structured light in scattering media
DESCRIPTION
Structured Light in Scattering Media. Srinivasa Narasimhan Sanjeev Koppal Robotics Institute Carnegie Mellon University. Shree Nayar Bo Sun Computer Science Columbia University. Sponsor : ONR. Natural illumination in Scattering Media. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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
Dv
• Irradiance due to Medium:
Camera
Source
SurfaceLight plane
)()( smediumssurface DxEDxEE
)(0 PeeLE yxmedium
)(0
vs DDsurface eRLE
)cos1(4
)(0
geLE yx
medium
Radiance
αx
y
Ds
• Irradiance due to Surface:
• Final Image Irradiance:
0L
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:
NoScattering
ModerateScattering
SignificantScattering
E
x
mediumE surfaceE
2)(
0 ||)cos1(4
||min geLE yx
medium ),( g
)(0
vs DDsurface eERL
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Experimental Setup
Calibration technique similar in spirit to [Grossberg-Nayar 01 ]
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VIDEO
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Floodlit Image Computed Appearance
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Smoke and Mirrors
Milk 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 ns
PSurface
Pure Air
sn .0 LEsurface
Image Irradiance:Surface normal
Source directionAlbedo
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Photometric Stereo in Scattering MediaScattering Medium
Parallel Rays from Distant Source
Orthographic
Camera α n s
P
Ds
DvSurface
sn .)cos1(0
sDsurface eLE
Image Irradiance:
)1()cos1( cos0
ss DDmedium eegLE
+ E
E
Optical Thickness
Phase Function
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Photometric Stereo in Scattering MediaScattering Medium
Parallel Rays from Distant Source
Orthographic
Camera α n s
P
Ds
DvSurface
5 Parameter Non-linear Optimization (4 per pixel, 1 global) :
E
Five Non-degenerate Sources are Necessary and Sufficient
||)(||min mediumsurface EEE
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Simulations: Error Histograms
0 0.05 0.10
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
0 0.05 0.10
50
100
150
200
250
300 ( x 10 )
0 0.05 0.10
50
100
150
200
250
300 ( x 10 )
0 0.05 0.10
50
100
150
200
250
300 ( x 10 )
Zero error with zero noise.
Robust estimation with 5% uniform noise.
Trials Trials Trials 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 Normals
Albedos
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Results: Depth from Photometric Stereo
3D Shape from Normals
Depth map
Impossible using traditional method
% RMS Error
3 ml 4 ml 5 ml 6 ml 12 ml15 ml
2.0 2.5 3.0 3.3 5.8 6.3
Milk Concentration
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• Surprising results possible
because of scattering
• Structured light improves visibility
Summary
• Physics of scattering crucial