“Multidimensional adaptive sampling and reconstruction for ray tracing” by Hachisuka, Jarosz, Weistroffer, Dale, Humphreys, et al. …

  • ©Toshiya Hachisuka, Wojciech Jarosz, Richard Peter Weistroffer, Kevin Dale, Greg Humphreys, Matthias Zwicker, and Henrik Wann Jensen




    Multidimensional adaptive sampling and reconstruction for ray tracing



    We present a new adaptive sampling strategy for ray tracing. Our technique is specifically designed to handle multidimensional sample domains, and it is well suited for efficiently generating images with effects such as soft shadows, motion blur, and depth of field. These effects are problematic for existing image based adaptive sampling techniques as they operate on pixels, which are possibly noisy results of a Monte Carlo ray tracing process. Our sampling technique operates on samples in the multidimensional space given by the rendering equation and as a consequence the value of each sample is noise-free. Our algorithm consists of two passes. In the first pass we adaptively generate samples in the multidimensional space, focusing on regions where the local contrast between samples is high. In the second pass we reconstruct the image by integrating the multidimensional function along all but the image dimensions. We perform a high quality anisotropic reconstruction by determining the extent of each sample in the multidimensional space using a structure tensor. We demonstrate our method on scenes with a 3 to 5 dimensional space, including soft shadows, motion blur, and depth of field. The results show that our method uses fewer samples than Mittchell’s adaptive sampling technique while producing images with less noise.


    1. Amidror, I. 2002. Scattered data interpolation methods for electronic imaging systems: a survey. Journal of Electronic Imaging 11, 2 (April), 157–176.Google ScholarCross Ref
    2. Berntsen, J., Espelid, T. O., and Genz, A. 1991. An adaptive algorithm for the approximate calculation of multiple integrals. ACM Transactions on Mathematical Software 17, 4, 437–451. Google ScholarDigital Library
    3. Bolin, M. R., and Meyer, G. W. 1998. A perceptually based adaptive sampling algorithm. Computer Graphics 32, Annual Conference Series, 299–309. Google ScholarDigital Library
    4. Chai, J.-X., Chan, S.-C., Shum, H.-Y., and Tong, X. 2000. Plenoptic sampling. In SIGGRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 307–318. Google ScholarDigital Library
    5. Clarberg, P., Jarosz, W., Akenine-Möller, T., and Jensen, H. W. 2005. Wavelet importance sampling: Efficiently evaluating products of complex functions. ACM Trans. Graph. 24, 3, 1166–1175. Google ScholarDigital Library
    6. Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed ray tracing. In Computer Graphics (SIGGRAPH ’84 Proceedings), vol. 18, 137–45. Google ScholarDigital Library
    7. Durand, F., Holzschuch, N., Soler, C., Chan, E., and Sillion, F. X. 2005. A frequency analysis of light transport. 1115–1126. Google ScholarDigital Library
    8. Dutré, P., Bala, K., Bekaert, P., and Shirley, P. 2006. Advanced Global Illumination. AK Peters Ltd. Google ScholarDigital Library
    9. Glassner, A. 1995. Principles of Digital Image Synthesis. Morgan Kaufmann. Google ScholarDigital Library
    10. Indyk, P., and Motwani, R. 1998. Approximate nearest neighbors: towards removing the curse of dimensionality. In Proceedings of the Symposium on Theory of Computation (STOC), 604–613. Google ScholarDigital Library
    11. Jensen, H. W. 2001. Realistic Image Synthesis Using Photon Mapping. A. K. Peters, Ltd., Natick, MA. Google ScholarDigital Library
    12. Kajiya, J. T. 1986. The rendering equation. In Computer Graphics (SIGGRAPH ’86 Proceedings), D. C. Evans and R. J. Athay, Eds., vol. 20, 143–150. Google ScholarDigital Library
    13. Kelemen, C., and Szirmay-Kalos, L. 2001. Simple and robust mutation strategy for metropolis light transport algorithm. Tech. Rep. TR-186-2-01-18, Institute of Computer Graphics and Algorithms, Vienna University of Technology, Favoritenstrasse 9-11/186, A-1040 Vienna, Austria, July. human contact: [email protected]Google Scholar
    14. Kirk, D., and Arvo, J. 1991. Unbiased sampling techniques for image synthesis. In Proceedings of SIGGRAPH ’91, ACM Press, New York, NY, USA, 153–156. Google ScholarDigital Library
    15. Landau, H., and Pollak, H. 1962. Prolate spheroidal functions, Fourier analysis and uncertainty, III. the dimension of the space of essentially time- and band-limited signals. Systems Technical Journal 41, 4 (July), 1295–1336.Google ScholarCross Ref
    16. Lawrence, J., Rusinkiewicz, S., and Ramamoorthi, R. 2004. Efficient brdf importance sampling using a factored representation. ACM Trans. Graph. 23, 3, 496–505. Google ScholarDigital Library
    17. Leeson, W. 2003. Rendering with adaptive integration. In Graphics programming methods, Charles River Media, Inc., Rockland, MA, USA, 271–278. Google ScholarDigital Library
    18. Mitchell, D. P. 1987. Generating antialiased images at low sampling densities. In Computer Graphics (Proceedings of SIGGRAPH 87), vol. 21, 65–72. Google ScholarDigital Library
    19. Mitchell, D., 1990. The antialiasing problem in ray tracing, Aug. SIGGRAPH 1990 Course Notes.Google Scholar
    20. Mitchell, D. P. 1991. Spectrally optimal sampling for distributed ray tracing. In Computer Graphics (Proceedings of SIGGRAPH 91), vol. 25, 157–164. Google ScholarDigital Library
    21. Pharr, M., and Humphreys, G. 2004. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann. Google ScholarDigital Library
    22. Press, W. H., and Farrar, G. R. 1990. Recursive stratified sampling for multidimensional monte carlo integration. Comput. Phys. 4, 2, 190–195. Google ScholarDigital Library
    23. Ramamoorthi, R., Mahajan, D., and Belhumeur, P. 2007. A first-order analysis of lighting, shading, and shadows. ACM Trans. Graph. 26, 1, 2. Google ScholarDigital Library
    24. Rigau, J., Feixas, M., and Sbert, M. 2003. Refinement criteria based on f-divergences. In Rendering Techniques, 260–269. Google ScholarDigital Library
    25. San Jose Estepar, R. 2005. Local Structure Tensor for Multidimensional Signal Processing. Applications to Medical Image Analysis. PhD thesis, University of Valladolid, Spain.Google Scholar
    26. Veach, E., and Guibas, L. J. 1997. Metropolis light transport. In Computer Graphics (SIGGRAPH Proceedings), 65–76. Google ScholarDigital Library
    27. Walter, B., Arbree, A., Bala, K., and Greenberg, D. P. 2006. Multidimensional lightcuts. In SIGGRAPH ’06: ACM SIGGRAPH 2006 Papers, ACM, New York, NY, USA, 1081–1088. Google ScholarDigital Library
    28. Ward, G. J., and Heckbert, P. 1992. Irradiance Gradients. In Third Eurographics Workshop on Rendering, 85–98.Google Scholar
    29. Ward, G. J., Rubinstein, F. M., and Clear, R. D. 1988. A ray tracing solution for diffuse interreflection. In Computer Graphics (SIGGRAPH ’88 Proceedings), J. Dill, Ed., vol. 22, 85–92. Google ScholarDigital Library
    30. Whitted, T. 1980. An improved illumination model for shaded display. Communications of the ACM 23, 6, 343–349. Google ScholarDigital Library

ACM Digital Library Publication: