# Investigations into Picture Defogging Techniques Based on Dark Channel Prior and Retinex Theory
## 1 Introduction
that haze concentration is correlated with the difference between brightness and saturation in hazy images. Based on this prior, a linear regression model extracts scene depth information from hazy images, which is then combined with the atmospheric scattering model for haze removal. Figure 1: Model of foggy images. In order to provide high-quality visual data, image fusion-based defogging algorithms aggregate and recombine pertinent or valuable information [31] from many input sources. This method usually uses certain enhancement approaches, first making hazy images clearer, then integrating the improved images using fusion algorithms to provide a dehazed output. For example, [PERSON] et al. applied nonlinear gamma correction [32] with different settings to strengthen hazy images, increasing the resilience of image defogging. The final haze-free image was then created by fusing four luminance-adjusted photos. For defogging, [PERSON] et al. combined multi-exposure image fusion with adaptive structural decomposition [33]. As deep learning has advanced, researchers have turned their attention to multi-feature fusion algorithms based on picture combining, which greatly enhance defogging efficiency through dynamic optimization mechanisms and multi-level feature interaction. In order to significantly improve detail recovery in areas with intense fog, [PERSON] et al. devised MFID-Net [34], which makes use of a multi-feature fusion (MF) module that dynamically weights channel and pixel-level information. The effectiveness of image enhancement techniques for defogging in the previously mentioned approach is limited; the excessive suppression of high-frequency components during the enhancement process can result in the blurring of edge details, and artifacts can be introduced during frequency domain inverse transformation. Nonetheless, some inhomogeneous haze conditions can be addressed by these techniques. They can produce better outcomes when paired with restoration-based defogging algorithms. While supervised deep learning-based fusion techniques typically require well-annotated samples (incurring acquisition costs), unsupervised methods (e.g., GANs) and synthetic data generation (e.g., 3D-rendered hazy images) offer alternatives to reduce annotation dependency. Nevertheless, hybrid approaches combining physical models with efficient learning remain competitive in latency-sensitive applications. In order to overcome problems including imprecise atmospheric light estimation, halo artifacts, and color distortion in sky regions that are inherent in the dark channel prior approach, this study combines the benefits of picture enhancement and restoration techniques. We suggest a defogging approach that integrates Retinex theory with the dark channel prior. This algorithm's primary contributions are as follows:  
1. In order to reduce the effects of non-uniform lighting on the estimation of atmospheric light intensity and transmission maps, improve contrast, and enrich detail information in foggy images, the Retinex algorithm with non-uniform illumination image enhancement that maintains naturalness should be applied. 2. Since the estimation of atmospheric light intensity is susceptible to the influence of bright objects, the Otsu algorithm and edge extraction are used to exclude the region of bright objects in the image to realize the accurate estimation of the atmospheric light value. 3. In order to solve the problem of the halo effect and the color distortion of the sky region in the defogged image, the dark channel is compensated by mean value filtering to suppress the halo effect, and transmittance is optimized, and furthermore, we solve the problem of color distortion by correcting the transmittance of the sky region of the dark channel using a CAP a priori estimation of the depth map. This paper's remaining sections are arranged as follows: Section 2 introduces the theoretical basis and key elements of Retinex-based image enhancement and dark channel a priori defogging.