1. 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

2. Computer Vision in Bad Weather
Mild Haze
Dense Haze
Computed Dehazed Image
3D Visualization
Removing Weather
Structure from Weather
Color
Contrast
Polarization
Models
Algorithms
(Narasimhan , Nayar ’00)
(Narasimhan , Nayar ’01)
(Narasimhan , Nayar ’02)
(Schechner et. al. ’01)

3. Light Sources in Bad Weather
Mist
Fog

4. Multiple Scattering in the Atmosphere
Phase Function
Incident Beam
Particle
Light Source
A T M O S P H E R E
Imaging
Plane
Glow
Pinhole

5. Radiance Rate of Change
Radiative Transfer
Infinitesimal Scattering Volume :
Direction
Exiting Beam
Radiance dR
Incident Beam
Radiance
Extinction
Radiative Transfer Equation :
Radiance Rate of Change
Source Function
Phase Function
Optical Thickness

6. Light Source in a Spherical Medium
Spherical Radiative Transfer Equation :
Phase Function
Light Field
Cosine of
Angle
Optical Thickness
[ Chandrasekhar 1960 ]
Scattered
Isotropic
Source
Homogeneous
Medium

7. Axially Symmetric Phase Functions
Exiting
Direction
Incident
Direction
Legendre Polynomial Expansion :
[ Ishimaru 1997 ] [ Henyey et al., 1941 ]
Legendre Polynomial
Forward Scattering Parameter

8. Light Source in a Spherical Medium
Scattered
Light Field
Isotropic
Source
Homogeneous
Medium
Spherical Radiative Transfer Equation :
[ Chandrasekhar 1960 ]
Cosine of
Angle
Optical Thickness
Light Field
Phase Function

9. Analytic Multiple Scattering Solution
Scattered Light Field :
Legendre Polynomial
Phase Function Parameter
Optical Thickness
Exponential Coefficients :
Source Radiant Intensity

10. Highlights of the Model
Single and Multiple Scattering
Absorbing and Purely Scattering Media
Isotropic and Anisotropic Phase Functions T m
160
120 60 30 10
Small Number of Coefficients (m) :

11. Scattered Light Field vs. Weather Condition
Angular PSF : Scattered Light Field at a Point
Mild Weather (T = 1.2)
Dense Weather (T = 4)

12. Validation : Multiple Scattering in Milk
Image acquired
With No Milk
Original Milk
Images
Increasing Milk Concentrations
Rendered Milk
Images

13. Model Fit Accuracy Low Milk Concentration High Milk Concentration
Number of Milk Concentrations :
Model Fitting Error : [ 1 % to 3 % ]
Diffusion Fitting Error : [ 20 % to 50 % ]

14. Rendering Glows using Convolution
Increasing Fog
Rendered Images
Original Image
Joint work with Ramamoorthi (submitted to TOG)

15. Single versus Multiple Scattering
Single Scattering
Original Image
Multiple Scattering (Mild Condition)
Multiple Scattering (Dense Condition)
Joint work with Ramamoorthi (submitted to TOG)

16. Inverse RTE : Weather from APSF
Measured APSF :
Objective Function :
Meteorological Visibility :
[ Middleton 1952]
Weather Condition :
[ Van de Hulst 1957] 1
Pure
Air
Small
Aerosols
Haze
Mist
Fog
Rain
0.1
0.4
0.7
0.9
0.8

17. Atmospheric Visibilities
A Camera-based Weather Station
45 images of a light source (WILD Database ECCV 02)
Computed
Atmospheric Visibilities
Estimated
Ground Truth
Computed
Weather Conditions
Estimated
Ground Truth

18. Active Visibility Meter for Ground Truth

19. Summary Analytic Multiple Scattering Model Validation using Milk
Volume Rendering as Convolution
Shedding Light on the Weather

20. Prior Work on Radiative Transfer
[ Chandrasekhar 1960 , Ishimaru 1997 ]
Sun
Distant Source
Plane Parallel
Medium
Scattered Light Field
Our Problem : Divergent Source Inside Medium

21. Scattering Space of Weather Conditions
Phase Function
Parameter, q
Single Scattering 1
Diffusion
Pure Air
Small Aerosols
Haze
Mist
Fog 10
Optical Thickness, T

22. Axially Symmetric Phase Functions
Exiting
Direction
Incident
Direction
Legendre Polynomial Expansion :
[ Ishimaru 1997 ]
Legendre Polynomial
Henyey – Greenstein Function :
[ Henyey, Greenstein 1941 ]
Forward Scattering Parameter

23. Effect of Source Visibility
315
240
180 90 30 o
Increasing Milk Concentrations
Observed Milk
Images

24. Scattering is Everywhere…
Computer Vision
Astronomy
Oceanography
Medical Imaging
Computer Graphics