# Investigations into Picture Defogging Techniques Based on Dark Channel Prior and Retinex Theory
## 1 Introduction  
Image quality is critically important in vision-based applications such as object detection, intelligent driving, and video surveillance systems. However, under foggy conditions, suspended atmospheric particles cause light absorption, refraction, and reflection, significantly degrading image visibility, contrast, texture details, and color fidelity. This degradation severely impairs the performance of computer vision algorithms, making defogging an essential preprocessing step for visual perception tasks. The critical importance of defogging is further underscored by its diverse applications: In intelligent driving systems, it restores obscured traffic elements (e.g., pedestrians and road signs), directly improving object detection accuracy and mitigating safety risks. For remote sensing and aerial monitoring, it corrects atmospheric distortions in satellite/UAV imagery, enabling preciseland cover classification and disaster assessment. In surveillance security systems, edge-preserving algorithms recover identifiable features (e.g., faces and license plates) from foggy footage for forensic analysis. For drone-based topographic mapping, it rectifies contrast loss in mountainous terrain where localized fog causes significant detail distortion. These mission-critical applications highlight defogging's societal impact in maintaining computer vision reliability under environmental degradation. To address these needs, current defogging algorithms are primarily categorized into three approaches: image enhancement methods [1; 2; 3], image restoration techniques [4; 5; 6; 7], and hybrid approaches [8; 9; 10]. Image enhancement techniques aim to improve the visual quality of images by enhancing contrast and sharpness. These methods directly process the image to remove haze and improve visual clarity. Although they do not explicitly model the physical effects of atmospheric scattering, they can effectively address issues such as uneven illumination and enhance image details. This makes them particularly useful for improving the accuracy of atmospheric light estimation and transmittance computation in hazy images. Early enhancement algorithms were based on the gray-level histogram of the image, such as histogram equalization [11], gamma correction [12], and logarithmic transformation [13]. These methods, however, often fail to consider the local relationships between pixels, leading to the potential over-enhancement or under-enhancement of the image. More recent approaches, such as those based on wavelet transforms [14] and Retinex theory [15; 16; 17; 18], have shown greater promise in addressing these limitations. Retinex theory, in particular, has gained significant attention in the field of image enhancement. This theory, which models the way the human visual system perceives color and brightness, decomposes an image into illumination and reflectance components. By manipulating these components, Retinex-based methods can effectively enhance image details and improve overall visual quality. For instance, the Center-Surround Retinex (CSR) model computes the local contrast of an image, which can be used to enhance details in dark areas and improve the overall image quality [15]. [PERSON] et al. [16] proposed a super-Laplacian prior for reflectance and used an L1-norm regularization for the multi-level gradient of the reflectance to highlight important structural elements and fine-scale details in images. In the context of non-uniform illumination, Retinex-based methods have been particularly effective. These methods simulate the perception of physical reflectance images by the visual system through the computation of contrast. The image is decomposed into perceived reflectance and perceived illumination components. Subsequently, the dynamic range of the illumination component is adjusted in accordance with the visual system's response to light intensity, thereby achieving image enhancement.