Shedding Light on the Weather

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. Light Sources in Bad Weather Mist Fog

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

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

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

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

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

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

9. Small Number of Coefficients (m) : m 160 120 60 30 10 1.02 1.2 1.4 1.6 1.8 T Highlights of the Model • Single and Multiple Scattering • Absorbing and Purely Scattering Media • Isotropic and Anisotropic Phase Functions

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

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

12. Number of Milk Concentrations : 15 Model Fitting Error : [ 1 % to 3 % ] Diffusion Fitting Error : [ 20 % to 50 % ] Model Fit Accuracy Low Milk Concentration High Milk Concentration

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

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

15. Measured APSF : Objective Function : MeteorologicalVisibility : [ Middleton 1952] Pure Air Small Aerosols Haze Mist Fog Rain WeatherCondition : [ Van de Hulst 1957] 0 0.1 0.4 0.7 0.8 0.9 1 Inverse RTE : Weather from APSF

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

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