“Gabor noise by example” by Galerne, Lagae, Lefebvre and Drettakis

Procedural noise is a fundamental tool in Computer Graphics. However, designing noise patterns is hard. In this paper, we present Gabor noise by example, a method to estimate the parameters of bandwidth-quantized Gabor noise, a procedural noise function that can generate noise with an arbitrary power spectrum, from exemplar Gaussian textures, a class of textures that is completely characterized by their power spectrum. More specifically, we introduce (i) bandwidth-quantized Gabor noise, a generalization of Gabor noise to arbitrary power spectra that enables robust parameter estimation and efficient procedural evaluation; (ii) a robust parameter estimation technique for quantized-bandwidth Gabor noise, that automatically decomposes the noisy power spectrum estimate of an exemplar into a sparse sum of Gaussians using non-negative basis pursuit denoising; and (iii) an efficient procedural evaluation scheme for bandwidth-quantized Gabor noise, that uses multi-grid evaluation and importance sampling of the kernel parameters. Gabor noise by example preserves the traditional advantages of procedural noise, including a compact representation and a fast on-the-fly evaluation, and is mathematically well-founded.

1. Beck, A., and Teboulle, M. 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Img. Sci. 2, 183–202. Google ScholarDigital Library
2. Bovik, A. C., Clark, M., and Geisler, W. S. 1990. Multichannel texture analysis using localized spatial filters. IEEE Trans. Pattern Anal. Mach. Intell. 12, 1, 55–73. Google ScholarDigital Library
3. Cardoso, J.-F., and Souloumiac, A. 1996. Jacobi angles for simultaneous diagonalization. SIAM J. Matrix Anal. Appl. 17, 161–164. Google ScholarDigital Library
4. Cook, R. L., and DeRose, T. 2005. Wavelet noise. ACM Trans. Graph. 24, 3, 803–811. Google ScholarDigital Library
5. Dischler, J.-M., and Ghazanfarpour, D. 1997. A procedural description of geometric textures by spectral and spatial analysis of profiles. Comp. Graph. Forum 16, 3, 129–139.Google ScholarCross Ref
6. Ferreira, P. 1998. A comment on the approximation of signals by gaussian functions. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 45, 2, 250–251.Google ScholarCross Ref
7. Francos, J. M., Meiri, A. Z., and Porat, B. 1993. A unified texture model based on a 2-D Wold-like decomposition. IEEE Trans. Signal Process. 41, 8, 2665–2678. Google ScholarDigital Library
8. Galerne, B., Gousseau, Y., and Morel, J. 2011. Random phase textures: Theory and synthesis. IEEE Trans. Image Process. 20, 1, 257–267. Google ScholarDigital Library
9. Ghazanfarpour, D., and Dischler, J.-M. 1995. Spectral analysis for automatic 3-d texture generation. Comp. & Graph. 19, 3, 413–422.Google Scholar
10. Ghazanfarpour, D., and Dischler, J.-M. 1996. Generation of 3d texture using multiple 2d models analysis. Comp. Graph. Forum 15, 3, 311–323.Google ScholarCross Ref
11. Gilet, G., and Dischler, J.-M. 2010. An image-based approach for stochastic volumetric and procedural details. Comp. Graph. Forum 29, 4, 1411–1419. Google ScholarDigital Library
12. Gilet, G., Dischler, J.-M., and Soler, L. 2010. Procedural descriptions of anisotropic noisy textures by example. In EG 2010 – Short papers, 77–80.Google Scholar
13. Goldberg, A., Zwicker, M., and Durand, F. 2008. Anisotropic noise. ACM Trans. Graph. 27, 3, 54:1–54:8. Google ScholarDigital Library
14. Heeger, D. J., and Bergen, J. R. 1995. Pyramid-based texture analysis/synthesis. In Proc. ACM SIGGRAPH 1995, 229–238. Google ScholarDigital Library
15. Hyvärinen, A., Karhunen, J., and Oja, E. 2001. Independent Component Analysis. John Wiley & Sons.Google Scholar
