridge are still not fully detected, the connectivity of the edges still needs to be improved and the visual effect is not yet friendly enough. All need to be further optimized to meet the needs of engineering applications.