“Polynomial texture maps” by Malzbender, Gelb and Wolters

  • ©Tom Malzbender, Dan Gelb, and Hans Wolters




    Polynomial texture maps



    In this paper we present a new form of texture mapping that produces increased photorealism. Coefficients of a biquadratic polynomial are stored per texel, and used to reconstruct the surface color under varying lighting conditions. Like bump mapping, this allows the perception of surface deformations. However, our method is image based, and photographs of a surface under varying lighting conditions can be used to construct these maps. Unlike bump maps, these Polynomial Texture Maps (PTMs) also capture variations due to surface self-shadowing and interreflections, which enhance realism. Surface colors can be efficiently reconstructed from polynomial coefficients and light directions with minimal fixed-point hardware. We have also found PTMs useful for producing a number of other effects such as anisotropic and Fresnel shading models and variable depth of focus. Lastly, we present several reflectance function transformations that act as contrast enhancement operators. We have found these particularly useful in the study of ancient archeological clay and stone writings.


    1. Banks, D.C., “Illumination in Diverse Codimensions”, Computer Graphics (SIGGRAPH 94 Proceedings), July 1994, pp. 327-334.
    2. Blinn, J.F., “Computer Display of Curved Surfaces”, Ph.D. Thesis, University of Utah, 1978.
    3. Blythe, D., McReynolds, T., “Lighting and Shading Techniques for Interactive Applications”, Course Notes (Siggraph 99 Course 1 2), August, 1999, p. 101.
    4. Born, Max, Wolf, Emil, “Principles of Optics”, 6 th edition, Appendix VII, Cambridge University Press, Cambridge, 1980.
    5. Cabral, B., Max, N., Springmeyer, R., “Bidirectional Reflection Functions from Surface Bump Maps”, Computer Graphics (SIGGRAPH 87 Proceedings), July 1987, pp. 273-281.
    6. Dana, K., Van Ginneken, B., Nayar, S., Koenderink, J., “Reflectance and Texture of Real-World Surfaces”, ACM Transactions on Graphics, Vol. 18, No. 1, January 1999, pp. 1-34.
    7. Debevec, P., Hawkins,T., Tchou, C., Duiker, H., Sarokin, W., Sagar, M., “Acquiring the Reflectance Field of a Human Face”, Computer Graphics (SIGGRAPH 2000 Proceedings), July 2000, pp. 145-156.
    8. Epstein, R., Hallinan, P., Yuille, A., “5 +/- 2 Eigenimages Suffice: An Empircal Investigation of Low- Dimensional Lighting Models, IEEE Workshop on Physics-Based Vision: 108-116, 1995.
    9. Epstein, R., Yuille, A.L., Belhumeur, P.N., “Learning Object Representations from Lighting Variations”, Object Representation in Computer Vision II Workshop, ECCV96, April 1996, pp.179-199.
    10. Georghiades, A., Belhumeur, P., Kriegman, “Illumination-Based Image Synthesis: Creating Novel Images of Human Faces Under Differing Pose and Lighting”, IEEE Workshop on Multi-View Modeling and Analysis of Visual Scenes, 1999, pp. 47-54.
    11. Golub, G., van Loan, C., “Matrix Computations”, Johns Hopkins University Press, Baltimore, 1989.
    12. Gortler, S., Grzeszczuk, R., Szeliski, R., Cohen, M., “The Lumigraph”, Computer Graphics (SIGGRAPH 96 Proceedings), August 1996, pp. 43-54.
    13. Hall, R. Illumination and Color in Computer Generated Imagery, Springer-Verlag New York Inc., New York, 1989, pp. 193-197.
    14. He, X., Torrance, K., Sillion, F., Greenberg, D., “A Comprehensive Physical Model for Light Reflection”, Computer Graphics (SIGGRAPH 9 1 Proceedings), July 1991, pp.175-186.
    15. Heidrich, W., Seidel, H., “Realistic, Hardwareaccelerated Shading and Lighting”, Computer Graphics (SIGGRAPH 99 Proceedings), August 1999, pp.171-178.
