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 1997 - Depth Cues from Iso-Intensities

Nayar & Narasimhan 1999 - Complete Structure ; Restricted weather conditions

General Color Framework forAnalysis of Bad Weather Images

OUR GOAL :

Direct Transmission and Airlight Models

Object

Observer

d

( Allard, 1876 )

Direct Transmissiond

E

0E

SunlightDiffuseSkylight

DiffuseGround Light

( Koschmieder, 1924 )

Airlight

EE

d

Dichromatic Atmospheric Scattering Model

B

G

R

Model :

ADE qp 2d

erEp

d

)1( deEq

( Nayar & Narasimhan, 1999 )

EDp Direct Transmission

(True Color )

Aq Airlight (Fog / Haze Color)

Dichromatic Planes

1E

Direct Transmission Color

Airlight Color

A

D

O

Dichromatic Plane

2E

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)

(1)1E

(1)2E

(1)D

O

1N

(2)1E

(2)2E

Plane 2 (Scene Point O)

(2)D

2N

Weather Condition 1

Weather Condition 2

A

Airlight Color from Planes : i

2)(Mini

N A

Depth from Unknown Weather Conditions

Ratio of Direct Transmissions :de

E

E

p

p )(

2

1 21

2

1

Scattering Coefficients : 1 2, ( Unknown )

Sky Brightnesses : 2E, ( Unknown )1E

Depth of a Scene Point :

2

1

2

1

21lnln)(pp

E

Ed

Direct Transmission RatioScaled Depth

Sky Brightness Ratio

Direct Transmission Ratio

Dichromatic Plane

Direct Transmission Color

Airlight Color

A

D

1E 2E

O

C1A

1p

2A

2p

CE

OE

2

1

2

1 p

p

Direct Transmission Ratio :

Sky Brightnesses

Relation Between Sky Brightnesses

12

1

2OC

E

p

pE

Dichromatic Plane

Direct Transmission Color

Airlight Color

A

D

1E 2E

O

C1A

1p

2A

2p

Relative Airlight

Depth of a Scene Point

ln)( 21 d2

1

E

Eln

2

1

pp

Results with a Synthetic Scene

Color Patches

Recovered Structure

Fog 1 + Noise Fog 2 + Noise

Rotated Structure

Simulation Results

Noise

Estimated

Estimated

Depth Error (%)

0

100

255

0.0

1E

2E

)(

Actual Values = }255,100,5.0{},,{2121 EE

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

}400,200,67.0{},,{2121 EEActual Values =

Noise

Estimated

Estimated

Depth Error (%)

0

200

400

0.0

1E

2E

)( 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

Scene under two different Hazy Conditions

Computed Depth Map

Structure from Two Weather Conditions

Structure from Two Weather Conditions

Scene under two different Foggy Conditions

Computed Depth Map

True Color Recovery - Color Cube Boundary Algorithm

RG

B

1

2

3

O

d

d

)(

~

12

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