This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Wavelet Representation of Reflectance Functions
October-December 1997 (vol. 3 no. 4)
pp. 329-336

Abstract—Analytical models of light reflection are in common use in computer graphics. However, models based on measured reflectance data promise increased realism by making it possible to simulate many more types of surfaces to a greater level of accuracy than with analytical models. They also require less expert knowledge about the illumination models and their parameters. There are a number of hurdles to using measured reflectance functions, however. The data sets are very large. A reflectance distribution function sampled at five degrees angular resolution, arguably sparse enough to miss highlights and other high frequency effects, can easily require over a million samples, which in turn amount to over four megabytes of data. These data then also require some form of interpolation and filtering to be used effectively.

In this paper, we examine issues of representation of measured reflectance distribution functions. In particular, we examine a wavelet basis representation of reflectance functions, and the algorithms required for efficient point-wise reconstruction of the BRDF. We show that the nonstandard wavelet decomposition leads to considerably more efficient algorithms than the standard wavelet decomposition. We also show that thresholding allows considerable improvement in running times, without unduly sacrificing image quality.

[1] J.F. Blinn, "Models of Light Reflection for Computer Synthesized Pictures," Computer Graphics, vol. 11, no. 2, 1977, pp. 192-198.
[2] B. Cabral, N. Max, and R. Springmeyer, “Bi-Directional Reflection from Surface Bump Maps,” Computer Graphics, vol. 21, no. 4, pp. 273-282, 1987.
[3] J. Cohen, D.P. Greenberg, D.S. Immel, and P.J. Brock, "An Efficient Radiosity Approach for Realistic Image Synthesis," IEEE Computer Graphics and Applications, vol. 6, no. 3, pp. 26-35, Mar. 1986.
[4] R.L. Cook and K.E. Torrance, "A Reflectance Model for Computer Graphics," ACM Trans. Graphics, vol. 1, no. 1, pp. 7-24, Jan. 1982.
[5] I. Daubechies,“Ten lectures on wavelets,” SIAM CBMS-61, 1992.
[6] J. DeYoung, P. Lalonde, and A. Fournier, "Acquiring and Using Realistic Reflectance Data in Computer Graphics Images," Proc. Arkansas Computer Conf., pp. 77-82,Searcy, Ark., Mar.7-8, 1996.
[7] A. Fournier, "Separating Reflection Functions for Linear Radiosity," Proc. Eurographics Rendering Workshop 1995, June 1995.
[8] J.S. Gondek, G.W. Meyer, and J.G. Newman, “Wavelength Dependent Reflectance Functions,” Computer Graphics, pp. 213-220, 1994.
[9] S.J. Gortler, P. Schroder, M.F. Cohen, and P. Hanrahan, "Wavelet Radiosity," Computer Graphics Proc., Ann. Conf. Series: SIGGRAPH '93,Anaheim, Calif., pp. 221-230, Aug. 1993.
[10] P. Hanrahan and W. Krueger, “Reflection from Layered Surfaces due to Subsurface Scattering,” Computer Graphics, pp. 165-174, 1993.
[11] D.S. Immel, M.F. Cohen, and D.P. Greenberg, "A Radiosity Method for Non-Diffuse Environments," Computer Graphics (Proc. SIGGRAPH '86), D.C. Evans and R.J. Arthay, eds., vol. 20, pp. 133-142, Aug. 1986.
[12] American Nat'l Standards Inst., ANSI Standard Nomenclature and Definitions for Illuminating Engineering.New York: ANSI/IES RP-16-1986, Illuminating Eng. Soc.
[13] J.T. Kajiya, "Anisotropic Reflection Models," Computer Graphics (SIGGRAPH '85 Proc.), B.A. Barsky, ed., vol. 19, no. 3, pp. 15-21, July 1985.
[14] J. Kajiya, “The Rendering Equation,” Computer Graphics, pp. 143-150, 1986.
[15] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[16] P. Lalonde and A. Fournier, "Filtered Local Shading the Wavelet Domain," Proc. Eighth Eurographics Workshop Rendering,St. Etienne, France, June 1997.
[17] P. Lalonde and A. Fournier, "Generating Reflected Directions From BRDF Data," Computer Graphics Forum, Eurographics '97 Conf. Issue, vol. 16, Sept. 1997.
[18] R.R. Lewis and A. Fournier, "Light-Driven Global Illumination With a Wavelet Representation of Light Transport," Proc. Seventh Eurographics Workshop Rendering,Porto, Portugal, June 1996.
[19] B.-T. Phong, "Illumination for Computer Generated Pictures," Comm. ACM, vol. 18, no. 6, 1975, pp. 311-317.
[20] P. Schröder and W. Sweldens, "Spherical Wavelets: Efficiently Representing Functions on the Sphere," Proc. SIGGRAPH '95 Conf., pp. 161-172, 1995.
[21] F.X. Sillion et al., "A Global Illumination Solution for General Reflectance Distributions," Computer Graphics Proc.(Siggraph 91), ACM Press, New York, 1991, pp. 187-196.
[22] B.E. Smits and G. Meyer, "Newton's Colors: Simulating Interference Phenomena in Realistic Image synthesis," Proc. Eurographics Workshop Photosimulation, Realism, and Physics in Computer Graphics, pp. 185-194,Rennes, France, June 1990.
[23] E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, "Wavelets for Computer Graphics: A Primer, Part 1," IEEE Computer Graphics and Applications, Vol. 15, No. 3, May 1995, pp. 76-84.
[24] G.J. Ward, “Measuring and Modeling Anisotropic Reflection,” Computer Graphics, vol. 26, no. 2, pp. 265-272, 1992.
[25] G Ward, F. Rubinstein, and R. Clear, "A Ray Tracing Solution for Diffuse Interreflection," Proc. ACM Siggraph, vol. 22, no. 4, 1988, pp. 85-92.
[26] S.H. Westin, J.R. Arvo, and K.E. Torrance, “Predicting Reflectance Functions from Complex Surfaces,” Computer Graphics, vol. 26, no. 2, pp. 255-264, 1992.
[27] T. Whitted, “An Improved Illumination Model for Shaded Display,” Comm. ACM, vol. 23, no. 6, pp. 343-349, 1980.

Index Terms:
Reflectance models, bidirectional reflectance, distribution functions, local shading, local illumination, wavelets, compression.
Citation:
Paul Lalonde, Alain Fournier, "A Wavelet Representation of Reflectance Functions," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 4, pp. 329-336, Oct.-Dec. 1997, doi:10.1109/2945.646236
Usage of this product signifies your acceptance of the Terms of Use.