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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 ConferenceOctober 2005, Beijing, China
Active illumination in Scattering Media
[Levoy et al., Narasimhan-Nayar, Kocak-Caimi, Jaffe et al., Schechner et al., Negahdaripour et al. ]
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
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
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
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
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
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
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
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
Results: Traditional Photometric Stereo
3D Shape from Normals
Too Flat
Albedos
Scattering effects present
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