a photometric approach for estimating normals and tangents michael holroyd university of virginia...
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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
. . .
Input: Images under varying point lighting
Output: Estimate of surface orientation
Normal Field Tangent Field
Related Work Lambertian photometric stereo
[Woodham 1980]
Discard specular highlight[Coleman and Jain 1982; Mallick et al. 2005]
[Klette et al. 1998]
Fit to low-dimensional parametric models[Georghiades 2003; Goldman et al. 2005]
Fit non-parametric curves (isotropic only)[Alldrin et al. 2008]
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
Our Approach
Our Approach
Our Approach
Half-angle parameterization
2D slice of the BRDF (fixed view)
Our Approach
Half-angle parameterization
2D slice of the BRDF (fixed view)
Our Approach
Analysis of microfacet-based models:
Microfacet distributionAlmost all analytic and measured distributions exhibit these symmetries.
Analysis of microfacet-based models:
Images: Ngan et al. 2005
Analysis of microfacet-based models:
1
-90° 90°
Fresnel TermWell approximated by , and is asymmetric only at grazing angles.
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]
Restrict light positions
Symmetry Distance
Symmetry Distance
viewview
normal
Restriction of light positions
view
normal
Restriction of light positions
Restriction of light positions
view
normal
Validation
Normal Error Tangent Error
BRDF from Ngan et al. 2005
Normal Error Tangent Error
BRDF from Ngan et al. 2005
Validation
Anisotropic Ward
PurpleSatin
YellowSatin
BrushedMetal
Measured
Ngan et al. 2005
Error Analysis (Torrance-Sparrow)N
orm
al E
rror
(D
egre
es) Our approach
Photometric stereoSpecularity stereo
Diffuse Shiny
Acquisition
Calibrated spherical gantry
1,500 1024x1024 HDR images
2.3 GB
45 minutes
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
Implementation
Independent at each pixel
42x Dual 1.6 Ghz Opertons
10 minutes
(~7 hours for single machine)
Limitations
Interreflections
Limitations: Sampling density
1,512 743 380 172
Limitations
Non-symmetric microfacet distributions
Red velvet dataset from Ngan et al. [2005]
Conclusion
Main advantages: General, does not rely on parametric model First technique to directly recover tangent field
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