shedding light on the weather
DESCRIPTION
Shedding Light on the Weather. Srinivasa Narasimhan and Shree Nayar Computer Science Department Columbia University. IEEE CVPR Conference June 2003, Madison, USA. Sponsors : DARPA Human ID, NSF. Light Sources in Bad Weather. Mist. Fog. Phase Function. - PowerPoint PPT PresentationTRANSCRIPT
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Shedding Light on the Weather
Srinivasa Narasimhan and Shree NayarComputer Science Department
Columbia University
Sponsors : DARPA Human ID, NSF
IEEE CVPR ConferenceJune 2003, Madison, USA
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Light Sources in Bad Weather
Mist Fog
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Multiple Scattering in the Atmosphere
Incident Beam
Particle
Light Source
A T M O S P H E R E
Phase Function
Imaging Plane
GlowPinhole
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Radiative TransferInfinitesimal Scattering Volume :
),( TI
Extinction
Radiative Transfer Equation :
TI
Radiance Rate of Change
dwTIP )',()',(41
Source Function
Phase Function Optical Thickness
dRdT
Incident BeamRadiance
Exiting BeamRadiance
dR
Direction
II
I
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Light Source in a Spherical Medium
Isotropic
Source
Homogeneous Medium
Spherical Radiative Transfer Equation :
'')',()',(41),(1 2
0
1
1
2
ddTIPTIITT
I
Phase FunctionLight FieldCosine of Angle Optical Thickness
[ Chandrasekhar 1960 ]
ScatteredLight Field
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Axially Symmetric Phase Functions
Legendre Polynomial Expansion : [ Ishimaru 1997 ] [ Henyey et al., 1941 ]
)(cos])12[()(cos0
mm
m LqmP
Legendre Polynomial
Forward Scattering Parameter
IncidentDirection
Exiting Direction
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Light Source in a Spherical Medium
Isotropic
Source
Homogeneous Medium
Spherical Radiative Transfer Equation :
'')',()',(41),(1 2
0
1
1
2
ddTIPTIITT
I
Phase FunctionLight FieldCosine of Angle Optical Thickness
[ Chandrasekhar 1960 ]
ScatteredLight Field
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])1(12)1([exp)( 10 Tq
mmTmITg m
m
Phase Function ParameterOptical Thickness
Exponential Coefficients :
Source Radiant Intensity
Legendre Polynomial
Analytic Multiple Scattering Solution
)())()((),( 10
mmm
m LTgTgTI
Scattered Light Field :
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Highlights of the Model
1.02 1.2 1.4 1.6 1.8 T
m160120 60 30 10
• Small Number of Coefficients (m) :
• Absorbing and Purely Scattering Media
• Single and Multiple Scattering
• Isotropic and Anisotropic Phase Functions
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Scattered Light Field vs. Weather Condition
Mild Weather (T = 1.2) Dense Weather (T = 4)
Angular PSF : Scattered Light Field at a Point
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Validation : Multiple Scattering in Milk
Original Milk Images
Increasing Milk Concentrations
Rendered Milk Images
Image acquiredWith No Milk
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Number of Milk Concentrations : 15Model Fitting Error : [ 1 % to 3 % ]Diffusion Fitting Error : [ 20 % to 50 % ]
Model Fit AccuracyLow Milk Concentration High Milk Concentration
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Original Image
Rendering Glows using Convolution
Increasing Fog
Rendered Images
Joint work with Ramamoorthi (submitted to TOG)
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Original Image Single Scattering
Multiple Scattering (Mild Condition)Multiple Scattering (Dense Condition)
Single versus Multiple Scattering
Joint work with Ramamoorthi (submitted to TOG)
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Inverse RTE : Weather from APSF
Measured APSF : ),( TI
Meteorological Visibility :
RT
V 912.3
[ Middleton 1952]
Weather Condition :[ Van de Hulst 1957]
q0 1
PureAir
SmallAerosols Haze Mist Fog Rain
0.1 0.4 0.7 0.90.8
|||| )()),(),((),(minarg 10,
mmm
m LqTgqTgTIqT
Objective Function :
qT ,qT ,qT ,
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Computed Atmospheric Visibilities
A Camera-based Weather Station
45 images of a light source (WILD Database ECCV 02)
Computed Weather Conditions
Ground TruthEstimated
Ground TruthEstimated
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Volume Rendering as Convolution
Analytic Multiple Scattering
)())()((),( 10
mmm
m LTgTgTI
Shedding Light on the Weather
Model Validation using Milk
Summary