“A Non-Parametric-Factor Microfacet Model for Isotropic BRDFs” by Nowrouzezahrai, Mahdi and Snyder

  • ©Derek Nowrouzezahrai, Mohammed Bagher Mahdi, and John M. Snyder




    A Non-Parametric-Factor Microfacet Model for Isotropic BRDFs

Session/Category Title: MATERIALS




    We investigate the expressiveness of the microfacet model for isotropic bidirectional reflectance distribution functions (BRDFs) measured from real materials by introducing a non-parametric factor model that represents the model’s functional structure but abandons restricted parametric formulations of its factors. We propose a new objective based on compressive weighting that controls rendering error in high-dynamic-range BRDF fits better than previous factorization approaches. We develop a simple numerical procedure to minimize this objective and handle dependencies that arise between microfacet factors. Our method faithfully captures a more comprehensive set of materials than previous state-of-the-art parametric approaches yet remains compact (3.2KB per BRDF). We experimentally validate the benefit of the microfacet model over a naïve orthogonal factorization and show that fidelity for diffuse materials is modestly improved by fitting an unrestricted shadowing/masking factor. We also compare against a recent data-driven factorization approach [Bilgili et al. 2011] and show that our microfacet-based representation improves rendering accuracy for most materials while reducing storage by more than 10 ×.


