# Improved Bilateral Filtering for a Gaussian Pyramid Structure-Based Image Enhancement Algorithm
## 1 Introduction  
With the development of intelligent monitoring technology, a large number of cameras have been deployed in intelligent cars, traffic monitoring, and military investigation. However, weather conditions have a great influence on the quality of video images. In particular, some foggy weather may need image enhancement rather than proceeding to the next step such as image monitoring [1; 2; 3]. The scattering of atmospheric particles in the fog introduces defects such as uneven exposure, low contrast, and serious color distortion in images captured by a Charge-coupled Device(CCD) camera. Since it is not possible to engineer these devices to eliminate the influence of atmospheric scattering due to the physical limitations of CCD sensors, the development of algorithms that reduce the effect of fluctuations in incident light--to improve the quality of images--is of great significance. Retinex theory was originally developed by [PERSON] as a model for explaining human color perception [4; 5; 6]. [PERSON] et al. [7; 8] subsequently extended this theory into a general-purpose image enhancement algorithm to address problems caused by changing the lighting and atmospheric conditions inherent to the process of acquiring images of Earth from space. The single-scale Retinex (SSR) algorithm provides the dynamic range compression, color constancy, and sharpening that are required to alleviate these problems. In essence, based on convolution with a Gaussian function with aspecific scale factor, it operates by separating incident light components from reflected light components to improve the contrast in an image. As such, it is suitable for processing multispectral satellite imagery, and applicable in diverse areas such as aerospace exploration [9], aviation safety [10; 11], medical radiography [12], underwater photography [13; 14], forensic investigations [15], and general-purpose photography [16; 17]. Several improvements have been made to the SSR algorithm since its initial development, in order to achieve a balance between dynamic range compression and tonal rendition. As the SSR's image enhancement effect depends on the scale factor of the Gaussian function, the multi-scale Retinex (MSR) algorithm [8] was developed to combine dynamic range compression, color consistency, and tonal rendition, producing images that compare favorably with human visual perception. Here, the input image is processed using three different scale factors (small, intermediate, and large), to ensure that the color fidelity and resolution of the image are retained. In the multi-scale Retinex with color restoration (MSRCR) algorithm, a supplementary color restoration process is included with the MSR algorithm to compensate for the color desaturation inherent in its operation. The resulting algorithm yields images with good color rendition even for severe gray-world violations. In Refs. [18] and [19], a different image enhancement framework based on the Retinex algorithm was proposed, in which the Gaussian filter (GSF) used in the traditional Retinex algorithm is replaced with a region covariance filter (RCF). In contrast to GSFs, for each pixel, the output of an RCF depends on the covariance between local image features. Therefore, an RCF is self-adapting to different pixels in an image, and it can thus estimate the nature of incident illumination more accurately than a GSF. Because of its ability to enhance contrast, eliminate noise, and enhance details in an image, the RCF-Retinex algorithm can be considered to have the best overall performance of the Retinex-based enhancement methods. [PERSON] et al. [20] proposed a mixed multi-Retinex method combined with fractional differentiation that can adjust its ambient illumination processing capacity. Hence, the dynamic range of an image captured in low light conditions can be modified to reduce noise caused by poor lighting and enhance the quality of nighttime images.