Chromatic Framework for Vision in Bad Weather

Conventional vision systemsare designedto perform in clear weather . However, any outdoorvision systemis incompletewithout mechanismsthat guaranteesatisfactory performanceunder poor weatherconditions. It is known that the atmospher e can significantly alter light energy reaching an observer . Therefore, atmosphericscattering modelsmustbe usedto make vision systemsrobust in bad weather . In this paper, we developa geometricframework for analyzingthe chromaticeffectsof atmosphericscattering. First, we studya simplecolor modelfor atmospheric scatteringand verify it for fog and haze. Then,basedon thephysicsof scattering, wederiveseveral geometricconstraints on scenecolor changes,causedby varying atmosphericconditions.Finally, usingtheseconstraints wedevelop algorithms for computingfog or hazecolor, depth segmentation,extracting three dimensionalstructure, and recovering “true” scenecolors, from two or more images takenunderdifferentbut unknownweatherconditions. 1 Vision and Bad Weather Currentvision algorithmsassumethat the radiancefrom a scenepoint reachesthe observer unaltered.However, it is well known from atmosphericphysicsthat the atmosphere scatterslight energyradiatingfromscenepoints.Ultimately, vision systemsmustdealwith realisticatmosphericconditions to be effective outdoors. Several modelsdescribing thevisualmanifestationsof theatmospherecanbefoundin atmosphericoptics(see[Mid52], [McC75]). Thesemodels canbeexploitedto notonly removebadweathereffects,but alsoto recovervaluablesceneinformation. Surprisingly, little work hasbeendonein computervision on weatherrelated issues. Cozmanand Krotkov[CK97] computeddepthcuesfrom iso-intensitypoints. Nayarand Narasimhan[NN99] usedwell establishedatmosphericscattering models,namely, attenuationand airlight, to extract completescenestructurefrom one or two images, irreThis work was supported in parts by a DARPA/ONR MURI Grant(N00014-95-1-0601), an NSF National Young InvestigatorAward, andaDavid andLucile PackardFellowship. specti ve of sceneradiances.They alsoproposeda dichromatic atmosphericscatteringmodel that describesthe dependenceof atmosphericscatteringon wavelength. However, thealgorithmthey developedto recoverstructureusing thismodel,requiresa cleardayimageof thescene. In thispaper , wedevelopageneralchromaticframework for theanalysisof imagestakenunderpoorweatherconditions. Thewidespectrumof atmosphericparticlesmakesageneral studyof vision in badweatherhard.So,we limit ourselves to weatherconditionsthatresultfrom fog andhaze.We begin by describingthekey mechanismsof scattering.Next, weanalyzethedichromaticmodelproposedin [NN99], and experimentallyverify it for fog andhaze.Then,we derive severalusefulgeometricconstraintsonscenecolor changes due to differentbut unknownatmosphericconditions. Finally, we developalgorithmsto computefog or hazecolor, to constructdepthmapsof arbitraryscenes, andto recover scenecolorsasthey wouldappearonaclearday. All of our methodsonly requireimagesof the scenetakenundertwo or morepoorweatherconditions,andnota cleardayimage of thescene. 2 Mechanisms of Scattering Theinteractionsof light with theatmospherecanbebroadly classifiedinto threecategories,namely, scattering,absorption and emission. Of these,scatteringdue to suspended atmosphericparticlesis mostpertinentto us. For a detailed treatmentof thescatteringpatternsandtheir relationshipto particleshapesandsizes,wereferthereaderto theworksof [Mid52] and[Hul57]. Here,wefocusonthetwo fundamental scatteringphenomena, namely, airlight andattenuation, which form thebasisof our framework.