Chromatic Framework for Vision in Bad Weather

Conventional vision systems are designed to perform in clear weather. However, any outdoor vision system is incomplete without mechanisms that guarantee satisfactory performance under poor weather conditions. It is known that the atmosphere can significantly alter light energy reaching an observer. Therefore, atmospheric scattering models must be used to make vision systems robust in bad weather. In this paper, we develop a geometric framework for analyzing the chromatic effects of atmospheric scattering. First, we study a simple color model for atmospheric scattering and verify it for fog and haze. Then, based on the physics of scattering, we derive several geometric constraints on scene color changes, caused by varying atmospheric conditions. Finally, using these constraints we develop algorithms for computing fog or haze color, depth segmentation, extracting three dimensional structure, and recovering “true” scene colors, from two or more images taken under different but unknown weather conditions. 1 Vision and Bad Weather Current vision algorithms assume that the radiance from a scene point reaches the observer unaltered. However, it is well known from atmospheric physics that the atmosphere scatters light energy radiating from scene points. Ultimately, vision systems must deal with realistic atmospheric conditions to be effective outdoors. Several models describing the visual manifestations of the atmosphere can be found in atmospheric optics (see [Mid52], [McC75]). These models can be exploited to not only remove bad weather effects, but also to recover valuable scene information. Surprisingly, little work has been done in computer vision on weather related issues. Cozman and Krotkov[CK97] computed depth cues from iso-intensity points. Nayar and Narasimhan[NN99] used well established atmospheric scattering models, namely, attenuation and airlight, to extract complete scene structure from one or two images, irre∗This work was supported in parts by a DARPA/ONR MURI Grant(N00014-95-1-0601), an NSF National Young Investigator Award, and a David and Lucile Packard Fellowship. spective of scene radiances. They also proposed a dichromatic atmospheric scattering model that describes the dependence of atmospheric scattering on wavelength. However, the algorithm they developed to recover structure using this model, requires a clear day image of the scene. In this paper, we develop a general chromatic framework for the analysis of images taken under poor weather conditions. The wide spectrum of atmospheric particles makes a general study of vision in bad weather hard. So, we limit ourselves to weather conditions that result from fog and haze. We begin by describing the key mechanisms of scattering. Next, we analyze the dichromatic model proposed in [NN99], and experimentally verify it for fog and haze. Then, we derive several useful geometric constraints on scene color changes due to different but unknown atmospheric conditions. Finally, we develop algorithms to compute fog or haze color, to construct depth maps of arbitrary scenes, and to recover scene colors as they would appear on a clear day. All of our methods only require images of the scene taken under two or more poor weather conditions, and not a clear day image of the scene. 2 Mechanisms of Scattering The interactions of light with the atmosphere can be broadly classified into three categories, namely, scattering, absorption and emission. Of these, scattering due to suspended atmospheric particles is most pertinent to us. For a detailed treatment of the scattering patterns and their relationship to particle shapes and sizes, we refer the reader to the works of [Mid52] and [Hul57]. Here, we focus on the two fundamental scattering phenomena, namely, airlight and attenuation, which form the basis of our framework.