# Underwater Degraded Image Restoration by Joint Evaluation and Polarization Partition Fusion
## 2 Underwater Degraded Image Restoration Methods
### Polarization Difference Recovery in Low Polarization Region  
Firstly, in this paper, the partitioned, pre-extracted images are subjected to maximum filtering; the advantage of maximum filtering is that it removes the dark spots present in the image and also increases the brightness of the image. It achieves the effect of enhancing the target outline and facilitates target extraction.  
\[g_{choose}(x,y)=\underset{(s,t)\in\Omega(x,y)}{max}(I_{choose}{}^{c}(s,t)) \tag{21}\]  
where \(I_{choose}{}^{c}\) is the image after the selected partition; \(\Omega(x,y)\) is the window at the pixel point; and \(c\) is the image three channels. After that, using the Otsu method, the image is binarized according to the probability of the variance distribution, and the target coordinate information is extracted separately. Next, edge recognition is performed using sobel operator, and finally, closure operation is performed to realize the extraction of multiple regions.  
The Otsu method (OTSU) is an algorithm for determining the threshold for binarized segmentation of an image, which is also known as the maximum inter-class variance method; it divides an image into two parts, the background and the foreground, according to the gray scale characteristics of the image. Since the variance is a measure of the uniformity of the gray scale distribution, the larger the inter-class variance between the background and the foreground, the larger the difference between the two parts of the image. The advantages of this method are that it is simple to understand, fast to compute, and applicable to most image segmentation problems.  
Figure 3: (**a**) The traditional method of low-polarized region recovery defects; (**b**) pseudo-color plot of polarization (the scale range on the right is the polarization value calculated by Equation (6)).  
The Sobel operator contains convolutional templates in both horizontal and vertical directions, as shown below.  
\[\begin{bmatrix}-1&-2&-1\\ 0&0&0\\ 1&2&1\end{bmatrix}\begin{bmatrix}-1&0&1\\ -2&0&2\\ -1&0&1\end{bmatrix}\]  
As can be seen from the previous section, using the traditional method to recover low polarization regions has defects, and the polarization difference method can overcome this defect; it uses two orthogonal polarization images for the difference, and low polarization regions are well recovered. Therefore, in this paper, the polarization difference method is used for the low polarization region. Assuming that the target light and the background scattered light are both perfectly linearly polarized, two orthogonally polarized images are then acquired and differenced. The active light source emits a light beam, which is first polarized by a linear polarizer \(P_{1}\) and then irradiated onto the target T. Another linear polarizer \(P_{2}\) is placed in front of the detector to act as a detector, as shown in Figure 4. When the direction of polarization of \(P_{2}\) is parallel to the direction of polarization of \(P_{1}\), the image of light intensity parallel to the direction of polarization of the incident light can be obtained, denoted as \(I_{\text{co}}\). When you rotate \(P_{2}\) so that its polarization direction is orthogonal to the polarization direction of \(P_{1}\), you can obtain an image of the light intensity orthogonal to the polarization direction of the incident light, denoted as \(I_{\text{cross}}\)[19]. Polarization differential imaging is the difference between the light intensities of the above two mutually perpendicular polarization states: \(I_{\text{difference}}=I_{\text{co}}-I_{\text{cross}}\).