This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Adjoints and Importance in Rendering: An Overview
July-September 2003 (vol. 9 no. 3)
pp. 329-340

Abstract—This survey gives an overview of the use of importance, an adjoint of light, in speeding up rendering. The importance of a light distribution indicates its contribution to the region of most interest—typically the directly visible parts of a scene. Importance can therefore be used to concentrate global illumination and ray tracing calculations where they matter most for image accuracy, while reducing computations in areas of the scene that do not significantly influence the image. In this paper, we attempt to clarify the various uses of adjoints and importance in rendering by unifying them into a single framework. While doing so, we also generalize some theoretical results—known from discrete representations—to a continuous domain.

[1] J. Arvo, Analytic Methods for Simulated Light Transport PhD thesis, Yale Univ., 1995.
[2] J. Arvo and D. Kirk, Particle Transport and Image Synthesis Computer Graphics (Proc. SIGGRAPH '90), pp. 63-66, Aug. 1990.
[3] L. Aupperle, Hierarchical Algorithms for Illumination PhD thesis, Princeton Univ., 1993.
[4] L. Aupperle and P. Hanrahan, Importance and Discrete Three Point Transport Proc. Fourth Eurographics Workshop Rendering, pp. 85-94, June 1993.
[5] P. Bekaert, Hierarchical and Stochastic Algorithms for Radiosity PhD thesis, Katholieke Univ., Leuven, Belgium, 1999.
[6] P. Bekaert and Y. Willems, A Progressive Importance-Driven Rendering Algorithm Proc. 10th Spring School Computer Graphics, pp. 58-67, June 1994.
[7] P. Bekaert and Y. Willems, Importance-Driven Progressive Refinement Radiosity Rendering Techniques '95 (Proc. Sixth Eurographics Workshop Rendering), pp. 316-325, 1995.
[8] P. Christensen, Hierarchical Techniques for Glossy Global Illumination PhD thesis, Univ. of Washington, 1995.
[9] P. Christensen, Importance for Ray Tracing Ray Tracing News, vol. 12, no. 2, Dec. 1999.
[10] P. Christensen, D. Lischinski, E. Stollnitz, and D. Salesin, Clustering for Glossy Global Illumination ACM Trans. Graphics, vol. 16, no. 1, pp. 3-33, Jan. 1997.
[11] P. Christensen, D. Salesin, and T. DeRose, A Continuous Adjoint Formulation for Radiance Transport Proc. Fourth Eurographics Workshop Rendering, pp. 95-104, June 1993.
[12] P. Christensen, E. Stollnitz, D. Salesin, and T. DeRose, Wavelet Radiance Proc. Fifth Eurographics Workshop Rendering, pp. 287-302, June 1994.
[13] P. Christensen, E. Stollnitz, D. Salesin, and T. DeRose, Global Illumination of Glossy Environments Using Wavelets and Importance ACM Trans. Graphics, vol. 15, no. 1, pp. 37-71, Jan. 1996.
[14] M. Cohen, S. Chen, J. Wallace, and D. Greenberg, A Progressive Refinement Approach to Fast Radiosity Image Generation Computer Graphics (Proc. SIGGRAPH '88), pp. 75-84, Aug. 1988.
[15] M. Cohen and J. Wallace, Radiosity and Realistic Image Synthesis. Academic Press, 1993.
[16] R. Cook, T. Porter, and L. Carpenter, Distributed Ray Tracing Computer Graphics (Proc. SIGGRAPH '84), pp. 137-145, July 1984.
[17] R. Coveyou, V. Cain, and K. Yost, Adjoint and Importance in Monte Carlo Application Nuclear Science and Eng., vol. 27, pp. 219-234, 1967.
[18] J. Danskin and P. Hanrahan, Fast Algorithms for Volume Ray Tracing Computer Graphics (Proc. 1992 Workshop Volume Visualization), pp. 91-98, 1992.
