“Frequency Analysis and Sheared Filtering for Shadow Light Fields of Complex Occluders” by Egan, Hecht, Durand and Ramamoorthi

  • ©Kevin Egan, Florian Hecht, Frédo Durand, and Ravi Ramamoorthi




    Frequency Analysis and Sheared Filtering for Shadow Light Fields of Complex Occluders



    Monte Carlo ray tracing of soft shadows produced by area lighting and intricate geometries, such as the shadows through plant leaves or arrays of blockers, is a critical challenge. The final image often has relatively smooth shadow patterns, since it integrates over the light source. However, Monte Carlo rendering exhibits considerable noise even at high sample counts because of the large variance of the integrand due to the intricate shadow function. This article develops an efficient diffuse soft shadow technique for mid to far occluders that relies on a new 4D cache and sheared reconstruction filter. For this, we first derive a frequency analysis of shadows for planar area lights and complex occluders. Our analysis subsumes convolution soft shadows for parallel planes as a special case. It allows us to derive 4D sheared filters that enable lower sampling rates for soft shadows. While previous sheared-reconstruction techniques were able primarily to index samples according to screen position, we need to perform reconstruction at surface receiver points that integrate over vastly different shapes in the reconstruction domain. This is why we develop a new light-field-like 4D data structure to store shadowing values and depth information. Any ray tracing system that shoots shadow rays can easily incorporate our method to greatly reduce sampling rates for diffuse soft shadows.


