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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