2. 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

3. ... Input: Images under varying point lighting

4. Output: Estimate of surface orientation Normal FieldTangent Field

5. Related Work Lambertian photometric stereo [Woodham 1980] Discard specular highlight [Coleman and Jain 1982; Mallick et al. 2005] [Klette et al. 1998]

6. Fit to low-dimensional parametric models [Georghiades 2003; Goldman et al. 2005] Fit non-parametric curves (isotropic only) [Alldrin et al. 2008]

7. 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

8. Our Approach

11. Half-angle parameterization 2D slice of the BRDF (fixed view)‏ Our Approach

12. Half-angle parameterization 2D slice of the BRDF (fixed view)‏ Our Approach

16. Analysis of microfacet-based models:

17. Microfacet distribution Almost all analytic and measured distributions exhibit these symmetries. Analysis of microfacet-based models: Images: Ngan et al. 2005

18. Analysis of microfacet-based models: 1 -90°90° Fresnel Term Well approximated by, and is asymmetric only at grazing angles.

19. 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]

20. Restrict light positions

22. Symmetry Distance

24. view normal Restriction of light positions

25. view normal Restriction of light positions

26. view normal

27. Validation Normal ErrorTangent Error BRDF from Ngan et al. 2005

28. Normal ErrorTangent Error BRDF from Ngan et al. 2005 Validation

29. Anisotropic Ward Purple Satin Yellow Satin Brushed Metal Measured Ngan et al. 2005

30. Error Analysis (Torrance-Sparrow)‏ Normal Error (Degrees)‏ Our approach Photometric stereo Specularity stereo DiffuseShiny

31. Acquisition Calibrated spherical gantry 1,500 1024x1024 HDR images 2.3 GB 45 minutes

32. 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

33. Implementation Independent at each pixel 42x Dual 1.6 Ghz Opertons 10 minutes (~7 hours for single machine) ‏

39. Limitations Interreflections

40. Limitations: Sampling density 1,512743380172

41. Limitations Non-symmetric microfacet distributions Red velvet dataset from Ngan et al. [2005]

42. Conclusion Main advantages: General, does not rely on parametric model First technique to directly recover tangent field

43. 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