1. Shree Nayar and Srinivasa Narasimhan Computer Science Columbia University ICCV Conference Korfu, Greece, September 1999 Sponsors: NSF Vision in Bad Weather

2. Rain Dense Fog Noon Haze Vision and Bad Weather Clear Day

3. Weather Conditions and Particle Sizes ( McCartney, 1975 ) CONDITION PARTICLE TYPE RADIUS (  m) CONCENTRATION (cm ) AIR HAZE FOG CLOUD RAIN Molecule Aerosol Water Droplet Water Drop -3

4. Particle Scattering Mechanisms Single Scattering : Incident Beam Size: 0.01 Size: 0.1 Size: 1 Multiple Scattering : Incident Beam First Order Third Order Second Order ( Mie 1908 )

5. Atmospheric Optics Overviews : Middleton 1952, McCartney 1976 Haze : Hulburt 1946, Hidy 1972 Fog : Koshmeider 1924, George 1951, Myers 1968 Clouds and Rain : Laws 1943, Houghton 1951, Mason 1975 Snow : Ohtake 1970 Vision : Koenderink & Richards 1992, Cozman & Krotkov 1997

6. Attenuation Model Total Flux Scattered by Lamina (dx) : ( McCartney, 1975 ) Scattering Medium Unit Cross Section X = 0 dx X = d Collimated Incident Beam Attenuated Exiting Beam Total Scattering Coefficient

7. Direct Transmission Beam Irradiance at Distance d : Attenuation of Diverging Beams : Optical Thickness : ( Allard’s Law, 1876 ) (Bouguer’s Law, 1729)

8. Airlight Model Sunlight Diffuse Skylight Diffuse Ground Light Radiant Intensity of Volume (dV) : ( Koschmieder, 1924 ) Object Observer d dx x dV dw

9. Airlight Image Irradiance due to Volume dV : Image Irradiance due a Path of Length d : Horizon Radiance

10. Light Sources in Night Fog Attenuation Model : Image Irradiance for Camera Response s( ) : Camera Window Street Lamp No Environmental Illumination

11. Depth of Sources from Two Night Images Ratio of Image Irradiances : Difference in Optical Thickness (DOT) : Relative Depths from Two Sources (i, j): Two Weather Conditions :, ( Unknown )

12. Depth of Sources from Attenuation Clear Day Clear Night Foggy Night Computed Source Locations

13. Structure from Airlight Using a Single Image Image Irradiance Relative to the Horizon : Airlight Model for Camera Response s( ) : Weather Condition : ( Dense Haze or Fog) Optical Thickness :

14. Structure from Airlight Mountain Range Foggy Day Image Computed Depth Map 3D Structure Urban Scene Foggy Day Image Computed Depth Map 3D Structure Stereo ? Motion ?

15. Illumination Occlusion Problem Scene Point Observer

16. Dichromatic Atmospheric Scattering Model Image Irradiance and Wavelength : Direct Transmission Airlight Surface Radiance Horizon Radiance Rayleigh’s Law : For Fog : ( Middleton 1952 )

17. Dichromatic Atmospheric Scattering Model B G R E Finite-Dimensional Color Space : E dt E a (volume) (surface + volume) Final Model :

18. True Color from Two Images Clear Day Image Foggy Day Image Defogged and Enhanced Windows

19. Chromatic Decomposition Using Two Images Clear Day Image Foggy Day Image Recovered True Color Computed Depth Map 3D Structure

20. Summary No Escape from Bad Weather Image Processing will Not Suffice Bad Weather can be Good for Vision