Fog is a common condition that reduces the contrast of an image

bleaches the surface color

and considerably reduces the value of outdoor images. To address this problem

we propose a defogging method for a single degraded image on the basis of dark channel and incident light assumption. We scan the image with a window to determine the window with the maximum mean brightness. We use the obtained average value as the atmosphere light. The dark channel prior assumption raised by He is not suitable to images that contain a large scene

so we weaken the assumption. We assume that a channel of a pixel whose value is zero exists. Basing on this assumption

we identify the darkest pixel value in the entire image and use the darkest pixel value as the global dark channel. We use the ratio of the grayscale of the point to the atmospheric light as the basis transmission of the image. Using this basis transmission

we conduct the initial dehazing. The transmission rate of the image will then be stretched to the [0

1] range. Images taken under a foggy weather almost have no shadow. We therefore assume that the incident light during a foggy day is uniform. We estimate the transmission by using a multi-scale approach combined with retinex theory that uses Gaussian convolution to estimate illumination. According to the haze imaging model

we can recover a high-quality

haze-free image by using this transmission map and the initial dehazing image. By weakening the dark channel prior assumption of He

we considerably improve its accuracy and perform the initial dehazing on the basis of the weakened assumption. Unlike in other methods

the transmission map of our algorithm does not exhibit an apparent object contour. The fuzzy transmission map is obviously reasonable according to the scattering characteristic of fog. Experimental results indicate that the algorithm can provide an accurate estimation of the transmission

and the restored images show natural colors and clear details. The algorithm also exhibits low computational complexity and almost does not need to set any parameters. Our algorithm shows good results and substantially increases the computing speed compared with haze removal theory on the basis of the dark channel prior of He. The proposed algorithm is not limited by a poor capability in processing images with thick fog

which is a key concern in Fattal's method. This study proposes a new method to assume transmission on the basis of incident light assumption and retinex illumination estimation principle. A large number of comparative experiments show that the algorithm can significantly restore the quality of an image degraded by fog. Our method is effective for images taken under thin and thick fog

demonstrates wide applicability

and involves a simple principle. The proposed method is also applicable to grayscale.