    16. Kilgard. M.,”A Practical and Robust Bump-mapping Technique for Today’s GPUs”, Game Developers Conference (GDC) 2000: Advanced OpenGL, also available at nvidia.com.
    17. Lafortune, E., Foo, S.-C., Torrance, K., Greenberg, D., “Non-Linear Approximation of Reflectance Functions”, Computer Graphics (SIGGRAPH 97 Proceedings), August 1997, pp. 117-126.
    18. Levoy, M., Hanrahan, P., “Light Field Rendering”, Computer Graphics (SIGGRAPH 96 Proceedings), August 1996, pp. 31-42.
    19. Malzbender, T., Gelb, D., Wolters, H., Zuckerman, B., “Enhancement of Shape Perception by Surface Reflectance Transformation”, Hewlett-Packard Technical Report HPL-2000-38, March 2000.
    20. Marschner, S., Westin, S., Lafortune, E., Torrance, K., Greenberg, D., “Image-Based BRDF Measurement Including Human Skin”, Rendering Techniques 99: Proceedings of the 1 0 th Eurographics Workshop on Rendering, June 1999, ISBN 3-211-83382-X, pp. 131-144.
    21. Motta, G., “Compression of Polynomial Texture Maps”, Hewlett-Packard Laboratories Technical Report, HPL- 2000-143, October 30, 2000.
    22. Nicodemus, F.E., Richmond, J.C., Hsai, J.J., “Geometrical Considerations and Nomenclature for Reflectance”, U.S. Dept. of Commerce, National Bureau of Standards, October 1977.
    23. Nimeroff, J., Simoncelli, E., Dorsey, J., “Efficient Re-rendering of Naturally Illuminated Environments”, Eurographics Rendering Workshop Proceedings 1994, pp. 359- 374.
    24. Nishino, K., Sato, Y., Katsushi, I., “Eigen-texture Method – Appearance Compression based on 3D Model”, IEEE Computer Vision and Pattern Recognition, June 23-25 1999, Vol. 1, pp.618-624.
    25. Phong, B.-T., “Illumination for Computer Generated Images”, Communications of the ACM 18, 6, June 1975, pp. 311- 317.
    26. , Ramamoorthi, R. and Hanrahan, P., “An Efficient Representation for Environment Irradiance Maps”, Computer Graphics (SIGGRAPH 0 1 Proceedings), August 2001.
    27. Rushmeier, H., Taubin, G., Gueziec, A., “Applying Shape from Lighting Variation to Bump Map Capture”, Eurographics Rendering Workshop Proceedings 1997, pp. 35-44, 1997.
    28. Schilling, A., Knittel, G., Strasser, W., “Texram: A Smart Memory for Texturing”, IEEE Computer Graphics and Applications, Vol. 16, No. 3, May 1996, pp. 32-41.
    29. Schilling, A., “Towards Real-Time Photorealistic Rendering: Challenges and Solutions”, Proceedings of the 1 997 Siggraph/Eurographics Workshop on Graphics Hardware, Aug. 3-4, 1997, pp.7-15.
    30. Sillion, F., Arvo, J., Westin, S., Greenberg, D., “A Global Illumination Solution for General Reflectance Distributions”, Computer Graphics (SIGGRAPH 9 1 Proceedings), July 1991, pp.187-196.
    31. Stalling, D., Zockler, M., Hege, H.-C., “Fast Display of Illuminated Field Lines”, IEEE Transactions on Visualization and Computer Graphics, 3(2):118-128, 1997.
    32. Stam, J., “Diffraction Shaders”, Computer Graphics (SIGGRAPH 99 Proceedings), August 1999, pp.101-110.
    33. Teo, P., Simoncelli, E., Heeger, D., “Efficient Linear Rerendering for Interactive Lighting Design”, Stanford Computer Science Department Technical Report STAN-CS-TN-97-60. October 1997.
    34. Watson, G.A., “Approximation Theory and Numerical Methods”, A.J.Wiley & Sons, Chichester, 1980.
    35. Wood, D., Azuma, D., Aldlinger, K., Curless, B., Duchamp, T., Salesin, D., Stuetzle, W., “Surface Light Fields for 3D Photography”, Computer Graphics (Siggraph 2000 Proceedings), July 2000, pp. 287-296
    36. Wong, T., Heng, P, Or, S, Ng, W., “Image-based Rendering with Controllable Illumination”, Rendering Techniques 97: Proceedings of the 8 th Eurographics Workshop on Rendering, June 16-18, 1997, ISBN 3-211-83001-4, pp. 13-22.

ACM Digital Library Publication: