An Overview of BRDF Models

This paper is focused on the Bidirectional Reflectance Distribution Function (BRDF) in the context of algorithms for computational production of realistic synthetic images. We provide a review of most relevant analytical BRDF models proposed in the literature which have been used for realistic rendering. We also show different approaches used for obtaining efficient models from acquired reflectance data, and the related function fitting techniques, suitable for using that data in efficient rendering algorithms. We consider the algorithms for computation of BRDF integrals, by using Monte-Carlo based numerical integration. In this context, we review known techniques to design efficient BRDF sampling schemes for both analytical and measured BRDF models.

[1]  Christophe Schlick,et al.  An Inexpensive BRDF Model for Physically‐based Rendering , 1994, Comput. Graph. Forum.

[2]  James F. Blinn,et al.  Models of light reflection for computer synthesized pictures , 1977, SIGGRAPH.

[3]  James Arvo,et al.  Applications of irradiance tensors to the simulation of non-Lambertian phenomena , 1995, SIGGRAPH.

[4]  Pierre Poulin,et al.  A model for anisotropic reflection , 1990, SIGGRAPH.

[5]  H. Sebastian Seung,et al.  Algorithms for Non-negative Matrix Factorization , 2000, NIPS.

[6]  M. Minnaert The reciprocity principle in lunar photometry , 1941 .

[7]  Jason Lawrence,et al.  Eurographics Symposium on Rendering (2007) Efficient Basis Decomposition for Scattered Reflectance Data , 2022 .

[8]  David Geisler-Moroder,et al.  A New Ward BRDF Model with Bounded Albedo , 2010, Comput. Graph. Forum.

[9]  Nelson L. Max,et al.  Bidirectional reflection functions from surface bump maps , 1987, SIGGRAPH.

[10]  Arne Dür,et al.  An Improved Normalization for the Ward Reflectance Model , 2006, J. Graph. Tools.

[11]  Szymon Rusinkiewicz,et al.  Efficient BRDF importance sampling using a factored representation , 2004, SIGGRAPH 2004.

[12]  Gregory J. Ward,et al.  Measuring and modeling anisotropic reflection , 1992, SIGGRAPH.

[13]  Jan Kautz,et al.  Fast Arbitrary BRDF Shading for Low-Frequency Lighting Using Spherical Harmonics , 2002, Rendering Techniques.

[14]  Philippe Bekaert,et al.  Advanced global illumination , 2006 .

[15]  Philip E. Gill,et al.  Practical optimization , 1981 .

[16]  J. Arvo Analytic methods for simulated light transport , 1995 .

[17]  Jan Kautz,et al.  Interactive rendering with arbitrary BRDFs using separable approximations , 1999, SIGGRAPH '99.

[18]  Hermann von Helmholtz,et al.  Treatise on Physiological Optics , 1962 .

[19]  Murat Kurt,et al.  Representing BRDFs using SOMs and MANs , 2008, COMG.

[20]  Peter Shirley,et al.  A microfacet-based BRDF generator , 2000, SIGGRAPH.

[21]  Peter Shirley,et al.  The halfway vector disk for BRDF modeling , 2006, TOGS.

[22]  Loïc Barthe,et al.  Wavelet encoding of BRDFs for real-time rendering , 2007, GI '07.

[23]  Peter Shirley,et al.  A practitioners' assessment of light reflection models , 1997, Proceedings The Fifth Pacific Conference on Computer Graphics and Applications.

[24]  F. Clarke,et al.  Helmholtz Reciprocity: its validity and application to reflectometry , 1985 .

[25]  James T. Kajiya,et al.  The rendering equation , 1986, SIGGRAPH.

[26]  Parris K. Egbert,et al.  Importance resampling for global illumination , 2005, EGSR '05.

[27]  Szymon Rusinkiewicz,et al.  A New Change of Variables for Efficient BRDF Representation , 1998, Rendering Techniques.

[28]  S K Nayar,et al.  Visual appearance of matte surfaces , 1995, Science.

[29]  Greg Humphreys,et al.  Physically Based Rendering: From Theory to Implementation , 2004 .

[30]  Alain Fournier,et al.  Separating Reflection Functions for Linear Radiosity , 1995, Rendering Techniques.

[31]  Murat Kurt,et al.  Linear approximation of Bidirectional Reflectance Distribution Functions , 2008, Comput. Graph..

[32]  Leonidas J. Guibas,et al.  Robust Monte Carlo methods for light transport simulation , 1997 .

[33]  Miguel Lastra,et al.  Generic BRDF Sampling - A Sampling Method for Global Illumination , 2008, GRAPP.

[34]  Robert L. Cook,et al.  A Reflectance Model for Computer Graphics , 1987, TOGS.

[35]  Andreas Kolb,et al.  Homomorphic factorization of BRDF-based lighting computation , 2002, ACM Trans. Graph..

[36]  Shree K. Nayar,et al.  Generalization of Lambert's reflectance model , 1994, SIGGRAPH.

[37]  Andrew S. Glassner,et al.  Principles of Digital Image Synthesis , 1995 .

[38]  Andrea J. van Doorn,et al.  Bidirectional Reflection Distribution Function Expressed in Terms of Surface Scattering Modes , 1996, ECCV.

