“A frequency analysis of light transport” by Durand, Holzschuch, Soler, Chan and Sillion

We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatment of both space and angle.We show that occlusion, a multiplication in the primal, amounts in the Fourier domain to a convolution by the spectrum of the blocker. Propagation corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As shown by previous work, reflection is a convolution in the primal and therefore a multiplication in the Fourier domain. Our work shows how the spatial components of lighting are affected by this angular convolution.Our framework predicts the characteristics of interactions such as caustics and the disappearance of the shadows of small features. Predictions on the frequency content can then be used to control sampling rates for rendering. Other potential applications include precomputed radiance transfer and inverse rendering.

1. Annen, T., Kautz, J., Durand, F., and Seidel, H.-P. 2004. Spherical harmonic gradients for mid-range illumination. In Rendering Techniques 2004 (Proc. EG Symposium on Rendering 2004). Google ScholarDigital Library
2. Arvo, J. 1994. The irradiance Jacobian for partially occluded polyhedral sources. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 343–350. Google ScholarDigital Library
3. Basri, R., and Jacobs, D. 2003. Lambertian reflectance and linear subspaces. IEEE Trans. Pattern Anal. Mach. Intell. 25, 2. Google ScholarDigital Library
4. Becker, B. G., and Max, N. L. 1993. Smooth transitions between bump rendering algorithms. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 183–190. Google ScholarDigital Library
5. Bolin, M. R., and Meyer, G. W. 1995. A frequency based ray tracer. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 409–418. Google ScholarDigital Library
6. Bolin, M. R., and Meyer, G. W. 1998. A perceptually based adaptive sampling algorithm. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 299–309. Google ScholarDigital Library
7. Camahort, E., Lerios, A., and Fussell, D. 1998. Uniformly sampled light fields. In Rendering Techniques ’98 (Proc. of EG Workshop on Rendering ’98), Eurographics, 117–130.Google Scholar
8. Chai, J.-X., Chan, S.-C., Shum, H.-Y. and Tong, X. 2000. Plenoptic sampling. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 307–318. Google ScholarDigital Library
9. Chen, M., and Arvo, J. 2000. Theory and application of specular path perturbation. ACM Trans. Graph. 19, 4, 246–278. Google ScholarDigital Library
10. Do Carmo, M. 1976. Differential Geometry of Curves and Surfaces. Prentice Hall.Google Scholar
11. Ferwerda, J. A., Shirley, P., Pattanaik, S. N., and Greenberg, D. P. 1997. A model of visual masking for computer graphics. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 143–152. Google ScholarDigital Library
12. Frolova, D., Simakov, D., and Basri, R. 2004. Accuracy of spherical harmonic approximations for images of Lambertian objects under far and near lighting. In ECCV 2004, European Conference on Computer Vision, 574–587.Google Scholar
13. Goodman, J. W. 1996. Introduction To Fourier Optics. McGraw-Hill.Google Scholar
14. Gortler, S. J., Schröder, P., Cohen, M. F., and Hanrahan, P. 1993. Wavelet radiosity. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 221–230. Google ScholarDigital Library
15. Halle, M. 1994. Holographic stereograms as discrete imaging systems. In SPIE Proc. Vol. 2176: Practical Holography VIII. S. Benton, Ed., SPIE, 73–84.Google Scholar
16. Heckbert, P. 1989. Fundamentals of Texture Mapping and Image Warping. Master’s thesis, University of California at Berkeley, Computer Science Division.Google Scholar
17. Holzschuch, N., and Sillion, F. X. 1998. An exhaustive error-bounding algorithm for hierarchical radiosity. Computer Graphics Forum 17, 4.Google ScholarCross Ref
18. Igehy, H. 1999. Tracing ray differentials. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH. Google ScholarDigital Library
19. Isaksen, A., Mcmillan, L., and Gortler, S. J. 2000. Dynamically reparameterized light fields. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 297–306. Google ScholarDigital Library
20. Keller, A. 2001. Hierarchical monte carlo image synthesis. Mathematics and Computers in Simulation 55, 1–3 (Feb.), 79–92. Google ScholarDigital Library
