“Frequency analysis and sheared reconstruction for rendering motion blur” by Egan, Tseng, Holzschuch, Durand and Ramamoorthi

Motion blur is crucial for high-quality rendering, but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes can be approximated by a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that is aligned to the first-order direction of motion and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.

1. Akenine-Möller, T., Munkberg, J., and Hasselgren, J. 2007. Stochastic Rasterization using Time-Continuous Triangles. In Graphics Hardware, 7–16. Google ScholarDigital Library
2. Arikan, O., 2009. Pixie – Open Source RenderMan. http://www.renderpixie.com.Google Scholar
3. Cammarano, M., and Jensen, H. W. 2002. Time Dependent Photon Mapping. In EG Symposium on Rendering, 135–144. Google ScholarDigital Library
4. Catmull, E. 1984. An Analytic Visible Surface Algorithm for Independent Pixel Processing. In Computer Graphics (Proceedings of SIGGRAPH 84), ACM, vol. 18, 109–115. Google ScholarDigital Library
5. Chai, J., Tong, X., Chan, S., and Shum, H. 2000. Plenoptic Sampling. In Proceedings of SIGGRAPH 2000, ACM, 307–318. Google ScholarDigital Library
6. Christmas, W. J. 1998. Spatial Filtering Requirements for Gradient-Based Optical Flow Measurement. In British Machine Vision Conference, 185–194.Google Scholar
7. Cook, R. L., Porter, T., and Carpenter, L. 1984. Distributed Ray Tracing. In Computer Graphics (Proceedings of SIGGRAPH 84), ACM, vol. 18, 137–145. Google ScholarDigital Library
8. Cook, R. L., Carpenter, L., and Catmull, E. 1987. The Reyes Image Rendering Architecture. In Computer Graphics (Proceedings of SIGGRAPH 87), ACM, vol. 21, 95–102. Google ScholarDigital Library
9. Durand, F., Holzschuch, N., Soler, C., Chan, E., and Sillion, F. X. 2005. A Frequency Analysis of Light Transport. ACM Transactions on Graphics (SIGGRAPH) 24, 3, 1115–1126. Google ScholarDigital Library
10. 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 Transactions on Graphics (SIGGRAPH) 27, 3, 33:1–33:10. Google ScholarDigital Library
11. Haeberli, P., and Akeley, K. 1990. The Accumulation Buffer: Hardware Support for High-Quality Rendering. In Computer Graphics (Proceedings of SIGGRAPH 90), ACM, vol. 24, 309–318. Google ScholarDigital Library
12. Halton, J. H. 1960. On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals. Numerische Mathematik 2, 1, 84–90.Google ScholarDigital Library
13. Isaksen, A., McMillan, L., and Gortler, S. J. 2000. Dynamically Reparameterized Light Fields. In Proceedings of SIGGRAPH 2000, ACM, 297–306. Google ScholarDigital Library
14. Korein, J., and Badler, N. 1983. Temporal Anti-Aliasing in Computer Generated Animation. In Computer Graphics (Proceedings of SIGGRAPH 83), ACM, vol. 17, 377–388. Google ScholarDigital Library
15. Levin, A., Sand, P., Cho, T. S., Durand, F., and Freeman, W. T. 2008. Motion-Invariant Photography. ACM Transactions on Graphics (SIGGRAPH) 27, 3, 71:1–71:9. Google ScholarDigital Library
16. Loviscach, J. 2005. Motion Blur for Textures by Means of Anisotropic Filtering. In EG Symposium on Rendering, 105–110. Google ScholarDigital Library
17. Mahajan, D., Shlizerman, I. K., Ramamoorthi, R., and Belhumeur, P. 2007. A Theory of Locally Low Dimensional Light Transport. ACM Transactions on Graphics (SIGGRAPH) 27, 3, 62:1–62:10. Google ScholarDigital Library
18. Max, N. L., and Lerner, D. M. 1985. A Two-and-a-Half-D Motion-Blur Algorithm. In Computer Graphics (Proceedings of SIGGRAPH 85), ACM, vol. 19, 85–93. Google ScholarDigital Library
19. Mitchell, D. 1991. Spectrally Optimal Sampling for Distribution Ray Tracing. In Computer Graphics (Proceedings of SIGGRAPH 91), ACM, vol. 25, 157–164. Google ScholarDigital Library
20. Pharr, M., and Humphreys, G. 2004. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann. Google ScholarDigital Library
21. Potmesil, M., and Chakravarty, I. 1983. Modeling Motion Blur in Computer-Generated Images. In Computer Graphics (Proceedings of SIGGRAPH 83), ACM, vol. 17, 389–399. Google ScholarDigital Library
22. Ramamoorthi, R., Koudelka, M., and Belhumeur, P. 2004. A Fourier Theory for Cast Shadows. In European Conference on Computer Vision 2004, I-146–I-162.Google Scholar
23. Ramamoorthi, R., Mahajan, D., and Belhumeur, P. 2007. A First-Order Analysis of Lighting, Shading, and Shadows. ACM Transactions on Graphics 26, 1, 2:1–2:21. Google ScholarDigital Library
24. Soler, C., and Sillion, F. 1998. Fast Calculation of Soft Shadow Textures Using Convolution. In Proceedings of SIGGRAPH 98, ACM, 321–332. Google ScholarDigital Library
25. Soler, C., Subr, K., Durand, F., Holzschuch, N., and Sillion, F. 2009. Fourier Depth of Field. ACM Transactions on Graphics 28, 2, 18:1–18:18. Google ScholarDigital Library
26. Sung, K., Pearce, A., and Wang, C. 2002. Spatial-Temporal Antialiasing. IEEE Transactions on Visualization and Computer Graphics 8, 2, 144–153. Google ScholarDigital Library
27. Walter, B., Arbree, A., Bala, K., and Greenberg, D. P. 2006. Multidimensional Lightcuts. ACM Transactions on Graphics (SIGGRAPH) 25, 3, 1081–1088. Google ScholarDigital Library