A Photometric Approach for Estimating Normals and Tangents

2. A Photometric Approach for Estimating Normals and Tangents

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

4. Output: Estimate of surface orientation Normal Field Tangent 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

9. Our Approach

10. Our Approach

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

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

16. Analysis of microfacet-based models:

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

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

19. Analysis of microfacet-based models: • Shadowing/MaskingSmooth and can be greatly simplified. 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

23. Symmetry Distance

24. Restriction of light positions view view normal

25. Restriction of light positions view normal

26. Restriction of light positions view normal

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

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

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

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

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

32. Algorithm 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

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 1,512 743 380 172

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. Thank You 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