[19] P. Dutré, Mathematical Frameworks and Monte Carlo Algorithms for Global Illumination in Computer Graphics PhD thesis, Katholieke Univ., Leuven, Belgium, 1996.
[20] P. Dutré, P. Bekaert, F. Suykens, and Y. Willems, Bidirectional Radiosity Rendering Techniques '97 (Proc. Eighth Eurographics Workshop Rendering), pp. 205-216, 1997.
[21] P. Dutré, E. Lafortune, and Y. Willems, A Mathematical Framework for Global Illumination Algorithms Proc. Winter School of Computer Graphics '94, pp. 75-84, Jan. 1994.
[22] P. Dutré and Y. Willems, Importance-Driven Monte Carlo Light Tracing Proc. Fifth Eurographics Workshop Rendering, pp. 185-194, June 1994.
[23] P. Dutré and Y. Willems, Potential-Driven Monte Carlo Particle Tracing for Diffuse Environments with Adaptive Probability Density Functions Rendering Techniques '95 (Proc. Sixth Eurographics Workshop Rendering), pp. 306-315, 1995.
[24] I. Fredholm, Sur une Classe d'Équations Fonctionelles Acta Mathematica, vol. 27, pp. 365-390, Mar. 1903.
[25] A. Glassner, Principles of Digital Image Synthesis. Morgan Kaufmann, 1995.
[26] G. Goertzel, Quota Sampling and Importance Functions in Stochastic Solution of Particle Problems Technical Report 434, Oak Ridge National Laboratory, June 1949.
[27] R. Hall and D. Greenberg, A Testbed for Realistic Image Synthesis IEEE Computer Graphics and Applications, vol. 3, no. 8, pp. 10-20, Nov. 1983.
[28] P. Hanrahan, D. Salzman, and L. Aupperle, A Rapid Hierarchical Radiosity Algorithm Computer Graphics (Proc. SIGGRAPH '91), pp. 197-206, July 1991.
[29] H. Jensen, Importance Driven Path Tracing Using the Photon Map Rendering Techniques '95 (Proc. Sixth Eurographics Workshop Rendering), pp. 326-335, 1995.
[30] H. Jensen, Global Illumination Using Photon Maps Rendering Techniques '96 (Proc. Seventh Eurographics Workshop Rendering), pp. 21-30, 1996.
[31] H. Jensen, F. Suykens, and P. Christensen, A Practical Guide to Global Illumination Using Photon Mapping SIGGRAPH 2001 Course Note #38, Aug. 2001.
[32] H. Kahn, Modifications of the Monte Carlo Method Technical Report P-132, Rand Corp., Nov. 1949.
[33] H. Kahn and T. Harris, Estimation of Particle Transmission by Random Sampling Monte Carlo Method, pp. 27-30, Nat'l Bureau of Standards, 1949.
[34] J. Kajiya, The Rendering Equation Computer Graphics (Proc. SIGGRAPH '86), pp. 143-150, Aug. 1986.
[35] M. Kalos, Importance Sampling in Monte Carlo Shielding Calculations Nuclear Science and Eng., vol. 16, pp. 227-234, 1963.
[36] M. Kalos and P. Whitlock, Monte Carlo Methods. John Wiley&Sons, 1986.
[37] A. Keller, Quasi-Monte Carlo Methods for Photorealistic Image Synthesis PhD thesis, Univ. of Kaiserslautern, Germany, 1998.
[38] A. Keller and I. Wald, Efficient Importance Sampling Techniques for the Photon Map Proc. Fifth Fall Workshop Vision, Modeling, and Visualization, pp. 271-279, Nov. 2000.
[39] E. Lafortune, Mathematical Models and Monte Carlo Algorithms for Physically Based Rendering PhD thesis, Katholieke Univ., Leuven, Belgium, 1996.
