Chromatic Framework for Vision in Bad Weather Srinivasa G. Narasimhan and Shree K. Nayar Computer Science Department Columbia University IEEE CVPR Conference June 2000, Hilton Head Island, USA Sponsors: ONR MURI, NSF

The Colors of Bad Weather Clear Day B R G Dense Fog B R G Noon Haze B R G

Prior Work Overviews : Middleton 1952, McCartney 1976 Haze : Hulburt 1946, Hidy 1972 Fog : Koshmeider 1924, George 1951, Myers 1968 Vision : Cozman & Krotkov Depth Cues from Iso-Intensities Nayar & Narasimhan Complete Structure ; Restricted weather conditions General Color Framework for Analysis of Bad Weather Images OUR GOAL :

Direct Transmission and Airlight Models Object Observer d ( Allard, 1876 ) Direct Transmission E Sunlight Diffuse Skylight Diffuse Ground Light ( Koschmieder, 1924 ) Airlight E

Dichromatic Atmospheric Scattering Model B G R Model : ( Nayar & Narasimhan, 1999 ) E Direct Transmission (True Color ) Airlight (Fog / Haze Color)

Dichromatic Planes Direct Transmission Color Airlight Color Dichromatic Plane Scene (800 x 600 pixels) Avg. Error (degrees) Foggy Hazy 0.25 º 0.31 º Verification :

Direction of Airlight ( Fog or Haze ) Color Plane 1 (Scene Point X) Plane 2 (Scene Point O) Weather Condition 1 Weather Condition 2 Airlight Color from Planes :

Depth from Unknown Weather Conditions Ratio of Direct Transmissions : Scattering Coefficients :, ( Unknown ) Sky Brightnesses :, ( Unknown ) Depth of a Scene Point : Direct Transmission Ratio Scaled Depth Sky Brightness Ratio

Direct Transmission Ratio Dichromatic Plane Direct Transmission Color Airlight Color Direct Transmission Ratio :

Sky Brightnesses Relation Between Sky Brightnesses Dichromatic Plane Direct Transmission Color Airlight Color Relative Airlight Depth of a Scene Point

Results with a Synthetic Scene Color Patches Recovered Structure Fog 1 + Noise Fog 2 + Noise Rotated Structure

Simulation Results Noise Estimated Depth Error (%) Actual Values = Actual Values = Noise Estimated Depth Error (%)

Scene under two different Hazy Conditions Computed Depth Map Structure from Two Weather Conditions

Scene under two different Foggy Conditions Computed Depth Map

True Color Recovery - Color Cube Boundary Algorithm R G B O Min Minimum Time to Collision First Collision with Color Boundary

True Color Recovery Scene under two different Foggy Conditions Computed True Color ( Brightened )

Summary Scene Depth from Dichromatic Constraints Airlight Color from Dichromatic Planes True Color from Color Boundary Constraint Color Framework for Vision in Bad Weather