“Anisotropic spherical Gaussians”
Conference:
Type(s):
Title:
- Anisotropic spherical Gaussians
Session/Category Title: Fast, Cheap and Out-of-Core Rendering
Presenter(s)/Author(s):
Abstract:
We present a novel anisotropic Spherical Gaussian (ASG) function, built upon the Bingham distribution [Bingham 1974], which is much more effective and efficient in representing anisotropic spherical functions than Spherical Gaussians (SGs). In addition to retaining many desired properties of SGs, ASGs are also rotationally invariant and capable of representing all-frequency signals. To further strengthen the properties of ASGs, we have derived approximate closed-form solutions for their integral, product and convolution operators, whose errors are nearly negligible, as validated by quantitative analysis. Supported by all these operators, ASGs can be adapted in existing SG-based applications to enhance their scalability in handling anisotropic effects. To demonstrate the accuracy and efficiency of ASGs in practice, we have applied ASGs in two important SG-based rendering applications and the experimental results clearly reveal the merits of ASGs.
References:
1. Ashikhmin, M., and Shirley, P. 2000. An anisotropic phong brdf model. Journal of Graphics Tools 5, 2 (Feb.), 25–32.
2. Bingham, C. 1974. An antipodally symmetric distribution on the sphere. Annals of Statistic 2, 6, 1201–1225.
3. Cook, R. L., and Torrance, K. E. 1982. A reflectance model for computer graphics. ACM Trans. Graph. 1, 1, 7–24.
4. de Rousiers, C., Bousseau, A., Subr, K., Holzschuch, N., and Ramamoorthi, R. 2012. Real-time rendering of rough refraction. IEEE Trans. Vis. Comput. Graph. 18, 10, 1591–1602.
5. Dong, Y., Wang, J., Tong, X., Snyder, J., Lan, Y., BenEzra, M., and Guo, B. 2010. Manifold bootstrapping for svbrdf capture. ACM Trans. Graph. 29, 4, 98:1–98:10.
6. Edwards, D., Boulos, S., Johnson, J., Shirley, P., Ashikhmin, M., Stark, M., and Wyman, C. 2006. The halfway vector disk for brdf modeling. ACM Trans. Graph. 25, 1 (Jan.), 1–18.
7. Fisher, R. 1953. Dispersion on a sphere. Proc. Roy. Soc. London Ser. A, 217, 1130, 295–305.
8. Green, P., Kautz, J., Matusik, W., and Durand, F. 2006. View-dependent precomputed light transport using nonlinear gaussian function approximations. In Proceedings of I3D, ACM, 7–14.
9. Green, P., Kautz, J., and Durand, F. 2007. Efficient reflectance and visibility approximations for environment map rendering. Computer Graphics Forum 26, 3, 495–502.
10. Han, C., Sun, B., Ramamoorthi, R., and Grinspun, E. 2007. Frequency domain normal map filtering. ACM Trans. Graph. 26, 3.
11. Irawan, P., and Marschner, S. 2012. Specular reflection from woven cloth. ACM Trans. Graph. 31, 1 (Feb.), 11:1–11:20.
12. Iwasaki, K., Dobashi, Y., and Nishita, T. 2012. Interactive bi-scale editing of highly glossy materials. ACM Trans. Graph. 31, 6 (Nov.), 144:1–144:7.
13. Iwasaki, K., Furuya, W., Dobashi, Y., and Nishita, T. 2012. Real-time rendering of dynamic scenes under all-frequency lighting using integral spherical gaussian. Computer Graphics Forum 31, 727–734.
14. Jakob, W., Arbree, A., Moon, J. T., Bala, K., and Marschner, S. 2010. A radiative transfer framework for rendering materials with anisotropic structure. ACM Trans. Graph. 29, 4 (July), 53:1–53:13.
15. Kajiya, J. T. 1985. Anisotropic reflection models. ACM SIGGRAPH Computer Graphics 19, 3, 15–21.
16. Kajiya, J. T. 1986. The rendering equation. SIGGRAPH Comput. Graph. 20, 4 (Aug.), 143–150.
17. Kent, J. T. 1982. The fisher-bingham distribution on the sphere. J. Royal. Stat. Soc. 44, 1, 71–80.
18. Kurt, M., Szirmay-Kalos, L., and Křivánek, J. 2010. An anisotropic brdf model for fitting and monte carlo rendering. SIGGRAPH Computer Graphics 44, 1 (Feb.), 3:1–3:15.
