Matrix radiance transfer

ABSTRACT

Precomputed Radiance Transfer allows interactive rendering of objects illuminated by low-frequency environment maps, including self-shadowing and interreflections. The expensive integration of incident lighting is partially precomputed and stored as matrices.Incorporating anisotropic, glossy BRDFs into precomputed radiance transfer has been previously shown to be possible, but none of the previous methods offer real-time performance. We propose a new method, matrix radiance transfer, which significantly speeds up exit radiance computation and allows anisotropic BRDFs. We generalize the previous radiance transfer methods to work with a matrix representation of the BRDF and optimize exit radiance computation by expressing the exit radiance in a new, directionally locally supported basis set instead of the spherical harmonics. To determine exit radiance, our method performs four dot products per vertex in contrast to previous methods, where a full matrix-vector multiply is required. Image quality can be controlled by adapting the number of basis functions. We compress our radiance transfer matrices through principal component analysis (PCA). We show that it is possible to render directly from the PCA representation, which also enables the user to trade interactively between quality and speed.

REFERENCES

• 1: Michael Ashikhmin , Peter Shirley, An anisotropic phong BRDF model, Journal of Graphics Tools, v.5 n.2, p.25-32, Dec. 2000
• 2: Michael Ashikhmin , Peter Shirley, Steerable illumination textures, ACM Transactions on Graphics (TOG), v.21 n.1, p.1-19, January 2002 [doi>10.1145/504789.504790]
• 3: James F. Blinn , Martin E. Newell, Texture and reflection in computer generated images, Communications of the ACM, v.19 n.10, p.542-547, Oct. 1976 [doi>10.1145/360349.360353]
• 4: Brian Cabral , Nelson Max , Rebecca Springmeyer, Bidirectional reflection functions from surface bump maps, Proceedings of the 14th annual conference on Computer graphics and interactive techniques, p.273-281, August 1987
• 5: Brian Cabral , Marc Olano , Philip Nemec, Reflection space image based rendering, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.165-170, July 1999 [doi>10.1145/311535.311553]
• 6: Paul Debevec, Rendering synthetic objects into real scenes: bridging traditional and image-based graphics with global illumination and high dynamic range photography, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.189-198, July 1998 [doi>10.1145/280814.280864]
• 7: EDMONDS, A. 1960. Angular Momentum in Quantum Mechanics. Princeton University, Princeton, NJ.
• 8: Rafael C. Gonzales , Paul Wintz, Digital image processing (2nd ed.), Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1987
• 9: N Greene, Applications of world projections, Proceedings on Graphics Interface '86/Vision Interface '86, p.108-114, August 1986, Vancouver, British Columbia, Canada
• 10: Ned Greene, Environment mapping and other applications of world projections, IEEE Computer Graphics and Applications, v.6 n.11, p.21-29, November 1986 [doi>10.1109/MCG.1986.276658]
• 11: Wolfgang Heidrich , Hans-Peter Seidel, Realistic, hardware-accelerated shading and lighting, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.171-178, July 1999 [doi>10.1145/311535.311554]
• 12: Wolfgang Heidrich , Katja Daubert , Jan Kautz , Hans-Peter Seidel, Illuminating micro geometry based on precomputed visibility, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.455-464, July 2000 [doi>10.1145/344779.344984]
• 13: KAUTZ, J., AND MCCOOL, M. 2000. Approximation of Glossy Reflection with Prefiltered Environment Maps. In Proceedings Graphics Interface, 119--126.
• 14: Jan Kautz , Pere-Pau Vázquez , Wolfgang Heidrich , Hans-Peter Seidel, Unified Approach to Prefiltered Environment Maps, Proceedings of the Eurographics Workshop on Rendering Techniques 2000, p.185-196, June 26-28, 2000
• 15: Jan Kautz , Peter-Pike Sloan , John Snyder, Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics, Proceedings of the 13th Eurographics workshop on Rendering, June 26-28, 2002, Pisa, Italy
• 16: KREYSZIG, E. 1989. Introductory Functional Analysis with Applications. Wiley, New York.
• 17: Lutz Latta , Andreas Kolb, Homomorphic factorization of BRDF-based lighting computation, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 18: Tom Malzbender , Dan Gelb , Hans Wolters, Polynomial texture maps, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.519-528, August 2001 [doi>10.1145/383259.383320]
• 19: MAX, N. 1988. Horizon Mapping: Shadows for Bump-Mapped Surfaces. The Visual Computer 4, 2 (July), 109--117.
• 20: David K. McAllister , Anselmo Lastra , Wolfgang Heidrich, Efficient rendering of spatial bi-directional reflectance distribution functions, Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, September 01-02, 2002, Saarbrucken, Germany
• 21: Bui Tuong Phong, Illumination for computer generated pictures, Communications of the ACM, v.18 n.6, p.311-317, June 1975 [doi>10.1145/360825.360839]
• 22: Ravi Ramamoorthi , Pat Hanrahan, A signal-processing framework for inverse rendering, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.117-128, August 2001 [doi>10.1145/383259.383271]
• 23: Ravi Ramamoorthi , Pat Hanrahan, An efficient representation for irradiance environment maps, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.497-500, August 2001 [doi>10.1145/383259.383317]
• 24: Ravi Ramamoorthi , Pat Hanrahan, Frequency space environment map rendering, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 25: Peter Shirley , Kenneth Chiu, A low distortion map between disk and square, Journal of Graphics Tools, v.2 n.3, p.45-52, 1997
• 26: Peter-Pike Sloan , Jan Kautz , John Snyder, Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 27: Stephen H. Westin , James R. Arvo , Kenneth E. Torrance, Predicting reflectance functions from complex surfaces, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.255-264, July 1992

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.3 Picture/Image Generation
          Subjects: Bitmap and framebuffer operations

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

Keywords:
orthogonal projection, reflectance & shading models, shading, spherical harmonics