Chromatic framework for vision in bad weather

Chromatic Framework for Vision in Bad Weather?Srinivasa G.Narasimhan and Shree K.Nayar

Department of Computer Science,Columbia University

New York,New York10027

Email:{srinivas,nayar}@74ef393c5727a5e9856a61a3

Abstract

Conventional vision systems are designed to perform in clear weather.However,any outdoor vision system is in-complete without mechanisms that guarantee satisfactory performance under poor weather conditions.It is known that the atmosphere can signi?cantly 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 scatter-ing.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 con-straints on scene color changes,caused by varying atmo-spheric conditions.Finally,using these constraints we de-velop 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.

1Vision 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 condi-tions 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 scat-tering 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 dichro-matic atmospheric scattering model that describes the de-pendence of atmospheric scattering on wavelength.How-ever,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 be-gin 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.Fi-nally,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.

2Mechanisms of Scattering

The interactions of light with the atmosphere can be broadly classi?ed into three categories,namely,scattering,absorp-tion 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 fundamen-tal scattering phenomena,namely,airlight and attenuation, which form the basis of our framework.

2.1Airlight

While observing an extensive landscape,we quickly notice that the scene points appear progressively lighter as our at-tention shifts from the foreground toward the horizon.This phenomenon,known as airlight(see[Kos24]),results from the scattering of environmental light toward the observer, by the atmospheric particles within the observer’s cone of vision.

1063-6919/00 $10.00 ? 2000 IEEE

The radiance of airlight increases with pathlength d and is given by(see[McC75]and[NN99]),

L(d,λ)=L∞(λ)(1?e?β(λ)d).(1)β(λ)is called the total scattering coef?cient and it repre-sents the ability of a volume to scatter?ux of a given wave-lengthλ,in all directions.β(λ)d is called the optical thick-ness for the pathlength d.L∞(λ)is known as the“horizon”radiance.More precisely,it is the radiance of the airlight for an in?nite pathlength.As expected,the airlight at the observer(d=0)is zero.

Assuming a camera with a linear radiometric response,the image irradiance due to airlight can be written as E(d,λ)= gL∞(λ)(1?e?β(λ)d),where g accounts for the camera pa-rameters.Substituting

E∞(λ)=gL∞(λ),(2) we obtain

E(d,λ)=E∞(λ)(1?e?β(λ)d).(3)

2.2Attenuation

As a light beam travels from a scene point through the atmo-sphere,it gets attenuated due to scattering by atmospheric particles.The attenuated?ux that reaches an observer from a scene point,is termed as direct transmission[McC75]. The direct transmission for collimated light beams is given by Bouguer’s exponential law[Bou30]:

E(d,λ)=g L0(λ)e?β(λ)d,(4) where E(d,λ)is the attenuated irradiance at the observer, and L0(λ)is the radiance of the scene point prior to atten-uation.Again,g accounts for the camera parameters.Al-lard’s law[All76]modi?es the above model for divergent light beams from point sources as

E(d,λ)=g I0(λ)e?β(λ)d

d

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