# Visual Image Dehazing Using Polarimetric Atmospheric Light Estimation
## 3 Atmospheric Light Estimation
### Polarimetric Degree-Based Atmospheric Light Estimation  
Based on the observations mentioned in Section 3.3, we propose a new atmospheric light estimation approach for the dark channel dehazing technique. The prerequisite for using our approach is that we acquire the energy images in four polarization directions, denoted as \(i_{0},i_{45},i_{90}\), and \(i_{135}\), for a natural scene image. The polarimetric degrees for each pixel in the captured image are calculated using Equations (9) and (11).  
Next, we search for the lowest 0.1% polarimetric degree pixels in the polarization image and record their positions. From the corresponding positions in the intensity image, we find the brightest pixel to estimate the atmospheric light.  
In our practical implementation (introduced in Section 4), due to detector noise, there might be cases of the incorrect computation of sky polarimetric states, leading to errors in the polarimetric degree statistics and automatic identification of erroneous sky regions and atmospheric light estimation. To address these issues, we made certain adjustments to the algorithm. The revised polarimetric degree calculation method is as follows:  
\[p^{\prime}(x,y)=\frac{\sum_{i\in\Omega_{xy}}p_{i}}{N_{xy}} \tag{12}\]  
In the equation above, \(p^{\prime}(x,y)\) represents the corrected polarimetric degree of pixel \((x,y)\), \(\Omega_{xy}\) is the spatial neighborhood of pixel \((x,y)\), \(p_{i}\) is the polarimetric degree of pixel in the original polarimetric degree image, and \(N_{xy}\) is the number of pixels in \(\Omega_{xy}\). The correction in Equation (12) effectively removes polarimetric degree fluctuations caused by noise and bad pixels in the original polarimetric degree image. After this correction, the modified polarimetric degrees may deviate from the true values, but it ensures that no errors are introduced when seeking the region with the minimum polarimetric degree.  
Due to the lowest response energy limitation of the polarimetric detector, when the incident light is very low, the pixel grayscale values will be in a very low state, causing the signal intensities of the four polarized angles to be close. As a result, the calculated polarimetric degree will be close to 0, leading to lower polarimetric degrees in non-sky regions compared to the sky regions. If there is a certain region of low signal pixels in the image (with a pixel count exceeding 0.1%), it may lead to errors in estimating the atmospheric light intensity. Therefore, we also make a modification to the atmospheric light estimation approach. We set a threshold \(\theta\), and all pixels with polarimetric degrees below this threshold are recorded with their coordinate positions and involved in the subsequent atmospheric light estimation process.  
Figure 4: The statistics of the polarimetric degree in the sky region.  
As shown in Section 3.3, in the vast majority of images, the polarimetric degree of atmospheric light is less than 10% of the average polarimetric degree of the entire image. Considering the algorithm's tolerance, we set the value of \(\theta\) to 0.15. Firstly, we calculate the average polarimetric degree of the image, denoted as \(p^{\prime}\). Then, we calculate \(p_{t}=\theta\times p^{\prime}\). Next, we record the coordinates of all pixels with a polarimetric degree less than \(p_{t}\). Finally, we select the brightest pixel at the corresponding coordinates in the input image as the estimate of atmospheric light.