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Polarization-based Inverse Polarization-based Inverse Rendering from Single ViewRendering from Single View
Daisuke MiyazakiRobby T. Tan
Kenji HaraKatsushi Ikeuchi
2
Modeling cultural assetsModeling cultural assets
Integrated framework for obtaining 3 types of information
Geometrical Photometrical Environmental
3
Related workRelated work
Geometry Photometry Environment
Tominaga et.al. 2000
Zheng et.al. 1991
Nayar et.al. 1996
Sato et.al. 1999
Ramamoorthi et.al. 2001
Nishino et.al. 2001
Hara et.al. 2002
Proposed method
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OutlineOutline
1. Reflection componentsseparation
2. Shape from polarizationusing diffuse light
3. Light source estimationfrom intensity peak
4. Reflection parametersestimation by l.s.m. Minimize
Ks, σ
renderedimage
realimage
2
1. Reflection components separation1. Reflection components separation
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Dichromatic reflection modelDichromatic reflection model
Incident lightSpecularly
reflected lightDiffusely
reflected light
Air
Object
Surfacenormal
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Reflection components separationReflection components separation
DiffuseInput Specular
[Tan2002]
•Shape•Illumination•Reflection parameters
2. Shape from polarization2. Shape from polarization
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Related workRelated work
Object Reflection View
Koshikawa 1979 Opaque Specular 1
Wolff 1990 Opaque Diffuse 2
Rahmann et.al. 2001 Opaque Diffuse 2~5
Miyazaki et.al. 2002 Transparent Specular 2
Proposed method Opaque Diffuse 1
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PolarizationPolarization
Incident lightSpecularly
reflected lightDiffusely
reflected light
Air
Object
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Surface normalSurface normal
Object
Surface normal
Polarizer
Camera
Zenith angle
Azimuth angle
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Azimuth angleφ and intensity differenceAzimuth angleφ and intensity difference
Rotationangle
ofpolarizer
Inten
sity
255
0
Imax
3601 2
-ambiguity
Imin
Azimuth angle
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PropagationPropagation
[Ikeuchi&Horn1981]
Determination of azimuth angle Propagate φ from occluding boundary to inner part of object area (Assumption: smooth surface)
object
Cannot apply to “dimples”(=perfect concave)
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Zenith angleθ and DOPρZenith angleθ and DOPρ
0
1
90°
Zenith angle θ
DOP ρ
DegreeOfPolarization
ρ
θ
minmax
minmax
II
II
22222
22
sincos4sin122
sin1
nnnn
nn
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ModificationModification
0
0.5
90°
Zenithangle
θ
DOP ρ
DegreeOfPolarization
22222
22
sincos4sin122
sin1
nnnn
nn
uII
II
minmax
minmax
minmax
minmax
II
II
u: modification factor•Raises DOP•Assumption
•Closed smooth object•“u” is constant
Definition of DOP:
Modified DOP:
u
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Surface normalSurface normal
φ
θSurface normal
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HeightHeight
• Relaxation method
dxdyqy
Hp
x
H22
Minimize: where,
x
Hp
y
Hq
Gradient Height H
y
q
x
pyxHyxH ii
4
1),(),( )()1(Iteratively update:
[Ikeuchi1984]
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1
qp
qp T
nSurface
normal
3. Illumination estimation3. Illumination estimation
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Illumination sphereIllumination sphere
θ=0°
θ=90°θ=90°
θ=180°
Object
Light source is represented in polar coordinate system (θ, φ)
φ=0°
φ=90°
φ=180°
φ=270°
L1=(θ1, φ1)L2=(θ2, φ2)
L3=(θ3, φ3)
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Illumination estimationIllumination estimation
Detect position of intensity peakDetermine light source orientation from the peak
1.Project to (θ, φ)-space 2.Thresholding 3.Detect intensity peak
4. Reflection parameters estimation4. Reflection parameters estimation
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Torrance-Sparrow reflection modelTorrance-Sparrow reflection model
Specular reflection
2
2
2
cos
1cos
α
θθ eKKI
rsid
Diffuse reflection
Incidentlight
Surfacenormal
ViewBisector
Object surface
αθi θr
Known: θi, θr, α
Unknown:•Diffuse reflection scale; Kd
•Specular reflection scale; Ks
•Surface roughness; σ
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Reflection parameters estimationReflection parameters estimation
Solve the following least-square problemby steepest-descent method
MinimizeKs, σ
renderedimage
realimage
2
2
2
2
cos
1 α
θeK
rs
Experimental resultExperimental result
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InputInput
Intensity I
Azimuth angleφ
DOPρ
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Result of shape estimationResult of shape estimation
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Result of illumination estimationResult of illumination estimation
Actual illumination distribution Estimated illumination distribution
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Rendering resultRendering result
Input
Synthesizedimage Rendered image under
different illumination & view
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Result for another objectResult for another object
Input
Synthesizedimage
Estimatedshape
Rendered image underdifferent illumination & view
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ConclusionsConclusions
• Estimated geometrical, photometrical, environmental information in one integrated framework– Shape from polarization– Surface reflection parameters from iterative
computation– Illumination from intensity peak
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Application to digital archiving projectApplication to digital archiving project• Multiple View
• Modeling a statue in a room– IBR with
• surface normal• reflection parameters
Photorealistic preservation
FinFin
(c) Daisuke Miyazaki 2003(c) Daisuke Miyazaki 2003All rights reserved.All rights reserved.
http://www.cvl.iis.u-tokyo.ac.jp/D. Miyazaki, R. T. Tan, K. Hara, K. Ikeuchi,
"Polarization-based Inverse Rendering from Single View," in Proceedings of International Symposium on the CREST Digital Archiving Project, pp.51-65, Tokyo,
Japan, 2003.05
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