[39]  Kristin J. Dana BRDF/BTF measurement device , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[40]  Jitendra Malik,et al.  Representing and Recognizing the Visual Appearance of Materials using Three-dimensional Textons , 2001, International Journal of Computer Vision.

[41]  Paul L. Rosin Techniques for Assessing Polygonal Approximations of Curves , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  László Szirmay-Kalos,et al.  Compact Metallic Reflectance Models , 1999, Comput. Graph. Forum.

[43]  Peter Shirley,et al.  An Anisotropic Phong BRDF Model , 2000, J. Graphics, GPU, & Game Tools.

[44]  Wojciech Matusik,et al.  A data-driven reflectance model , 2003, ACM Trans. Graph..

[45]  Stephen H. Westin,et al.  Automated three-axis gonioreflectometer for computer graphics applications , 2006 .

[46]  Frédo Durand,et al.  Experimental analysis of BRDF models , 2005, EGSR '05.

[47]  Alan H. Strahler,et al.  Investigation on the Torrance-Sparrow specular BRDF model , 1998, IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings. (Cat. No.98CH36174).

[48]  Donald P. Greenberg,et al.  Non-linear approximation of reflectance functions , 1997, SIGGRAPH.

[49]  Eric P. Lafortune,et al.  Using the modified Phong reflectance model for physically based rendering , 1994 .

[50]  Thomas A. Germer,et al.  Goniometric Optical Scatter Instrument for Out-of-Plane Ellipsometry Measurements , 1999 .

[51]  H. Jensen Realistic Image Synthesis Using Photon Mapping , 2001 .

[52]  Robert R. Lewis,et al.  Making Shaders More Physically Plausible , 1994, Comput. Graph. Forum.

[53]  Donald P. Greenberg,et al.  A comprehensive physical model for light reflection , 1991, SIGGRAPH.

[54]  Christophe Schlick,et al.  A Fast Alternative to Phong's Specular Model , 1994, Graphics Gems.

[55]  Gary W. Meyer,et al.  A BRDF Database Employing the Beard-Maxwell Reflection Model , 2002, Graphics Interface.

[56]  Csaba Kelemen,et al.  A Microfacet Based Coupled Specular-Matte BRDF Model with Importance Sampling , 2001, Eurographics.

[57]  Mathias Paulin,et al.  A wavelet-based framework for acquired radiometric quantity representation and accurate physical rendering , 2006, The Visual Computer.

[58]  H. Jensen,et al.  Wavelet importance sampling: efficiently evaluating products of complex functions , 2005, SIGGRAPH 2005.

[59]  Paul Lalonde,et al.  A Wavelet Representation of Reflectance Functions , 1997, IEEE Trans. Vis. Comput. Graph..

[60]  Wolfgang Heidrich,et al.  A simple layered RGB BRDF model , 2003, Graph. Model..

[61]  Thomas A. Germer,et al.  Goniometric optical scatter instrument for bidirectional reflectance distribution function measurements with out-of-plane and polarimetry capabilities , 1997, Optics & Photonics.

[62]  Paul S. Strauss,et al.  A realistic lighting model for computer animators , 1990, IEEE Computer Graphics and Applications.

[63]  Stephen H. Westin,et al.  Predicting reflectance functions from complex surfaces , 1992, SIGGRAPH.

[64]  David Salesin,et al.  A fast and accurate light reflection model , 1992, SIGGRAPH.

[65]  Mathias Paulin,et al.  Spectral BRDF modeling using wavelets , 2002, SPIE Defense + Commercial Sensing.

[66]  James Arvo,et al.  A framework for the analysis of error in global illumination algorithms , 1994, SIGGRAPH.

[67]  Michael D. McCool,et al.  Homomorphic factorization of BRDFs for high-performance rendering , 2001, SIGGRAPH.

[68]  Bui Tuong Phong Illumination for computer generated pictures , 1975, Commun. ACM.

[69]  Thomas A. Germer,et al.  A Goniometric Optical Scatter Instrument for Bidirectional Reflectance Distribution Function Measurements with Out-of-plane and Polarimetry Capabilities, ed. by Z.H. Gu and A.A. Maradudin , 1997 .

[70]  Peter Schröder,et al.  Spherical wavelets: efficiently representing functions on the sphere , 1995, SIGGRAPH.

[71]  J. Beard,et al.  Bidirectional Reflectance Model Validation and Utilization. , 1973 .

[72]  Peter Shirley,et al.  Physically based lighting calculations for computer graphics , 1991 .

[73]  Mathias Paulin,et al.  BRDF Measurement Modelling using Wavelets for Efficient Path Tracing , 2003, Comput. Graph. Forum.

[74]  Szymon Rusinkiewicz,et al.  Adaptive numerical cumulative distribution functions for efficient importance sampling , 2005, EGSR '05.

[75]  K. Torrance,et al.  Off-Specular Peaks in the Directional Distribution of Reflected Thermal Radiation , 1966 .

[76]  Ravi Ramamoorthi,et al.  Reflectance sharing: predicting appearance from a sparse set of images of a known shape , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[77]  Ravi Ramamoorthi,et al.  An Analysis of the In‐Out BRDF Factorization for View‐Dependent Relighting , 2008, Comput. Graph. Forum.