    1. Sameer Agarwal, Keir Mierle, and Others. 2014. Ceres Solver. http://ceres-solver.org. (2014).
    2. Michael Ashikhmin and Simon Premozze. 2007. Distribution-Based BRDFs. Technical Report. Department of Computer Science, University of Utah.
    3. Michael Ashikhmin and Peter Shirley. 2000. An anisotropic phong BRDF model. J. Graph. Tools 5, 2 (Feb. 2000), 25–32. DOI:http://dx.doi.org/10.1080/10867651.2000.10487522 
    4. Michael Ashikmin, Simon Premože, and Peter Shirley. 2000. A microfacet-based BRDF generator. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’00). ACM Press/Addison-Wesley Publishing Co., New York, NY, 65–74. DOI:http://dx.doi.org/10.1145/344779.344814 
    5. M. Mahdi Bagher, Cyril Soler, and Nicolas Holzschuch. 2012. Accurate fitting of measured reflectances using a shifted gamma micro-facet distribution. Comput. Graph. Forum 31, 4 (June 2012), 1509–1518. DOI:http://dx.doi.org/10.1111/j.1467-8659.2012.03147.x 
    6. Aner Ben-Artzi, Ryan Overbeck, and Ravi Ramamoorthi. 2006. Real-time BRDF editing in complex lighting. ACM Trans. Graph. 25, 3 (July 2006), 10. DOI:http://dx.doi.org/10.1145/1141911.1141979 
    7. Ahmet Bilgili, Aydin Öztürk, and Murat Kurt. 2011. A general BRDF representation based on tensor decomposition. Comput. Graph. Forum 30, 8 (2011). http://dblp.uni-trier.de/db/journals/cgf/cgf30.html#BilgiliOK11
    8. James F. Blinn. 1977. Models of light reflection for computer synthesized pictures. SIGGRAPH Comput. Graph. 11, 2 (July 1977), 192–198. DOI:http://dx.doi.org/10.1145/965141.563893 
    9. C. Bourlier, G. Berginc, and Joseph Saillard. 2002. One- and two-dimensional shadowing functions for any height and slope stationary uncorrelated surface in the monostatic and bistatic configurations. IEEE Trans. Antenna. Propagat. 50, 3 (2002), 312–324. DOI:http://dx.doi.org/10.1109/8.999622
    10. G. S. Brown. 1980. Shadowing by non-Gaussian random surfaces. IEEE Trans. Antenna. Propagat. 28, 6 (1980), 788–790. DOI:http://dx.doi.org/10.1109/TAP.1980.1142437
    11. Brent Burley. 2012. Physically-Based Shading at Disney. Technical Report. Walt Disney Animation Studios.
    12. R. J. Carroll and D. Ruppert. 1998. Translation and Weighting in Regression. Chapman and Hall, New York, NY. 
    13. Robert L. Cook and Kenneth E. Torrance. 1981. A reflectance model for computer graphics. SIGGRAPH Comput. Graph. 15, 3 (Aug. 1981), 307–316. DOI:http://dx.doi.org/10.1145/965161.806819 
    14. Paul Debevec. 2001. Light Probe Image Gallery. http://www.pauldebevec.com/Probes/. (2001).
    15. Paul Debevec. 2008. High-Resolution Light Probe Image Gallery. http://gl.ict.usc.edu/Data/HighResProbes/. (2008).
    16. Julie Dorsey, Holly Rushmeier, and Franois Sillion. 2008. Digital Modeling of Material Appearance. Morgan Kaufmann Inc., San Francisco, CA. 
    17. Jonathan Dupuy, Eric Heitz, Jean-Claude Iehl, Pierre Poulin, and Victor Ostromoukhov. 2015. Extracting microfacet-based BRDF parameters from arbitrary materials with power iterations. Comput. Graph. Forum (2015), 10. https://hal.inria.fr/hal-01168516 
    18. EPA. 2003. Method 8000C, SW846, Revision 3. Technical Report. U.S. Environmental Protetction Agency. http://www.epa.gov/osw/hazard/testmethods/pdfs/8000c_v3.pdf.
    19. Abhijeet Ghosh, Tim Hawkins, Pieter Peers, Sune Frederiksen, and Paul Debevec. 2008. Practical modeling and acquisition of layered facial reflectance. ACM Trans. Graph. 27, 5, Article 139 (Dec. 2008), 10 pages. 
    20. Franklin A. Graybill and Hariharan K. Iyer. 1994. Regression Analysis: Concepts and Applications. Duxbury Press, Belmont, CA.
    21. Jan Kautz and Michael D. McCool. 1999. Interactive rendering with arbitrary BRDFs using separable approximations. In Rendering Techniques. 
    22. Tamara G. Kolda and Brett W. Bader. 2009. Tensor decompositions and applications. SIAM Rev. 51, 3 (Aug. 2009), 455–500. DOI:http://dx.doi.org/10.1137/07070111X 
    23. Eric P. F. Lafortune, Sing-Choong Foo, Kenneth E. Torrance, and Donald P. Greenberg. 1997. Non-linear approximation of reflectance functions. In Proceedings of SIGGRAPH. ACM Press/Addison-Wesley Publishing Co., New York, NY, 117–126. DOI:http://dx.doi.org/10.1145/258734.258801 
    24. Jason Lawrence, Aner Ben-Artzi, Christopher DeCoro, Wojciech Matusik, Hanspeter Pfister, Ravi Ramamoorthi, and Szymon Rusinkiewicz. 2006. Inverse shade trees for non-parametric material representation and editing. ACM Transactions on Graphics (Proc. SIGGRAPH) 25, 3 (July 2006). 
    25. Jason Lawrence, Szymon Rusinkiewicz, and Ravi Ramamoorthi. 2004. Efficient BRDF importance sampling using a factored representation. ACM Trans. Graph. 23, 3 (Aug. 2004), 496–505. DOI:http://dx.doi.org/10.1145/1015706.1015751 
