# An Improved Wavelet Modulus Algorithm Based on Fusion of Light Intensity and Degree of Polarization
## 3 Experimental Results and Analysis  
In order to verify the effectiveness of the improved wavelet modulus maxima algorithm based on the fusion of light intensity and degree of polarization in a complex environment, we conducted edge detection simulation experiments on the original image and the image with added noise, and used the subjective and objective evaluation methods to measure the effectiveness of the algorithm proposed in this paper. The images used in the experiment were from the \" Database of polarimetric and multispectral images in the visible and NIR regions\" [18]; we selected two groups of polarization images in the visible light band, and the polarization directions were 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\), respectively. To facilitate edge detection, we convert the original image to grayscale, as shown in Figure 5. These two groups of images were affected by factors such as lighting, and there was a problem of poor contrast. For example, in region 1 of the glass image and region 2 of the liquid image, no matter the angle, the polarized image was unable to distinguish the internal details of the object information. Using the Stokes vector to calculate the above two sets of images and obtain the total light intensity image and the degree of polarization image, the specific calculation method was as follows:  
\[I=I_{0}+I_{90}, \tag{15}\]  
\[p=\frac{\sqrt{\left(I_{0}-I_{90}\right)^{2}+\left(I_{45}-I_{135}\right)^{2}}}{ \frac{1}{2}\left(I_{0}+I_{90}\right)}, \tag{16}\]  
where \(I\) is the total light intensity, \(p\) is the degree of polarization, and \(I_{0}\), \(I_{45}\), \(I_{90}\), and \(I_{135}\) are the linearly polarized light intensities of 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\) respectively. The calculation results are shown in Figure 6. It can be seen from the figure that the total light intensity image was not much different from the polarization image at different angles, the contrast of the degree of polarization image in area 1 and area 2 was significantly improved, and the edge and detail information were highlighted. Since the degree of polarization image had the function of \"weakening strong light and strengthening weak light\", more complete edge information could be obtained by combining the edge of the light intensity image with the edge of the degree of polarization image. Figure 5: Polarization images at different angles. 1 and 2 are areas with poor contrast. In order to verify the superiority of the improved wavelet modulus maxima algorithm in this paper and the edge extraction integrity of the improved wavelet modulus maxima algorithm based on the fusion of light intensity and degree of polarization, we used the Sobel algorithm, Canny algorithm, traditional wavelet modulus maxima algorithm, and improved the wavelet modulus maxima algorithm to perform edge detection on the total light intensity image, and used the fusion improved wavelet modulus maxima algorithm on the degree of polarization image in Figure 6. The detection results are shown in Figure 7. As can be seen from Figure 7, the Sobel algorithm had the problem of a thick edge in edge detection; the Canny algorithm was sensitive to noise, and there were a lot of noise false edges in the edge detection results. The wavelet modulus maxima algorithm had a strong ability to suppress noise. It is obvious that, compared with the Sobel algorithm and Canny algorithm, there were fewer noise edges, but there was the problem of poor edge continuity. The improved wavelet modulus maxima algorithm also had a strong ability to suppress noise; compared with the traditional wavelet modulus algorithm, the threshold selection was more accurate, and the edge connectivity was stronger. It can be clearly seen that the red regions of (d1) and (d2) in Figure 7 had better edge connectivity than the (c1) and (c2) regions. The edge extraction of the improved wavelet modulus maxima algorithm based on the fusion of light intensity and degree of polarization was more complete.