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Vision in Bad Weather . Shree Nayar and Srinivasa Narasimhan Computer Science Columbia University ICCV Conference Korfu, Greece, September 1999 Sponsors: NSF. Dense Fog. Rain. Noon Haze. Vision and Bad Weather. Clear Day.

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Vision in bad weather

Vision in Bad Weather

Shree Nayar and Srinivasa Narasimhan

Computer Science

Columbia University

ICCV Conference

Korfu, Greece, September 1999

Sponsors: NSF


Vision and bad weather

Dense Fog

Rain

Noon Haze

Vision and Bad Weather

Clear Day


CONDITION PARTICLE TYPE RADIUS (m) CONCENTRATION (cm )

-3

Molecule

Aerosol

Water Droplet

Water Droplet

Water Drop

AIR

HAZE

FOG

CLOUD

RAIN

Weather Conditions and Particle Sizes

( McCartney, 1975 )


Incident Beam

Size: 0.01

Size: 0.1

Size: 1

  • Multiple Scattering :

First Order

Third Order

Incident Beam

Second Order

Particle Scattering Mechanisms

( Mie 1908 )

  • Single Scattering :


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


Scattering

Medium

Attenuated

Exiting Beam

X = d

Collimated

Incident Beam

Unit

Cross

Section

dx

X = 0

Total Flux Scattered by Lamina (dx) :

Total Scattering Coefficient

Attenuation Model

( McCartney, 1975 )


Direct Transmission

Beam Irradiance at Distance d :

(Bouguer’s Law, 1729)

Attenuation of Diverging Beams :

( Allard’s Law, 1876 )

Optical Thickness :


Sunlight

Diffuse

Skylight

Diffuse

Ground Light

Radiant Intensity of Volume (dV) :

Airlight Model

( Koschmieder, 1924 )

Object

dV

Observer

dw

dx

x

d


Horizon Radiance

Airlight

Image Irradiance due to Volume dV :

Image Irradiance due a Path of Length d :


Street Lamp

Window

Camera

Attenuation Model :

Image Irradiance for Camera Response s() :

Light Sources in Night Fog

No Environmental

Illumination


,

( Unknown )

Two Weather Conditions :

Ratio of Image Irradiances :

Difference in Optical Thickness (DOT) :

Relative Depths from Two Sources (i, j):

Depth of Sources from Two Night Images


Computed Source Locations

Clear Night

Foggy Night

Depth of Sources from Attenuation

Clear Day


Weather Condition :

( Dense Haze or Fog)

Airlight Model for Camera Response s() :

Image Irradiance Relative to the Horizon :

Optical Thickness :

Structure from Airlight Using a Single Image


Mountain Range

Urban Scene

Foggy Day Image

Foggy Day Image

Computed Depth Map

Computed Depth Map

3D Structure

Stereo ? Motion ?

3D Structure

Structure from Airlight


Illumination Occlusion Problem

Observer

Scene Point


Airlight

Direct Transmission

Surface Radiance

Horizon Radiance

Rayleigh’s Law :

For Fog :

( Middleton 1952 )

Dichromatic Atmospheric Scattering Model

Image Irradiance and Wavelength :


Dichromatic atmospheric scattering model

Finite-Dimensional Color Space :

E

dt

(surface +

volume)

E

a

(volume)

Final Model :

Dichromatic Atmospheric Scattering Model

B

E

G

R


True color from two images
True Color from Two Images

Clear Day Image

Defogged and Enhanced Windows

Foggy Day Image


Chromatic decomposition using two images

Recovered True Color

Computed Depth Map

3D Structure

Chromatic Decomposition Using Two Images

Clear Day Image

Foggy Day Image


Summary

  • No Escape from Bad Weather

  • Image Processing will Not Suffice

  • Bad Weather can be Good for Vision


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