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A Photometric Approach for Estimating Normals and Tangents Michael Holroyd University of Virginia Jason Lawrence University of Virginia Greg Humphreys University of Virginia Todd Zickler Harvard University
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... Input: Images under varying point lighting
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Output: Estimate of surface orientation Normal FieldTangent 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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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 distribution Almost 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 Term Well approximated by, and is asymmetric only at grazing angles.
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Shadowing/Masking Smooth and can be greatly simplified. Analysis of microfacet-based models: Shadowing/Masking function from 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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view normal Restriction of light positions
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view normal Restriction of light positions
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view normal
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Validation Normal ErrorTangent Error BRDF from Ngan et al. 2005
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Normal ErrorTangent Error BRDF from Ngan et al. 2005 Validation
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Anisotropic Ward Purple Satin Yellow Satin Brushed Metal Measured Ngan et al. 2005
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Error Analysis (Torrance-Sparrow) Normal Error (Degrees) Our approach Photometric stereo Specularity stereo DiffuseShiny
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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 1,512743380172
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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
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