M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

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.

M. Stark, J. Arvo, and B. Smits, “Barycentric parameterizations for isotropic BRDFs,” IEEE Trans. Vis. Comput. Graph. 11, 126–138 (2005).

[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]

M. Ashikhmin and S. Premoze, “Distribution-based BRDFs,” Tech. Rep. (University of Utah, 2007).

C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2007).

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]

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]

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003).

[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.

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.

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]

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).

[CrossRef]

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]

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]

P. Debevec, “Light probe image gallery,” http://www.debevec.org/Probes.

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]

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.

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]

R. A. Fisher, “Dispersion on a sphere,” Proc. R. Soc. Lond. A 217, 295–305 (1953).

[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]

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]

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.

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).

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]

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]

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]

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]

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.

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).

M. Pharr and G. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2004).

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]

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]

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]

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]

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]

J. H. Lambert, “Photometria sive de mensura de gratibus luminis colorum et umbrae,” (Eberhard Klett, 1760).

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).

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003).

[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. 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.

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003).

[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.

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]

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]

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.

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).

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]

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.

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]

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.

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]

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003).

[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.

M. Pharr and G. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2004).

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).

[CrossRef]

M. Ashikhmin and S. Premoze, “Distribution-based BRDFs,” Tech. Rep. (University of Utah, 2007).

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]

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2nd ed., Springer Series in Statistics (Springer, 2005).

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).

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.

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.

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]

C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Computer Graphics Forum 13, 233–246 (1994).

[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]

J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 2nd ed., Springer Series in Statistics (Springer, 2005).

M. Stark, J. Arvo, and B. Smits, “Barycentric parameterizations for isotropic BRDFs,” IEEE Trans. Vis. Comput. Graph. 11, 126–138 (2005).

[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]

M. Stark, J. Arvo, and B. Smits, “Barycentric parameterizations for isotropic BRDFs,” IEEE Trans. Vis. Comput. Graph. 11, 126–138 (2005).

[CrossRef]

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

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]

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).

[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]

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.

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]

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]

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]

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]

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.

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]

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759–769(2003).

[CrossRef]

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7–24 (1982).

[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]

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).

[CrossRef]

C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Computer Graphics Forum 13, 233–246 (1994).

[CrossRef]

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]

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]

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]

M. Stark, J. Arvo, and B. Smits, “Barycentric parameterizations for isotropic BRDFs,” IEEE Trans. Vis. Comput. Graph. 11, 126–138 (2005).

[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]

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).

C. M. Bishop, Pattern Recognition and Machine Learning (Springer, 2007).

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.

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. Ashikhmin and S. Premoze, “Distribution-based BRDFs,” Tech. Rep. (University of Utah, 2007).

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]

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.

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]

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]

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).

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).