    1. Agrawala, M., Ramamoorthi, R., Heirich, A., and Moll, L. 2000. Efficient image-based methods for rendering soft shadows. In Proceedings of the SIGGRAPH Conference. 375–384.
    2. Annen, T., Dong, Z., Mertens, T., Bekaert, P., Seidel, H.-P., and Kautz, J. 2008. Real-Time, all-frequency shadows in dynamic scenes. ACM Trans. Graph. 27, 3, 1–8.
    3. Arikan, O., Forsyth, D. A., and O’Brien, J. F. 2005. Fast and detailed approximate global illumination by irradiance decomposition. In Proceedings of the SIGGRAPH Conference. 1108–1114.
    4. Assarsson, U. and Akenine-Möller, T. 2003. A geometry-based soft shadow volume algorithm using graphics hardware. ACM Trans. Graph. 22, 3, 511–520.
    5. Bala, K., Dorsey, J., and Teller, S. 1999. Radiance interpolants for accelerated bounded-error ray tracing. ACM Trans. Graph. 18, 3, 213–256.
    6. Ben-Artzi, A., Ramamoorthi, R., and Agrawala, M. 2006. Efficient shadows from sampled environment maps. J. Graph. Tools 11, 1, 13–36.
    7. Bracewell, R., Chang, K., Jha, A., and Wang, Y. 1993. Affine theorem for two-dimensional fourier transform. Electron. Lett. 29, 304.
    8. Chai, J., Tong, X., Chan, S., and Shum, H. 2000. Plenoptic sampling. In Proceedings of the SIGGRAPH Conference, K. Akeley, Ed. ACM Press, 307–318.
    9. Chen, W.-C., Bouguet, J.-Y., Chu, M. H., and Grzeszczuk, R. 2002. Light field mapping: Efficient representation and hardware rendering of surface light fields. ACM Trans. Graph. 21, 3, 447–456.
    10. Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed ray tracing. Comput. Graph. 18. ACM, 137–145.
    11. Durand, F. 1999. 3D Visibility: Analytical study and applications. Ph.D. thesis, Université Joseph Fourier, Grenoble I.
    12. Durand, F., Holzschuch, N., Soler, C., Chan, E., and Sillion, F. X. 2005. A frequency analysis of light transport. ACM Trans. Graph. 24, 3, 1115–1126.
    13. Egan, K., Tseng, Y.-T., Holzschuch, N., Durand, F., and Ramamoorthi, R. 2009. Frequency analysis and sheared reconstruction for rendering motion blur. ACM Trans. Graph. 28, 3, 93:1–93:13.
    14. Gortler, S., Grzeszczuk, R., Szeliski, R., and Cohen, M. 1996. The lumigraph. In Proceedings of the SIGGRAPH Conference. 43–54.
    15. Hachisuka, T., Jarosz, W., Weistroffer, R., Dale, K., Humphreys, G., Zwicker, M., and Jensen, H. 2008. Multidimensional adaptive sampling and reconstruction for ray tracing. ACM Trans. Graph. 27, 3, 33:1–33:10.
    16. Hart, D., Dutré, P., and Greenberg, D. P. 1999. Direct illumination with lazy visibility evaluation. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 147–154.
    17. Hasenfratz, J.-M., Lapierre, M., Holzschuch, N., and Sillion, F. 2003. A survey of real-time soft shadows algorithms. Comput. Graph. Forum 22, 4, 753–774.
    18. Isaksen, A., McMillan, L., and Gortler, S. J. 2000. Dynamically reparameterized light fields. In Proceedings of the SIGGRAPH Conference, K. Akeley, Ed. ACM Press, 297–306.
    19. Jensen, H. W. and Christensen, N. J. 1995. Efficiently rendering shadows using the photon map. In Proceedings of the Compugraphics Conference. 285–291.
    20. Johnson, G. S., Hunt, W. A., Hux, A., Mark, W. R., Burns, C. A., and Junkins, S. 2009. Soft irregular shadow mapping: Fast, high-quality, and robust soft shadows. In Proceedings of the Symposium on Interactive 3D Graphics and Games (I3D’09). 57–66.
    21. Lacewell, D., Burley, B., Boulos, S., and Shirley, P. 2008. Raytracing prefiltered occlusion for aggregate geometry. In Proceedings of the IEEE Symposium on Interactive Raytracing.
    22. Laine, S., Aila, T., Assarsson, U., Lehtinen, J., and Akenine-Möller, T. 2005. Soft shadow volumes for ray tracing. ACM Trans. Graph. 24, 3, 1156–1165.
    23. Lanman, D., Raskar, R., Agrawal, A., and Taubin, G. 2008. Shield fields: Modeling and capturing 3D occluders. ACM Trans. Graph. 27, 5.
    24. Levoy, M. and Hanrahan, P. 1996. Light field rendering. In Proceedings of the SIGGRAPH Conference. 31–42.
    25. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2003. All-Frequency shadows using non-linear wavelet lighting approximation. ACM Trans. Graph. 22, 3, 376–381.
    26. Overbeck, R., Ramamoorthi, R., and Mark, W. R. 2007. A real-time beam tracer with application to exact soft shadows. In Proceedings of the EuroGraphics Symposium on Rendering.
    27. Overbeck, R. S., Donner, C., and Ramamoorthi, R. 2009. Adaptive wavelet rendering. ACM Trans. Graph. 28, 5, 1–12.
    28. Ramamoorthi, R., Koudelka, M., and Belhumeur, P. 2005. A fourier theory for cast shadows. IEEE Trans. Patt. Anal. Mach. Intell. 27, 2, 288–295.
    29. Ramamoorthi, R., Mahajan, D., and Belhumeur, P. 2007. A first-order analysis of lighting, shading, and shadows. ACM Trans. Graph. 26, 1, 2:1–2:21.
    30. Robison, A. and Shirley, P. 2009. Image space gathering. In Proceedings of the Conference on High Performance Graphics (HPG’09). ACM, New York, 91–98.
    31. Shinya, M. 1993. Spatial anti-aliasing for animation sequences with spatio-temporal filtering. In Proceedings of the SIGGRAPH Conference. 289–296.
    32. Sintorn, E., Eisemann, E., and Assarsson, U. 2008. Sample-Based visibility for soft shadows using alias-free shadow maps. Comput. Graph. Forum 27, 4, 1285–1292.
    33. Soler, C. and Sillion, F. 1998. Fast calculation of soft shadow textures using convolution. In Proceedings of the SIGGRAPH Conference, M. Cohen, Ed. ACM Press, 321–332.
    34. Soler, C., Subr, K., Durand, F., Holzschuch, N., and Sillion, F. 2009. Fourier depth of field. ACM Trans. Graph. 28, 2, 18:1–18:18.
    35. Stewart, J., Yu, J., Gortler, S. J., and McMillan, L. 2003. A new reconstruction filter for undersampled light fields. In Proceedings of the 14th Eurographics Workshop on Rendering (EGRW’03). 150–156.
    36. Sun, B. and Ramamoorthi, R. 2009. Affine double and triple product wavelet integrals for rendering. ACM Trans. Graph. 28, 2, 1–17.
    37. van der Linden, J. 2003. Multiple light field rendering. In Proceedings of GRAPHITE. 197–ff.
    38. Walter, B., Arbree, A., Bala, K., and Greenberg, D. P. 2006. Multidimensional lightcuts. ACM Trans. Graph. 25, 3, 1081–1088.
    39. Yang, B., Feng, J., Guennebaud, G., and Liu, X. 2009. Packet-Based hierarchal soft shadow mapping. Comput. Graph. Forum 28, 4, 1121–1130.
    40. Zhou, K., Hu, Y., Lin, S., Guo, B., and Shum, H.-Y. 2005. Precomputed shadow fields for dynamic scenes. In Proceedings of the SIGGRAPH Conference. 1196–1201.
    41. Zwicker, M., Yea, S., Vetro, A., Forlines, C., Matusik, W., and Pfister, H. 2007. Display pre-filtering for multi-view video compression. In Proceedings of the 15th International Conference on Multimedia (MULTIMEDIA’07). 1046–1053.

ACM Digital Library Publication:

Overview Page: