Structured Light in Scattering Media Srinivasa Narasimhan Shree

Structured Light in Scattering Media Srinivasa Narasimhan Shree Nayar Sanjeev Koppal Bo Sun Robotics Institute Carnegie Mellon University Computer Science Columbia University ICCV Conference October 2005, Beijing, China Sponsor: ONR

Natural illumination in Scattering Media [ Narasimhan and Nayar, 99 - 03, Schechner et al, 01, 04 ]

Active illumination in Scattering Media [Levoy et al. , Narasimhan-Nayar, Kocak-Caimi, Jaffe et al. , Schechner et al. , Negahdaripour et al. ]

Floodlighting is Bad in Scattering Media Structured Light Critical for Good Visibility

Light Stripe Range Finding in Scattering in Clear Air Media Light plane Source Camera Surface

Light Striping Model in Scattering Media • Irradiance due to Medium: Extinction coefficient Light plane Phase Function x y Ds α Source • Irradiance due to Surface: Dv Camera Radiance • Final Image Irradiance: Surface

Light Striping Algorithm in Scattering Media Surface Intersection from Brightness Profile: No Scattering Moderate Scattering Significant Scattering 3 D by Triangulation or Temporal Analysis : Same as in clear air. Medium from Fall-off : “Clear-Air” Scene Appearance:

Experimental Setup Calibration technique similar in spirit to [Grossberg-Nayar 01 ]

Floodlit Image Computed Appearance

Smoke Milk and Mirrors Planar Mirror seen through Dilute Milk Light Striping of Mirrors (Dark Intersections) Reconstruct surfaces with any BRDF if light plane visible [Discussions with Marc Levoy]

Photometric Stereo in Clear Air Pure Air Distant Source Orthographic n Camera s P Surface Image Irradiance: Surface normal Three images required. Albedo Source direction [ Woodham 80, Horn 86 ]

Photometric Stereo in Scattering Media Scattering Medium Parallel Rays from Distant Source Orthographic Camera Ds α Dv Image Irradiance: n s P Surface Optical Thickness Phase Function +

Photometric Stereo in Scattering Media Scattering Medium Parallel Rays from Distant Source Orthographic Camera Ds α Dv n s P Surface 5 Parameter Non-linear Optimization (4 per pixel, 1 global) : Five Non-degenerate Sources are Necessary and Sufficient

Simulations: Error Histograms Trials 300 ( x 10 ) Trials ( x 10 ) 300 Trials 300 ( x 10 ) 250 250 200 200 150 150 100 100 50 50 0 0 0. 05 0. 1 Angular Error for Normals 0 0. 05 0. 1 Fractional Error for Optical Thickness 0 0. 05 0. 1 Fractional Error for Albedo ( x 10 ) 0 0. 05 0. 1 Fractional Error for Phase Function, g Zero error with zero noise. Robust estimation with 5% uniform noise.

Experiments: Teapot in Pure Water

Experiments: Teapot in Dilute Milk Low Contrast, Flat Appearance

Results: Traditional Photometric Stereo 3 D Shape from Normals Albedos Too Flat Scattering effects present

Results: Our Five-Source Algorithm 3 D Shape from Normals Albedos

Results: Depth from Photometric Stereo 3 D Shape from Normals Depth map Impossible using traditional method Milk Concentration 3 ml 4 ml 5 ml 6 ml 12 ml 15 ml % RMS Error 2. 0 2. 5 3. 0 3. 3 5. 8 6. 3

Summary • Structured light improves visibility • Physics of scattering crucial • Surprising results possible because of scattering