# Enhancing Image Dehazing with a Multi-DCP Approach with Adaptive Airlight and Gamma Correction
## 4 Proposed Method
### \(1\times 1\) Dark Channel Priors  
This section delineates the derivation of the multiple \(1\times 1\) DCPs from multiscale hazy, inverted, and Euclidean difference images that constitute the core component of our proposed method.  
4.1.1. Inverted and Euclidean Difference Images  
Hazy images often display notable differentiation between low-light and bright regions, resulting in significant discrepancies during transmission map estimation. To address this issue, we propose employing image inversion to enhance low-light portions and darken bright ones, thereby alleviating distortions caused by haze. The image inversion is carried out channel-wise and defined as follows:  
\[I_{c}^{rev}(x)=1-I_{c}(x) \tag{2}\]  
where \(I_{c}^{rev}(x)\) is the inverted image.  
To measure the disparity between the original and inverted images, we leverage the Euclidean difference image \(I_{c}^{c}(x)\), which is defined as follows:  
\[I_{c}^{e}(x)=\left\|I^{G}(x)-I_{c}^{s}(x)\right\| \tag{3}\]  
where \(I^{G}(x)\) is a grayscale image, and \(I_{c}^{s}(x)\) is the stretched \(I_{c}^{rev}(x)\).  
The Euclidean difference image improves the visibility of haze-affected regions and enhances transmission map estimation precision.  
For a unified analysis, the Euclidean difference images from R, G, and B channels are combined as follows:  
\[I^{e}(x)=\sqrt{(I_{R}^{e}(x))^{2}+(I_{G}^{e}(x))^{2}+(I_{B}^{e}(x))^{2}} \tag{4}\]  
where \(I^{e}(x)\) is the aggregate Euclidean difference image, enhancing the estimation's accuracy and reducing distortions in the haze removal process.  
4.1.2. Intermediate Transmission Maps  
In [PERSON]'s approach [4], DCP derived from the \(15\times 15\) patch size led to residual haze persisting around objects (halo artifacts). Conversely, DCP with \(1\times 1\) patch size focuses solely on pixel values, disregarding object boundaries and local patterns due to the absence of neighboring pixel information. Additionally, guided filters [18] coupled with multiscale processing are introduced to estimate a more precise transmission map.  
Specifically, as depicted in Figure 1, a hazy image \(I(x)\) is first resized to \(\times 0.5\) and \(\times 0.25\) of its original size. Subsequently, three distinct dark channels with a patch size of \(1\times 1\) are computed from these two resized images and \(I(x)\). Intermediate transmission maps for each dark channel are estimated with (1), along with our proposed airlight estimation method (Section 4.2). A guided filter [18] is then applied on each intermediate transmission map. Following this, the scaled intermediate transmission maps are restored to match the dimensions of \(I(x)\) and aggregated through averaging to yield \(t^{eq}(x)\).  
The same procedure is iterated for inverted image \(I_{c}^{rev}(x)\) and channel-wise Euclidean difference images \(I_{c}^{e}(x)\), resulting in intermediate transmission maps \(t^{rev}(x)\) and \(t^{e}(x)\), respectively. Multiscale processing and averaging are also applied to the \(I^{e}(x)\) obtained in (4).  
Figure 1: Overview of the proposed method. Our method consists of main modules such as multiscale and multiple features \(1\times 1\) DCP computation for enhanced transmission map estimation, airlight estimation, and adaptive gamma correction.