# A Polarization-Based Method for Maritime Image Dehazing
## 2 Related Work
### Polarimetric Dehazing Method Based on Stokes Vector  
The Stokes vector is utilized to characterize the polarization properties of the light that has been scattered. Polarimetric dehazing techniques, as referenced in prior research [14], rely on the Stokes vector to acquire four distinct images (I(0), I(45), I(90), and I(135)) corresponding to different polarization orientations (0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\)), and subsequently compute the Stokes vector according to the following formulation:  
\[\begin{array}{l}S_{0}=[I(0)+I(45)+I(90)+I(135)]/2\\ S_{1}=[I(0)-I(90)]\\ S_{2}=[I(45)-I(135)]\end{array} \tag{3}\]  
In Equation (3), \(S_{0}\) represents the total intensity, \(S_{1}\) represents the intensity difference between the vertical and horizontal polarized components, and \(S_{2}\) represents the intensity difference between the 45\({}^{\circ}\) and 135\({}^{\circ}\) polarized components with respect to the x axis. The AOP is derived from \(S_{1}\) and \(S_{2}\), which contain less direct light. Therefore, estimating the air light using the AOP can effectively suppress the influence of direct light. Subsequently, within the selected sky region in the image, \(\theta\) is calculated, and the most frequently occurring \(\theta\) is chosen as \(\theta_{A}\) for the sky region.  
\[\theta=\frac{1}{2}\text{arctan}\frac{S_{2}}{S_{1}} \tag{4}\]  
Then, the degree of polarization \(p\) is computed, and the maximum \(p\) value within the region where \(\theta\) equals \(\theta_{A}\) is selected as the degree of polarization of the air light, denoted as \(p_{A}\). Particularly, when the denominator equals 0 (i.e., \(\theta=k\pi\pm\frac{7}{4}\)), \(\theta=(1\pm 0.001)\cdot\theta_{A}\). Afterwards, the air light \(A\) is obtained as follows:  
\[p=\frac{S_{1}}{S_{0}(\cos^{2}\theta_{A}-\sin^{2}\theta_{A})} \tag{5}\]  
\[A=\frac{A_{p}}{p_{A}}=\frac{I(0)-S_{0}(1-p)/2}{p_{A}\cdot\cos^{2}\theta_{A}}= \frac{I(90)-S_{0}(1-p)/2}{p_{A}\cdot\sin^{2}\theta_{A}} \tag{6}\]  
In general, \(p_{A}\) is usually low. The noise within the air light \(A\), as calculated directly from Equation (6), may be considerably increased. To mitigate the noise within \(A\), a Gaussian low-pass filter is employed for noise reduction, as suggested in prior research [13].  
\[A^{\prime}=A*\frac{1}{2\pi\sigma^{2}}\exp[-\frac{\left(a-a_{0}\right)^{2}+ \left(b-b_{0}\right)^{2}}{2\sigma^{2}}] \tag{7}\]  
In Equation (7), the Gaussian kernel is centered at coordinates (\(a_{0}\),\(b_{0}\)), with (\(a\), \(b\)) representing the image coordinates. The parameter \(\sigma\) is defined in this research as 0.1% of the total image area. Typically, dehazing methods assume a constant value for the extinction coefficient \(\beta\), which may lead to discrepancies between the estimated transmittance (\(t\)) and the actual values. To address this issue, a bias coefficient \(\varepsilon_{1}\) is introduced to calibrate \(A_{\infty}\) and improve the accuracy of the estimated transmittance, \(t\). The optimal bias coefficient selection can be achieved by employing an evaluation function [14]. The final dehazed image can be obtained using Equation (8).  
\[L=\frac{I-A^{\prime}}{1-A^{\prime}/\varepsilon_{1}A_{\infty}} \tag{8}\]