1. 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

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

3. Prior Work Overviews : Middleton 1952, McCartney 1976 Haze : Hulburt 1946, Hidy 1972 Fog : Koshmeider 1924, George 1951, Myers 1968 Vision : Cozman & Krotkov 1997 - Depth Cues from Iso-Intensities Nayar & Narasimhan 1999 - Complete Structure ; Restricted weather conditions General Color Framework for Analysis of Bad Weather Images OUR GOAL :

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

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

6. 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 :

7. 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 :

8. 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

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

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

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

12. Simulation Results Noise Estimated Depth Error (%) 0 100 255 0.0 Actual Values = 0.5 100.02 255.02 0.42 1.0 100.55 256.61 0.58 1.5 100.65 258.2 0.76 2.0 101.26 260.13 0.82 2.5 103.23 0.89 3.0 104.84 263.45 0.96 255.4 Actual Values = Noise Estimated Depth Error (%) 0 200 400 0.0 0.5 200.02 400.02 0.36 1.0 200.23 400.60 0.53 1.5 200.65 401.1 0.54 2.0 200.96 403.6 0.63 2.5 201.4 0.79 3.0 202.1 405.8 0.93 400.4

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

14. Scene under two different Foggy Conditions Computed Depth Map

15. True Color Recovery - Color Cube Boundary Algorithm R G B 1 2 3 O Min Minimum Time to Collision First Collision with Color Boundary

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

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