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
Natural illumination in Scattering Media [ Narasimhan and Nayar, , 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 Clear Air Camera Source Surface Light plane Camera Source Surface Light plane Light Stripe Range Finding in Scattering Media
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
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
Experimental Setup Calibration technique similar in spirit to [Grossberg-Nayar 01 ]
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 ]
Floodlit ImageComputed Appearance
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?
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
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
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
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
Simulations: Error Histograms ( x 10 ) Fractional Error for Albedo Fractional Error for Phase Function, g Fractional Error for Optical Thickness Angular Error for Normals ( x 10 ) ( x 10 ) ( x 10 ) Zero error with zero noise. Robust estimation with 5% uniform noise. Trials
Experiments: Teapot in Pure Water
Experiments: Teapot in Dilute Milk Low Contrast, Flat Appearance
Results: Traditional Photometric Stereo 3D Shape from Normals Too Flat Albedos Scattering effects present
Results: Our Five-Source Algorithm 3D Shape from NormalsAlbedos
Results: Depth from Photometric Stereo 3D Shape from Normals Depth map Impossible using traditional method % RMS Error 3 ml4 ml5 ml6 ml12 ml15 ml Milk Concentration
Surprising results possible because of scattering Structured light improves visibility Summary Physics of scattering crucial