# Inhomogeneous Illumination Image Enhancement Under Extremely Low Visibility Condition
## 1 Introduction  
An optical imaging system usually employs a point-to-point mapping between the object and the image to capture pristine information. However, under extremely low visibility conditions, namely, imaging through the atmosphere over long distance, the optical transmission process is disturbed, resulting in poor imaging quality. During transmission, atmospheric absorption results in the degradation of ballistic light. On the other hand, atmospheric scattering produces snake light and diffuse scattered light, which introduce noise and background interference to the original light field, respectively [1]. These complex processes are considered irreversible and entropy gaining [2, 3]. Thus, it has been a challenge to extract information over long distances through dense fog, or thick scattering media [4]. Yet, for practical applications, extending the imaging distance through atmospheric scattering media to collect the desired light information is vital [5]. Although target recognition, object detection, or image enhancement techniques using the deep neural network (DNN) have seen significant advances in recent years, the application of the DNN is often limited to certain atmosphere or weather conditions. In low visibility condition, the method requires special image preprocessing before executing the DNN [6, 7, 8, 9]. To reconstruct images digitally under adverse weather conditions such as fog, haze, and sandstorms, numerous methods were developed [10, 11, 12, 13, 14]. The common idea acrossthese methods is to suppress the scattered light and to recover information by utilizing the ballistic light, which contains pristine information through the atmosphere. A comprehensive way is to amplify the captured image by reasonable mapping, maintaining the fidelity while increasing its magnitudes, thus enhancing the perceptibility of a system. Histogram equalization (HE) is an example as an efficient way of mapping [15], utilizing the image's cumulative density function (CDF) to enhance visual contrast. The evolution of HE follows Contrast Clipped Adaptive histogram equalization (CLAHE) [16], which includes dividing the image into fractions for localized HE and applying a bilinear interpolation between the boundaries of the blocks. The various algorithms based on CLAHE were subsequently proposed [17; 18; 19]. While these algorithms are quite successful in addressing the majority of scenarios involving atmospheric scattering, in situations with inhomogeneous illumination, the discontinuity of image blocks can nevertheless degrade the image quality. Generally, the inhomogeneity of illumination roots from the vignetting effects of the lenses, the inconformity of the camera pixel response, and the inhomogeneity of illumination. In digital processing, methods such as top-hat transformation [20] and low-rank and sparse decomposition [21] can help achieve good effects in general. However, preserving details of the image for a single image input is still a challenge. The Single Scale Retinex (SSR) uses Gaussian kernel to filter the image, which is effective [22]. However, the method requires a manual selection of filter parameters. The Multi Scale Retinex (MSR) [23] solves this issue by applying the linear combination of various kernel sizes. Despite this improvement, the enhancement achieved is typically limited to linear stretching or exponential transformation. While the MSR performs well under normal foggy conditions, its effectiveness diminishes significantly in extremely low visibility conditions, where the reconstruction effects are often inadequate. In a related study, [PERSON] et al. [24] proposed a method that combines the Retinex theory, color space conversion, and adaptive logarithmic transformation to enhance low-light images. Although this method does not specifically address extremely low visibility conditions, it aims to improve overall image perception. Recently, deep learning-based image enhancement techniques have become mainstream [25].