16. Jeschke, S., Cline, D., and Wonka, P. 2011. Estimating color and texture parameters for vector graphics. Comp. Graph. Forum 30, 2, 523–532.Google ScholarCross Ref
17. Kim, S.-J., Koh, K., Lustig, M., Boyd, S., and Gorinevsky, D. 2007. An interior-point method for large-scale l1-regularized least squares. IEEE J. Sel. Topics Signal Process. 1, 4, III–117–III–120.Google ScholarCross Ref
18. Kopf, J., Fu, C.-W., Cohen-Or, D., Deussen, O., Lischinski, D., and Wong, T.-T. 2007. Solid texture synthesis from 2D exemplars. ACM Trans. Graph. 26, 3, 2:1–2:9. Google ScholarDigital Library
19. Lagae, A., and Drettakis, G. 2011. Filtering solid Gabor noise. ACM Trans. Graph. 30, 4, 51:1–51:6. Google ScholarDigital Library
20. Lagae, A., Lefebvre, S., Drettakis, G., and Dutré, P. 2009. Procedural noise using sparse Gabor convolution. ACM Trans. Graph. 28, 3, 54:1–54:10. Google ScholarDigital Library
21. Lagae, A., Lefebvre, S., Cook, R., DeRose, T., Drettakis, G., Ebert, D. S., Lewis, J. P., Perlin, K., and Zwicker, M. 2010. A survey of procedural noise functions. Comp. Graph. Forum 29, 8, 2579–2600.Google ScholarCross Ref
22. Lagae, A., Vangorp, P., Lenaerts, T., and Dutré, P. 2010. Procedural isotropic stochastic textures by example. Comp. & Graph. 34, 4, 312–321. Google ScholarDigital Library
23. Lefebvre, S., and Hoppe, H. 2005. Parallel controllable texture synthesis. ACM Trans. Graph. 24, 3, 777–786. Google ScholarDigital Library
24. Lewis, J. P. 1989. Algorithms for solid noise synthesis. In Comp. Graph. (Proc. ACM SIGGRAPH 89), vol. 23, 263–270. Google ScholarDigital Library
25. Liu, F. 1997. Modeling spatial and temporal textures. PhD thesis, Massachusetts Institute of Technology. Google ScholarDigital Library
26. Mairal, J., Jenatton, R., Obozinski, G., and Bach, F. 2011. Convex and network flow optimization for structured sparsity. J. Mach. Learn. Res. 12, 2681–2720. Google ScholarDigital Library
27. Moisan, L. 2011. Periodic plus smooth image decomposition. J. Math. Imag. Vis. 39, 161–179. Google ScholarDigital Library
28. Papas, M., Jarosz, W., Jakob, W., Rusinkiewicz, S., Matusik, W., and Weyrich, T. 2011. Goal-based caustics. Comp. Graph. Forum 30, 2, 503–511.Google ScholarCross Ref
29. Papoulis, A., and Pillai, U. 2002. Probability, Random Variables and Stochastic Processes, 4rd ed. McGraw-Hill.Google Scholar
30. Perlin, K. 1985. An image synthesizer. In Comp. Graph. (Proc. ACM SIGGRAPH 85), vol. 19, 287–296. Google ScholarDigital Library
31. Press, W. H., Vetterling, W. T., Teukolsky, S. A., and Flannery, B. P. 2002. Numerical Recipes in C++: the art of scientific computing, 2nd ed. Cambridge University Press. Google ScholarDigital Library
32. Qin, X., and Yang, Y.-H. 2007. Aura 3d textures. Visualization and Computer Graphics, IEEE Transactions on 13, 2, 379–389. Google ScholarDigital Library
33. Vose, M. D. 1991. A linear algorithm for generating random numbers with a given distribution. IEEE Trans. Softw. Eng. 17, 972–975. Google ScholarDigital Library
34. Walker, A. J. 1977. An efficient method for generating discrete random variables with general distributions. ACM Trans. Math. Softw. 3, 3, 253–256. Google ScholarDigital Library
35. Wei, L.-Y., Lefebvre, S., Kwatra, V., and Turk, G. 2009. State of the art in example-based texture synthesis. In Eurographics 2009 State of the Art Reports, 93–117.Google Scholar
36. Xue, S., Dorsey, J., and Rushmeier, H. 2011. Stone weathering in a photograph. Comp. Graph. Forum 30, 4, 1189–1196. Google ScholarDigital Library
37. Yoon, J.-C., and Lee, I.-K. 2008. Stable and controllable noise. Graph. Models 70, 5, 105–115. Google ScholarDigital Library
38. Yoon, J.-C., Lee, I.-K., and Choi, J.-J. 2004. Editing noise. Comp. Anim. Virtual Worlds 15, 3-4, 277–287. Google ScholarDigital Library