# Adaptive Tolerance Dehazing Algorithm Based on Dark Channel Prior
## 1 Introduction  
Haze is a common natural phenomenon. Even on a clear summer day, distant targets are affected by haze due to the evaporation of surface water vapor. In weather conditions such as haze, the horizontal visibility [1] is significantly reduced due to the scattering of a large number of tiny droplets or aerosols suspended in the atmosphere. This change creates considerable difficulties in outdoor monitoring, automatic navigation, target tracking, etc., resulting in outdoor vision systems working improperly. Therefore, it is very important to study how to effectively treat the degraded images obtained in severe weather conditions. The processing of hazy images generally falls into two categories: enhancement-based algorithms and physics-based algorithms. Histogram equalization [2], homomorphic filtering [3] and Retinex [4] are all based on image enhancement algorithms. These algorithms can effectively improve the contrast of hazy images and highlight certain information in the image, but they do not consider the formation principle of hazy images and the degradation mechanism of the images. Another category is based on the atmospheric scattering model [5]. By analyzing the inverse process of the image degradation process and obtaining the relevant parameters of the degradation process, a clear image is recovered. The image restored by this method is real, and the image information can be more completely preserved. Therefore, a single image dehazing technology based on physical models has gained broad attention. [PERSON] [6] proposed removing haze from color images based on independent component analysis (ICA). However, ICA is ineffective for thicker hazy images due to the lack of color information. [PERSON] [7] used a median filter to calculate the minimum color component of the atmospheric veil. The medianfiltering of this method does not preserve the edges well, and the desired results cannot be obtained at deep discontinuous edges. [PERSON] et al. [8] proposed a dark channel prior, first calculating the rough transmission according to the atmospheric scattering model and the dark channel prior and then using the soft matting algorithm [9] to optimize the transmission to obtain haze-free images. To solve the issues of edge loss and halo artifacts in haze-free images, [PERSON] et al. proposed a series of DCP-based methods to enhance the estimation of atmospheric light, such as a modified joint trilateral filter (MJTF)-based DCP method [10], a modified gain intervention filter-based DCP method [11], and a fourth-order partial differential equation-based trilateral filter (FPDETF) dehazing method [12]. To reduce the color distortion, the DCP restoration model was also redefined. Recently, with the continuous development of deep learning, an increasing number of neural network algorithms have been used in the field of image processing and have achieved good results. Therefore, algorithms based on deep learning can be considered the third kind of dehazing algorithm. The existing learning-based dehazing algorithms mostly use deep learning to intelligently learn the haze feature and output the medium transmission map, and then recover the haze-free image through the atmospheric scattering model. For example, [PERSON] et al. [13] proposed a trainable end-to-end system, DehazeNet, for medium transmission estimation. [PERSON] et al. [14] proposed a dehazing algorithm based on residual depth CNN. Among the above algorithms, the DCP method proposed by [PERSON] [8] has been extensively studied due to its simple principle and superior results. However, this method has two drawbacks. (1) The soft matting algorithm [9] needs to perform iterative calculations, which leads to high algorithmic complexity. To improve the computational efficiency, [PERSON] [15] proposed a guided filter with edge-maintaining characteristics instead of the soft matting algorithm to refine the transmission map.