# An Improved Wavelet Modulus Algorithm Based on Fusion of Light Intensity and Degree of Polarization
## 3 Experimental Results and Analysis
The red areas of (e1) and (e2) in Figure 7 were the detailed edges that cannot be detected by any algorithm in the light intensity image. Figure 6: Total light intensity image and degree of polarization image obtained by calculation. 1 and 2 are areas where the contrast of degree of polarization images is higher than that of the total light intensity image. In order to further verify the effectiveness of the algorithm in this paper, 1%, 5%, and 10% uniform random noise were added to each original image, and the edge detection results are shown in Figure 8. In the figure, the first, third, and fifth lines correspond to the 1%, 5%, and 10% noise images of glass, and the second, fourth, and sixth lines correspond to the 1%, 5%, and 10% noise images of liquid, respectively. It can be seen that the Sobel algorithm for noisy images still had the problem of thick edges, and the Sobel algorithm had false noise edges. Although gaussian filtering exists in the Canny algorithm, false edges of noise are still generated, and the more noise there is, the more false edges are generated. The wavelet modulus maxima algorithm has poor sensitivity to noise. As can be seen from the figure, the wavelet modulus maxima algorithm generated fewer false edges compared with the Sobel algorithm and Canny algorithm, but it had the problem of poor edge continuity. The improved wavelet modulus maxima algorithm was less sensitive to noise and had stronger edge connectivity. It is obvious that the improved wavelet modulus maxima algorithm in Figure 8 had fewer noise edges than the traditional wavelet mode maximum algorithm, and the edge extraction was more complete. The red area in Figure 8 was the most obvious. The improved wavelet modulus maxima algorithm for the fusion of light intensity and polarization degree detected more details of edges. The red area (e) in Figure 8 detected edges that could not be reached by the light intensity image. Therefore, the fusion algorithm of light intensity and polarization degree had the best edge detection effect. Figure 7: Comparison of edge detection in original images. a1, b1, c1, d1, and e1 are the edge detection results of glass images, a2, b2, c2, d2, and e2 are the edge detection results of liquid images. (**a**) Sobel algorithm of light intensity image, (**b**) Canny algorithm of light intensity image, (**c**) Traditional wavelet modulus maxima algorithm of light intensity image, (**d**) Improved wavelet modulus maxima algorithm of light intensity image, (**e**) Improved wavelet modulus algorithm based on fusion of light intensity and degree of polarization. \[I=I_{0}+I_{90}, \tag{15}\]0 Comparison of edge detection in noisy images. (**a**) Sobel algorithm of the light intensity image, (**b**) Canny algorithm of the light intensity image, (**c**) Traditional wavelet modulus maxima algorithm of the light intensity image, (**d**) Improved wavelet modulus maxima algorithm of the light intensity image, and (**e**) Improved wavelet modulus algorithm based on the fusion of light intensity and degree of polarization. Next, we used the entropy function to evaluate the edge image quality obtained by the improved wavelet modulus algorithm based on the fusion of light intensity and degree of polarization. The definition of entropy in the image is:  
\[I=I_{0}+I_{90}, \tag{15}\]1  
where \(p_{i}\) is the probability of occurrence of pixel intensity \(i\), and \(H\) is the entropy of the image. The evaluation table of edge detection results is obtained as shown in \[I=I_{0}+I_{90}, \tag{15}\]2  
The smaller the value of \(H\), the less information the edge has, and the larger the value of \(H\), the existence of non-single-pixel edges and false noise edges. Therefore, the \(H\) of a good edge-detection algorithm should be between the maximum and minimum of different edge algorithms [19]. Figure 9 shows the graph analysis of the edge detection results.