## Directional statistics-based reflectance model for isotropic bidirectional reflectance distribution functions |

JOSA A, Vol. 28, Issue 1, pp. 8-18 (2011)

http://dx.doi.org/10.1364/JOSAA.28.000008

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### Abstract

We introduce a novel parametric bidirectional reflectance distribution function (BRDF) model that can accurately encode a wide variety of real-world isotropic BRDFs with a small number of parameters. The key observation we make is that a BRDF may be viewed as a statistical distribution on a unit hemisphere. We derive a novel directional statistics distribution, which we refer to as the hemispherical exponential power distribution, and model real-world isotropic BRDFs as mixtures of it. We derive a canonical probabilistic method for estimating the parameters, including the number of components, of this novel directional statistics BRDF model. We show that the model captures the full spectrum of real-world isotropic BRDFs with high accuracy, but a small footprint. We also demonstrate the advantages of the novel BRDF model by showing its use for reflection component separation and for exploring the space of isotropic BRDFs.

© 2011 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(290.1483) Scattering : BSDF, BRDF, and BTDF

**ToC Category:**

Scattering

**History**

Original Manuscript: September 14, 2010

Revised Manuscript: November 11, 2010

Manuscript Accepted: November 11, 2010

Published: December 16, 2010

**Citation**

Ko Nishino and Stephen Lombardi, "Directional statistics-based reflectance model for isotropic bidirectional reflectance distribution functions," J. Opt. Soc. Am. A **28**, 8-18 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-1-8

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### References

- F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometric considerations and nomenclature for reflectance,” (National Bureau of Standards, 1977).
- J. H. Lambert, “Photometria sive de mensura de gratibus luminis colorum et umbrae,” (Eberhard Klett, 1760).
- B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975). [CrossRef]
- J. F. Blinn, “Models of light reflection for computer sythesized pictures,” in SIGGRAPH ’77 Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 1977), pp. 192–198. [CrossRef]
- C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Computer Graphics Forum 13, 233–246 (1994). [CrossRef]
- R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982). [CrossRef]
- K. Torrance and E. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114(1967). [CrossRef]
- G. J. Ward, “Measuring and modeling anisotropic reflection,” in SIGGRAPH ’92 Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 1992), pp. 265–272. [CrossRef]
- S. K. Nayar and M. Oren, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995). [CrossRef]
- J. J. Koenderink and A. J. van Doorn, “Phenomenological description of bidirectional surface reflection,” J. Opt. Soc. Am. A 15, 2903–2912 (1998). [CrossRef]
- R. Ramamoorthi and P. Hanrahan, “A signal-processing framework for inverse rendering,” in SIGGRAPH ’01 Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 2001), pp. 117–128. [CrossRef]
- E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in SIGGRAPH ’97 Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 1997), pp. 117–126. [CrossRef]
- D. Edwards, S. Boulos, J. Johnson, P. Shirley, M. Ashikhmin, M. Stark, and C. Wyman, “The halfway vector disk for BRDF modeling,” ACM Trans. Graph. 25, 1–18 (2006). [CrossRef]
- P. Debevec, T. Hawkins, C. Tchou, H.-P.Duiker, and W. Sarokin, “Acquiring the reflectance field of a human face,” in SIGGRAPH ’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 2000), pp. 145–156. [CrossRef]
- W. Matusik, H. Pfister, M. Brand, and L. McMillan, “Efficient isotropic BRDF measurement,” in Proceedings of the 14th Eurographics Workshop on Rendering Techniques, P.H.Christensen, D.Cohen-Or, and S.N.Spencer, eds., Vol. 44 of ACM International Conference Proceeding Series (Eurographics Association, 2003), pp. 241–248.
- A. Ghosh, S. Achutha, W. Heidrich, and M. O’Toole., “BRDF acquisition with basis illumination,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), pp. 1–8.
- A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Estimating specular roughness and anisotropy from second order spherical gradient illumination,” Computer Graphics Forum 28, 1161–1170 (2009). [CrossRef]
- M. Ashikhmin and S. Premoze, “Distribution-based BRDFs,” Tech. Rep. (University of Utah, 2007).
- W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003). [CrossRef]
- F. Romeiro, Y. Vasilyev, and T. E. Zickler, “Passive reflectometry,” in Proceedings of the 10th European Conference on Computer Vision: Part IV (Springer, 2008), pp. 859–872.
- M. Stark, J. Arvo, and B. Smits, “Barycentric parameterizations for isotropic BRDFs,” IEEE Trans. Vis. Comput. Graph. 11, 126–138 (2005). [CrossRef]
- S. Rusinkiewicz, “A new change of variables for efficient BRDF representation,” presented at the 1998 Eurographics Workshop on Rendering, Vienna, Austria, 29 June–1July 1998.
- A. Ngan, F. Durand, and W. Matusik, “Experimental analysis of BRDF models,” in Proceedings of the Eurographics Symposium on Rendering 2005, (Eurographics Association, 2005), pages 117–226.
- R. A. Fisher, “Dispersion on a sphere,” Proc. R. Soc. Lond. A 217, 295–305 (1953). [CrossRef]
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1965).
- S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991). [CrossRef]
- C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2007).
- K. Hara, K. Nishino, and K. Ikeuchi, “Mixture of spherical distributions for single-view relighting,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 25–35 (2008). [CrossRef]
- D. A. Williams, “A test for differences between treatment means when several dose levels are compared with a zero dose control,” Biometrics 27, 103–117 (1971). [CrossRef]
- S. Cang and D. Partridge, “Determining the number of components in mixture models using Williams’ statistical test,” presented at the 8th International Conference on Neural Information Processing, Shanghai, China, 14–18 Nov. 2001.
- P. Debevec, “Light probe image gallery,” http://www.debevec.org/Probes.
- M. Pharr and G. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2004).
- J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2nd ed., Springer Series in Statistics (Springer, 2005).

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