Fast visibility restoration from a single color or gray level image

One source of difficulties when processing outdoor images is the presence of haze, fog or smoke which fades the colors and reduces the contrast of the observed objects. We introduce a novel algorithm and variants for visibility restoration from a single image. The main advantage of the proposed algorithm compared with other is its speed: its complexity is a linear function of the number of image pixels only. This speed allows visibility restoration to be applied for the first time within real-time processing applications such as sign, lane-marking and obstacle detection from an in-vehicle camera. Another advantage is the possibility to handle both color images or gray level images since the ambiguity between the presence of fog and the objects with low color saturation is solved by assuming only small objects can have colors with low saturation. The algorithm is controlled only by a few parameters and consists in: atmospheric veil inference, image restoration and smoothing, tone mapping. A comparative study and quantitative evaluation is proposed with a few other state of the art algorithms which demonstrates that similar or better quality results are obtained. Finally, an application is presented to lane-marking extraction in gray level images, illustrating the interest of the approach.

1. Introduction

In surveillance, intelligent vehicles, and remote sensing systems, the image appearance is subject to weather conditions and thus affected by haze, fog and smoke. On a gray level image, the model of the effect of the fog is established by Koschmieder as the following relationship [4]:

$$L(x,y)=L_{0}(x, y)e^{-kd(x,y)}+L_{s}(1-e^{-kd(x,y)})\eqno{\hbox{(1)}}$$ where is the apparent luminance at pixel , is the distance of the corresponding object with intrinsic luminance is the luminance of the sky and denotes the extinction coefficient of the atmosphere. This model is directly extended to a color image by applying the same model on each RGB component, assuming a camera with a linear response. The first effect of the fog is an exponential decay of the intrinsic luminance and of the intrinsic colors. Thus, the contrast of the object is reduced and thus its visibility in the scene. The second effect is the addition of a white atmospheric veil which is an increasing function of the object distance .