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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
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Natural illumination in Scattering Media [ Narasimhan and Nayar, 99 - 03, Schechner et al, 01, 04 ]
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Active illumination in Scattering Media [Levoy et al., Narasimhan-Nayar, Kocak-Caimi, Jaffe et al., Schechner et al., Negahdaripour et al. ]
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Floodlighting is Bad in Scattering Media Structured Light Critical for Good Visibility
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Light Stripe Range Finding in Clear Air Camera Source Surface Light plane Camera Source Surface Light plane Light Stripe Range Finding in Scattering Media
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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
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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
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Experimental Setup Calibration technique similar in spirit to [Grossberg-Nayar 01 ]
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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 ]
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Floodlit ImageComputed Appearance
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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?
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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
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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
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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
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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
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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
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Experiments: Teapot in Pure Water
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Experiments: Teapot in Dilute Milk Low Contrast, Flat Appearance
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Results: Traditional Photometric Stereo 3D Shape from Normals Too Flat Albedos Scattering effects present
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Results: Our Five-Source Algorithm 3D Shape from NormalsAlbedos
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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
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Surprising results possible because of scattering Structured light improves visibility Summary Physics of scattering crucial
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