A Photometric Approach for Estimating Normals and Tangents
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Transcript of A Photometric Approach for Estimating Normals and Tangents
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A Photometric Approach for Estimating Normals and
TangentsMichael Holroyd
University of Virginia
Jason LawrenceUniversity of
Virginia
Greg HumphreysUniversity of
Virginia
Todd ZicklerHarvard University
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. . .
Input: Images under varying point lighting
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Output: Estimate of surface orientation
Normal Field Tangent Field
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Related Work Lambertian photometric stereo
[Woodham 1980]
Discard specular highlight[Coleman and Jain 1982; Mallick et al. 2005]
[Klette et al. 1998]
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Fit to low-dimensional parametric models[Georghiades 2003; Goldman et al. 2005]
Fit non-parametric curves (isotropic only)[Alldrin et al. 2008]
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Locate mirror direction[Wang and Dana 2006; Chen et al. 2006; Ma et al. 2007; Francken et al. 2008; Nehab et al. 2008]
Image: Ma et al. 2007
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Our Approach
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Our Approach
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Our Approach
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Half-angle parameterization
2D slice of the BRDF (fixed view)
Our Approach
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Half-angle parameterization
2D slice of the BRDF (fixed view)
Our Approach
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Analysis of microfacet-based models:
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Microfacet distributionAlmost all analytic and measured distributions exhibit these symmetries.
Analysis of microfacet-based models:
Images: Ngan et al. 2005
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Analysis of microfacet-based models:
1
-90° 90°
Fresnel TermWell approximated by , and is asymmetric only at grazing angles.
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Shadowing/MaskingSmooth and can be greatly simplified.
Analysis of microfacet-based models:
Shadowing/Masking functionfrom Wang et al. 2008
[Torrance1987; Ashikhmin et al. 2000;
Ngan et al. 2005; Wang et al. 2008]
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Restrict light positions
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Symmetry Distance
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Symmetry Distance
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viewview
normal
Restriction of light positions
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view
normal
Restriction of light positions
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Restriction of light positions
view
normal
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Validation
Normal Error Tangent Error
BRDF from Ngan et al. 2005
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Normal Error Tangent Error
BRDF from Ngan et al. 2005
Validation
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Anisotropic Ward
PurpleSatin
YellowSatin
BrushedMetal
Measured
Ngan et al. 2005
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Error Analysis (Torrance-Sparrow)N
orm
al E
rror
(D
egre
es) Our approach
Photometric stereoSpecularity stereo
Diffuse Shiny
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Acquisition
Calibrated spherical gantry
1,500 1024x1024 HDR images
2.3 GB
45 minutes
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1. Reconstruct a continuous 2D slice of the BRDF at each pixel using barycentric interpolation of the original data.
2. Estimate by optimizing
3. Estimate by holding fixed and optimizing
Algorithm
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Implementation
Independent at each pixel
42x Dual 1.6 Ghz Opertons
10 minutes
(~7 hours for single machine)
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Limitations
Interreflections
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Limitations: Sampling density
1,512 743 380 172
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Limitations
Non-symmetric microfacet distributions
Red velvet dataset from Ngan et al. [2005]
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Conclusion
Main advantages: General, does not rely on parametric model First technique to directly recover tangent field
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Acknowledgments Jiajun Zhu for help with data capture NSF CAREER award CCF-0747220 NSF grant CCF-0811493 NVIDIA Professor Partnership award Fellowship from the Sloan Foundation
Thank You