[40] E. Lafortune and Y. Willems, Bi-Directional Path Tracing Proc. CompuGraphics '93, pp. 145-153, Dec. 1993.
[41] E. Lafortune and Y. Willems, A Theoretical Framework for Physically Based Rendering Computer Graphics Forum, vol. 13, no. 2, pp. 97-107, June 1994.
[42] E. Lafortune and Y. Willems, A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing Rendering Techniques '95 (Proc. Sixth Eurographics Workshop Rendering), pp. 11-20, 1995.
[43] E. Lafortune and Y. Willems, Rendering Participating Media with Bidirectional Path Tracing Rendering Techniques '96 (Proc. Seventh Eurographics Workshop Rendering), pp. 91-100, 1996.
[44] M. Levoy, Efficient Ray Tracing of Volume Data ACM Trans. Graphics, vol. 9, no. 3, pp. 245-261, July 1990.
[45] J. Lewins, Importance, The Adjoint Function. Pergamon Press, 1965.
[46] E. Lewis and W. Miller Jr., Computational Methods of Neutron Transport. John Wiley&Sons, 1984.
[47] D. Lischinski, Accurate and Reliable Algorithms for Global Illumination PhD thesis, Cornell Univ., 1994.
[48] D. Lischinski, B. Smits, and D. Greenberg, Bounds and Error Estimates for Radiosity Computer Graphics (Proc. SIGGRAPH '94), pp. 67-74, July 1994.
[49] A. Neumann, L. Neumann, P. Bekaert, Y. Willems, and W. Purgathofer, Importance-Driven Stochastic Ray Radiosity Rendering Techniques '96 (Proc. Seventh Eurographics Workshop Rendering), pp. 111-122, 1996.
[50] L. Neumann, M. Feda, M. Kopp, and W. Purgathofer, A New Stochastic Radiosity Method for Highly Complex Scenes Proc. Fifth Eurographics Workshop Rendering, pp. 195-206, June 1994.
[51] S. Pattanaik, Computational Methods for Global Illumination and Visualisation of Complex 3D Environments PhD thesis, Birla Inst. of Technology&Science, Pilani, India, 1993.
[52] S. Pattanaik, The Mathematical Framework of Adjoint Equations for Illumination Computations Graphics, Design, and Visualization (Proc. Int'l Conf. Computer Graphics '93), pp. 123-137, 1993.
[53] S. Pattanaik and K. Bouatouch, Interactive Walk-Through Using Particle Tracing Computer Graphics Developments in Virtual Environments (Proc. Computer Graphics Int'l '95), 1995.
[54] S. Pattanaik and S. Mudur, Efficient Potential Equation Solutions for Global Illumination Computation Computers&Graphics, vol. 17, no. 4, pp. 387-396, 1993.
[55] S. Pattanaik and S. Mudur, The Potential Equation and Importance in Illumination Computations Computer Graphics Forum, vol. 12, no. 2, pp. 131-136, June 1993.
[56] S. Pattanaik and S. Mudur, Adjoint Equations and Random Walks for Illumination Computation ACM Trans. Graphics, vol. 14, no. 1, pp. 77-102, Jan. 1995.
[57] K. Perlin and E. Hoffert, Hypertexture Computer Graphics (Proc. SIGGRAPH '89), pp. 253-262, July 1989.
[58] I. Peter and G. Pietrek, Importance Driven Construction of Photon Maps Rendering Techniques '98 (Proc. Ninth Eurographics Workshop Rendering), pp. 269-280, 1998.
[59] X. Pueyo, D. Tost, I. Martin, and B. Garcia, Radiosity for Dynamic Environments J. Visualization and Computer Animation, vol. 8, no. 4, pp. 221-231, Oct. 1997.
[60] J. Prikryl, P. Bekaert, and W. Purgathofer, Importance-Driven Hierarchical Stochastic Ray Radiosity Proc. Winter School of Computer Graphics 2000, Jan. 2000.
