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

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

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

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

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

6. Light Striping Model in Scattering Media Extinction coefficient D v Irradiance due to Medium: Camera Source Surface Light plane Radiance α x y D s Irradiance due to Surface: Final Image Irradiance: Phase Function

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

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

9. Experimental Setup and Calibration Light PlaneViewing Ray Glass No Refractive index and location of glass or medium No explicit calibration of camera and projector Similar in spirit to [ Levoy-Hanrahan 96, Grossberg-Nayar 01 ]

10. Floodlit ImageComputed Appearance

11. Triangulation IssueSurface Reflectance Issue CameraProjector Surface CameraProjector Still a problem  Solved if Light Plane is visible In Scattering Media: Surface How to Place the Camera and Projector?

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

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

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

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

16. Simulations: Error Histograms 00.050.1 0 50 100 150 200 250 300 ( x 10 ) Fractional Error for Albedo Fractional Error for Phase Function, g Fractional Error for Optical Thickness Angular Error for Normals 00.050.1 0 50 100 150 200 250 300 ( x 10 ) 00.050.1 0 50 100 150 200 250 300 ( x 10 ) 00.050.1 0 50 100 150 200 250 300 ( x 10 ) Zero error with zero noise. Robust estimation with 5% uniform noise. Trials

17. Experiments: Teapot in Pure Water

18. Experiments: Teapot in Dilute Milk Low Contrast, Flat Appearance

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

20. Results: Our Five-Source Algorithm 3D Shape from NormalsAlbedos

21. Results: Depth from Photometric Stereo 3D Shape from Normals Depth map Impossible using traditional method % RMS Error 3 ml4 ml5 ml6 ml12 ml15 ml 2.02.53.03.35.86.3 Milk Concentration

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