    26. István Lazányi and László Szirmay-Kalos. 2005. Fresnel term approximations for metals. In WSCG (Short Papers) (2005-08-01). 77–80.
    27. Daniel D. Lee and H. Sebastian Seung. 2000. Algorithms for non-negative matrix factorization. In NIPS. MIT Press, Cambridge, MA, 556–562.
    28. Joakim Löw, Joel Kronander, Anders Ynnerman, and Jonas Unger. 2012. BRDF models for accurate and efficient rendering of glossy surfaces. ACM Trans. Graph. 31, 1 (January 2012), 9:1–9:14. 
    29. Stephen R. Marschner, Stephen H. Westin, Eric P. F. Lafortune, Kenneth E. Torrance, and Donald P. Greenberg. 1999. Image-based BRDF measurement including human skin. In Proceedings of the 10th Eurographics Conference on Rendering (EGWR’99). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 131–144. DOI:http://dx.doi.org/10.2312/EGWR/EGWR99/131-144 
    30. Wojciech Matusik, Hanspeter Pfister, Matt Brand, and Leonard McMillan. 2003. A data-driven reflectance model. In ACM SIGGRAPH 2003 Papers (SIGGRAPH’03). ACM, New York, NY, 759–769. DOI:http://dx.doi.org/10.1145/1201775.882343 
    31. Stephen McAuley, Stephen Hill, Naty Hoffman, Yoshiharu Gotanda, Brian Smits, Brent Burley, and Adam Martinez. 2012. Practical physically-based shading in film and game production. In ACM SIGGRAPH 2012 Courses (SIGGRAPH’12). ACM, New York, NY, Article 10, 7 pages. DOI:http://dx.doi.org/10.1145/2343483.2343493 
    32. Michael D. McCool, Jason Ang, and Anis Ahmad. 2001. Homomorphic factorization of BRDFs for high-performance rendering. In SIGGRAPH. 
    33. Nathan Srebro Nati and Tommi Jaakkola. 2003. Weighted low-rank approximations. In 20th International Conference on Machine Learning. AAAI Press, 720–727.
    34. Addy Ngan, Frédo Durand, and Wojciech Matusik. 2005. Experimental analysis of BRDF models. In Proceedings of the Eurographics Symposium on Rendering. Eurographics Association, 117–226. 
    35. Jannik Boll Nielsen, Henrik Wann Jensen, and Ravi Ramamoorthi. 2015. On optimal, minimal BRDF sampling for reflectance acquisition. ACM Trans. Graph. 34, 6 (November 2015). DOI:http://dx.doi.org/10.1145/2816795.2818085 
    36. NIS. 2012. e-Handbook of Statistical Methods. Technical Report. NIST/SEMATECH. http://www.itl.nist.gov/div898/handbook.
    37. Romain Pacanowski, Oliver Salazar-Celis, Christophe Schlick, Xavier Granier, Poulin Pierre, and Cuyt Annie. 2012. Rational BRDF. IEEE Trans. Vis. Comput. Graph. 18, 11 (Feb. 2012), 1824–1835. DOI:http://dx.doi.org/10.1109/TVCG.2012.73 
    38. Matt Pharr and Greg Humphreys. 2010. Physically Based Rendering, Second Edition: From Theory To Implementation (2nd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA. 
    39. William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. 2007. Numerical Recipes 3rd Edition: The Art of Scientific Computing (3 ed.). Cambridge University Press, New York, NY. 
    40. Fabiano Romeiro, Yuriy Vasilyev, and Todd Zickler. 2008. Passive reflectometry. In Proceedings of the 10th European Conference on Computer Vision: Part IV (ECCV’08). Springer-Verlag, Berlin, 859–872. DOI:http://dx.doi.org/10.1007/978-3-540-88693-8_63 
    41. Christophe Schlick. 1994. An inexpensive BRDF model for physically-based rendering. Comput. Graph. Forum 13 (1994), 233–246.
    42. B. Smith. 1967. Geometrical shadowing of a random rough surface. IEEE Trans. Antenna. Propagat. 15, 5 (1967), 668–671. DOI:http://dx.doi.org/10.1109/TAP.1967.1138991
    43. Cyril Soler and Jean-Christophe Roche. 2014. High Quality Renderer (HQR). http://artis.imag.fr/∼Cyril.Soler/HQR/. (2014).
    44. Mauro Steigleder and Michael D. McCool. 2002. Factorization of the Ashikhmin BRDF for real-time rendering. J. Graph. GPU Game Tools 7, 4 (2002), 61–67. 
    45. Eino-Ville Talvala, Andrew Adams, Mark Horowitz, and Marc Levoy. 2007. Veiling glare in high dynamic range imaging. ACM Trans. Graph. 26, 3 (2007). 
    46. C. Tofallis. 2008. Least squares percentage regression. J. Mod. Appl. Stat. Methods 7 (2008), 526–534.
    47. Eric Veach. 1998. Robust Monte Carlo Methods for Light Transport Simulation. Ph.D. Dissertation. Stanford, CA, USA. Advisor(s) Guibas, Leonidas J. AAI9837162. 
    48. Bruce Walter, Stephen R. Marschner, Hongsong Li, and Kenneth E. Torrance. 2007. Microfacet models for refraction through rough surfaces. In Rendering Techniques. Eurographics Association, 195–206. 
    49. Jiaping Wang, Shuang Zhao, Xin Tong, John Snyder, and Baining Guo. 2008. Modeling anisotropic surface reflectance with example-based microfacet synthesis. ACM Trans. Graph. 27, 3 (Aug. 2008), 41:1–41:9. 
    50. Halbert White. 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 4 (1980).

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