[61] M. Sbert, Optimal Source Selection in Shooting Random Walk Monte Carlo Radiosity Computer Graphics Forum (Proc. Eurographics '97), pp. 301-308, Aug. 1997.
[62] M. Sbert, Optimal Absorption Probabilities for Random Walk Radiosity Graphical Models, vol. 62, no. 1, pp. 56-70, 2000.
[63] P. Schröder and P. Hanrahan, Wavelet Methods for Radiance Computations Proc. Fifth Eurographics Workshop Rendering, pp. 303-311, June 1994.
[64] F. Sillion and C. Puech, Radiosity and Global Illumination. Morgan Kaufmann, 1994.
[65] B. Smits, Efficient Hierarchical Radiosity in Complex Environments PhD thesis, Cornell Univ., 1994.
[66] B. Smits, J. Arvo, and D. Greenberg, A Clustering Algorithm for Radiosity in Complex Environments Computer Graphics (Proc. SIGGRAPH '94), pp. 435-442, July 1994.
[67] B. Smits, J. Arvo, and D. Salesin, An Importance-Driven Radiosity Algorithm Computer Graphics (Proc. SIGGRAPH '92), pp. 273-282, July 1992.
[68] H. Soodak, Pile Kinetics The Science and Eng. of Nuclear Power, C. Goodman, ed., vol. 2, chapter 8, pp. 89-102, Addison-Wesley, 1949.
[69] J. Spanier and E. Gelbard, Monte Carlo Principles and Neutron Transport Problems. Addison-Wesley, 1969.
[70] E. Stollnitz, T. DeRose, and D. Salesin, Wavelets for Computer Graphics. Morgan Kaufmann, 1996.
[71] F. Suykens and Y. Willems, Density Control for Photon Maps Rendering Techniques 2000 (Proc. 11th Eurographics Workshop Rendering), pp. 11-22, 2000.
[72] L. Szirmay-Kalos, Photorealistic Image Synthesis Using Ray-Bundles doctoral dissertation, Technical Univ. of Budapest, Hungary, 2000.
[73] L. Szirmay-Kalos, B. Csébfalvi, and W. Purgathofer, Importance Driven Quasi-Random Walk Solution of the Rendering Equation Computers and Graphics, vol. 23, no. 2, pp. 203-212, 1999.
[74] E. Veach, Non-Symmetric Scattering in Light Transport Algorithms Rendering Techniques '96 (Proc. Seventh Eurographics Workshop Rendering), pp. 81-90, 1996.
[75] E. Veach, Robust Monte Carlo Methods for Light Transport Simulation PhD thesis, Stanford Univ., 1997.
[76] E. Veach and L. Guibas, Bidirectional Estimators for Light Transport Proc. Fifth Eurographics Workshop Rendering, pp. 147-162, June 1994.
[77] E. Veach and L. Guibas, Optimally Combining Sampling Techniques for Monte Carlo Rendering Computer Graphics (Proc. SIGGRAPH '95), pp. 419-428, Aug. 1995.
[78] G. Ward, Adaptive Shadow Testing for Ray Tracing Proc. Second Eurographics Workshop Rendering, pp. 11-20, May 1991.
[79] G. Ward, F. Rubinstein, and R. Clear, A Ray Tracing Solution for Diffuse Interreflection Computer Graphics (Proc. SIGGRAPH '88), pp. 85-92, Aug. 1988.
[80] T. Whitted, An Improved Illumination Model for Shaded Display Comm. ACM, vol. 23, no. 6, pp. 343-349, June 1980.

Index Terms:
Rendering, adjoints, importance, light, ray tracing, global illumination, participating media, literature survey.
Citation:
Per H. Christensen, "Adjoints and Importance in Rendering: An Overview," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 3, pp. 329-340, July-Sept. 2003, doi:10.1109/TVCG.2003.1207441
Usage of this product signifies your acceptance of the Terms of Use.