# Underwater Degraded Image Restoration by Joint Evaluation and Polarization Partition Fusion
## 2 Underwater Degraded Image Restoration Methods  
### Underwater Polarization Image Restoration Model  
Most of the current methods, which are based on the Jaffe-McGlamery model, improve and optimize this basic underwater physical model. In this paper, this consists of an active light source, a polarizer, detection target, turbid water, polarizer, and polarization camera. Analyzing the known scattering properties of light, it can be seen that the information received by the polarization imaging model consists of a target light component, a forward-scattering component and a backward-scattering component. Target light is emitted by an active light source that is reflected on the surface of the target object. Forward-scattered light is reflected from the target, which is scattered by impurities in the water before entering the camera. Scattering is the cause of blurred images and the loss of contrast. Therefore, the construction of an underwater polarization image clarity model can effectively separate the forward and backward scattering information in the image and recover the target light, as shown in Figure 1a. Since the intensity of forward-scattered light is extremely low compared to backscattered light, considering forward-scattered light within the model will significantly increase the complexity of the algorithm and will not have much effect on the improvement of image quality. Therefore, this paper focuses on the relationship between the target light and the backscattered light in the underwater polarization imaging. Based on the active light underwater polarization imaging schematic, we know that the total optical signal I received by the system is expressed as:  
\[I_{(x,y)}=S_{(x,y)}+B_{(x,y)} \tag{1}\]  
where \(I_{(x,y)}\) is the image obtained by the underwater polarization imaging system, which is the original information received by the camera, \(S_{(x,y)}\) is the reflected light from the target, and \(B_{(x,y)}\) is the backscattered light. The goal of underwater image restoration is to solve \(S_{(x,y)}\) to overcome the effect of the backscattered light \(B_{(x,y)}\) in the original image \(I_{(x,y)}\). In this paper, the polarization information of light is described by Stokes vectors (parameters \(I\), \(Q\), \(U\), \(V\)), and a representation of Stokes vectors can be derived  
\[I=I(0^{\circ},\ 0)+I(90^{\circ},\ 0)\]  
Figure 1: (**a**) Schematic diagram of underwater polarization imaging of active light; (**b**) polarization orthogonal images. \[Q=I(0^{\circ},0)-I(90^{\circ},\ 0) \tag{3}\]  
\[U=I(45^{\circ},0)-I(135^{\circ},\ 0) \tag{4}\]  
\[V=I(45^{\circ},\pi/2)-I(135^{\circ},\pi/2) \tag{5}\]  
where \(I\) denotes the total light intensity, which is the sum of the light intensity components in the two polarization directions of \(0^{\circ}\) and \(90^{\circ}\), \(Q\) denotes the difference between the light intensity components in the two polarization directions of \(0^{\circ}\) and \(90^{\circ}\), \(U\) denotes the difference between the linearly polarized light components in the two polarization directions of \(45^{\circ}\) and \(135^{\circ}\), and \(V\) is the difference between the left rotationally polarized light and the right rotationally polarized light. In this paper, we mainly use line-polarized light for the original information acquisition, and do not acquire circularly polarized light, and the line polarization degree is used in the subsequent calculations, so we assume that the circularly polarized parameter \(V\) = 0. This assumption has a negligible effect on the subsequent image restoration, and can be ignored. According to the definition of polarization degree, the line polarization degree is expressed as follows:  
\[P=\frac{\sqrt{Q^{2}+U^{2}}}{I} \tag{6}\]  
The equations for the fitted curves of light intensity at different polarization angles are as follows:  
\[I(\alpha)=\left[I+Qcos2\alpha+Usin2\alpha\right]/2 \tag{7}\]  
where \(\alpha\) is the angle between the polarization direction and the standard direction.