21. Lawrence, J., Rusinkiewicz, S., and Ramamoorthi, R. 2004. Efficient BRDF importance sampling using a factored representation. ACM Transactions on Graphics (Proc. SIGGRAPH 2004) 23, 3 (Aug.), 496–505. Google ScholarDigital Library
22. Lensch, H. P. A., Kautz, J., Goesele, M., Heidrich, W., and Seidel, H.-P. 2001. Image-based reconstruction of spatially varying materials. In Rendering Techniques ’01 (Proc. EG Workshop on Rendering 2001), Eurographics, 104–115. Google ScholarDigital Library
23. Malik, J., and Rosenholtz, R. 1997. Computing local surface orientation and shape from texture for curved surfaces. International Journal of Computer Vision 23, 2, 149–168. Google ScholarDigital Library
24. Mccool, M. D. 1999. Anisotropic diffusion for monte carlo noise reduction. ACM Transactions on Graphics 18, 2, 171–194. Google ScholarDigital Library
25. Myszkowski, K. 1998. The visible differences predictor: applications to global illumination problems. In Rendering Techniques ’98 (Proc. EG Workshop on Rendering ’98), Eurographics.Google ScholarCross Ref
26. Ostromoukhov, V., Donohue, C., and Jodoin, P.-M. 2004. Fast hierarchical importance sampling with blue noise properties. ACM Transactions on Graphics (Proc. SIGGRAPH 2004) 23, 3 (Aug.), 488–495. Google ScholarDigital Library
27. Pentland, A. P. 1987. A new sense for depth of field. IEEE Transactions on Pattern Analysis and Machine Intelligence 9, 4 (July). Google ScholarDigital Library
28. Pharr, M., and Humphreys, G. 2004. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann. Google ScholarDigital Library
29. Ramamoorthi, R., and Hanrahan, P. 2001. An efficient representation for irradiance environment maps. In Computer Graphics Proceedings, Annual Conference Series. ACM SIGGRAPH. Google ScholarDigital Library
30. Ramamoorthi. R., and Hanrahan, P. 2001. A signal-processing framework for inverse rendering. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH. Google ScholarDigital Library
31. Ramamoorthi, R., and Hanrahan, P. 2002. Frequency space environment map rendering. ACM Transactions on Graphics (Proc. SIGGRAPH 2002) 21, 3, 517–526. Google ScholarDigital Library
32. Ramamoorthi, R., and Hanrahan, P. 2004. A signal-processing framework for reflection. ACM Transactions on Graphics 23, 4. Google ScholarDigital Library
33. Ramamoorthi, R. Koudelka, M., and Belhumeur, P. 2004. A Fourier theory for cast shadows. In ECCV 2004, European Conference on Computer Vision, 146–162.Google Scholar
34. Shinya, M., Takahashi, T., and Naito, S. 1987. Principles and applications of pencil tracing. Computer Graphics (Proc. SIGGRAPH ’87) 21, 4, 45–54. Google ScholarDigital Library
35. Sillion, F., and Drettakis, G. 1995. Feature-based control of visibility error: A multi-resolution clustering algorithm for global illumination. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 145–152. Google ScholarDigital Library
36. Sloan, P.-P., Kautz, J., and Snyder, J. 2002. Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Trans. on Graphics 21, 3, 527–536. Google ScholarDigital Library
37. Soler, C., and Sillion, F. X. 1998. Fast calculation of soft shadow textures using convolution. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 321–332. Google ScholarDigital Library
38. Stewart, J., Yu, J., Gortler, S. J., and Mcmillan, L. 2003. A new reconstruction filter for undersampled light fields. In Proc. EG Symposium on Rendering 2003, Eurographics, 150–156. Google ScholarDigital Library
39. Tomasi, C., and Manduchi, R. 1998. Bilateral filtering for gray and color images. In Proc. IEEE International Conference on Computer Vision, IEEE, 836–846. Google ScholarDigital Library
40. Ward, G. J., and Heckbert, P. 1992. Irradiance gradients. In Proc. of EG Workshop on Rendering ’92, Eurographics, 85–98.Google Scholar
41. Ward, G. J., Rubinstein, F. M., and Clear, R. D. 1988. A ray tracing solution for diffuse interreflection. Computer Graphics (Proc. SIGGRAPH ’88) 22, 4 (Aug.), 85–92. Google ScholarDigital Library
42. Wood, D. N., Azuma, D. I., Aldinger, K., Curless, B., Duchamp, T., Salesin, D. H., and Stuetzle, W. 2000. Surface light fields for 3D photography. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 287–296. Google ScholarDigital Library