19. Laurijssen, J., Wang, R., Dutré, P., and Brown, B. 2010. Fast estimation and rendering of indirect highlights. Computer Graphics Forum 29, 4, 1305–1313.
20. Lawrence, J., Ben-Artzi, A., DeCoro, C., Matusik, W., Pfister, H., Ramamoorthi, R., and Rusinkiewicz, S. 2006. Inverse shade trees for non-parametric material representation and editing. ACM Trans. Graph. 25, 3, 735–745.
21. Mardia, K. V., and Jupp, P. E. 1999. Directional Statistics. John Wiley & Sons, Inc.
22. Mardia, K. V. 1975. Statistics of directional data. J. R. Statist. Soc. B 37, 3, 349–393.
23. Ng, R., Ramamoorthi, R., and Hanrahan, P. 2003. All-frequency shadows using non-linear wavelet lighting approximation. ACM Trans. Graph. 22, 3, 376–381.
24. Ngan, A., Durand, F., and Matusik, W. 2005. Experimental analysis of brdf models. In Proceedings of EGSR, 117–126.
25. Olano, M., and Baker, D. 2010. Lean mapping. In Proceedings of I3D, ACM, New York, NY, USA, 181–188.
26. Pacanowski, R., Salazar Celis, O., Schlick, C., Granier, X., Poulin, P., and Cuyt, A. 2012. Rational brdf. IEEE Transactions on Visualization and Computer Graphics 18, 11, 1824–1835.
27. Ramamoorthi, R., and Hanrahan, P. 2001. An efficient representation for irradiance environment maps. In Proc. of SIGGRAPH, ACM, 497–500.
28. Sadeghi, I., Bisker, O., Deken, J. D., and Jensen, H. W. 2013. A practical microcylinder appearance model for cloth rendering. ACM Trans. Graph. 32, 2, 14:1–14:12.
29. Sloan, P.-P., Kautz, J., and Snyder, J. 2002. Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Trans. Graph. 21, 3, 527–536.
30. Sun, X., Hou, Q., Ren, Z., Zhou, K., and Guo, B. 2011. Radiance transfer biclustering for real-time all-frequency bi-scale rendering. IEEE Transactions on Visualization and Computer Graphics 17, 1, 64–73.
31. Torrance, K. E., and Sparrow, E. M. 1967. Theory for off-specular reflection from roughened surfaces. Journal of the Optical Society of America 57, 9, 1105–1112.
32. Tsai, Y.-T., and Shih, Z.-C. 2006. All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation. ACM Trans. Graph. 25, 3, 967–976.
33. Wang, J., Zhao, S., Tong, X., Snyder, J., and Guo, B. 2008. Modeling anisotropic surface reflectance with example-based microfacet synthesis. ACM Trans. Graph. 27, 3 (Aug.), 41:1–41:9.
34. Wang, J., Ren, P., Gong, M., Snyder, J., and Guo, B. 2009. All-frequency rendering of dynamic, spatially-varying reflectance. ACM Trans. Graph. 28, 5, 133:1–133:10.
35. Ward, G. J. 1992. Measuring and modeling anisotropic reflection. In Proceedings of Siggraph, 265–272.
36. Wu, H., Dorsey, J., and Rushmeier, H. 2011. Physically-based interactive bi-scale material design. ACM Trans. Graph. 30, 6 (Dec.), 145:1–145:10.
37. Xu, K., Jia, Y.-T., Fu, H., Hu, S.-M., and Tai, C.-L. 2008. Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer. IEEE Transaction on Visualization and Computer Graphics 14, 2, 454–467.
38. Xu, K., Ma, L.-Q., Ren, B., Wang, R., and Hu, S.-M. 2011. Interactive hair rendering and appearance editing under environment lighting. ACM Trans. Graph. 30, 6, 173:1–173:10.
39. Yan, L.-Q., Zhou, Y., Xu, K., and Wang, R. 2012. Accurate translucent material rendering under spherical gaussian lights. Computer Graphics Forum 31, 7, 2267–2276.
40. Zhao, S., Jakob, W., Marschner, S., and Bala, K. 2012. Structure-aware synthesis for predictive woven fabric appearance. ACM Trans. Graph. 31, 4 (July), 75:1–75:10.
41. Zhu, C., Byrd, R. H., Lu, P., and Nocedal, J. 1997. L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Software 23, 4 (Dec.), 550–560.
