Skip to main content
Springer Nature Link
Log in

Forced Random Sampling: fast generation of importance-guided blue-noise samples

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In computer graphics, stochastic sampling is frequently used to efficiently approximate complex functions and integrals. The error of approximation can be reduced by distributing samples according to an importance function, but cannot be eliminated completely. To avoid visible artifacts, sample distributions are sought to be random, but spatially uniform, which is called blue-noise sampling. The generation of unbiased, importance-guided blue-noise samples is expensive and not feasible for real-time applications. Sampling algorithms for these applications focus on runtime performance at the cost of having weak blue-noise properties. Blue-noise distributions have also been proposed for digital halftoning in the form of precomputed dither matrices. Ordered dithering with such matrices allows to distribute dots with blue-noise properties according to a grayscale image. By the nature of ordered dithering, this process can be parallelized easily. We introduce a novel sampling method called forced random sampling that is based on forced random dithering, a variant of ordered dithering with blue noise. By shifting the main computational effort into the generation of a precomputed dither matrix, our sampling method runs efficiently on GPUs and allows real-time importance sampling with blue noise for a finite number of samples. We demonstrate the quality of our method in two different rendering applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Abe, Y.: Digital halftoning with optimized dither array. 2001 IEEE Int. Symp. Circuits Syst 2, 517–520 (2001)

    Google Scholar 

  2. Ahmed, A.G.M., Perrier, H., Coeurjolly, D., Ostromoukhov, V., Guo, J., Yan, D.M., Huang, H., Deussen, O.: Low-discrepancy blue noise sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia 2016) 13(6), 247:1–247:13 (2016)

    Google Scholar 

  3. Balzer, M., Schlömer, T., Deussen, O.: Capacity-constrained point distributions: a variant of Lloyd’s method. ACM Trans. Graph. (Proc. SIGGRAPH 2009) 28(3), 86:1–86:8 (2009)

    Google Scholar 

  4. Bayer, B.E.: An optimum method for two-level rendition of continuous-tone pictures. IEEE International Conference on Communication, Conference Record pp. (26–11)–(26–15) (1973)

  5. Bowers, J., Wang, R., Wei, L.Y., Maletz, D.: Parallel poisson disk sampling with spectrum analysis on surfaces. ACM Trans. Graph. (SIGGRAPH Asia 2010 Papers) 29(6), 166:1–166:10 (2010)

    Google Scholar 

  6. Clarberg, P., Akenine-Möller, T.: Practical product importance sampling for direct illumination. Comput. Graph. Forum (Proc. Eurograph. 2008) 27(2), 681–690 (2008)

    Article  Google Scholar 

  7. Clarberg, P., Jarosz, W., Akenine-Möller, T., Jensen, H.W.: Wavelet importance sampling: efficiently evaluating products of complex functions. ACM Trans. Graph. (Proc. SIGGRAPH 2005) 24(3), 1166–1175 (2005)

    Article  Google Scholar 

  8. Cline, D., Egbert, P.K., Talbot, J.F., Cardon, D.L.: Two stage importance sampling for direct lighting. In: Proceedings of the 17th eurographics conference on rendering techniques, pp. 103–113. Eurographics Association (2006)

  9. Cook, R.L.: Stochastic sampling in computer graphics. ACM Trans. Graph. 5(1), 51–72 (1986)

    Article  Google Scholar 

  10. Georgiev, I., Fajardo, M.: Blue-noise Dithered Sampling. In: ACM SIGGRAPH 2016 Talks, pp. 35:1–35:1. ACM (2016)

  11. Gjøl, M., Svendsen, M.: High fidelity, low complexity–the rendering of INSIDE. Game Developers Conference Europe 2016 (2016)

  12. de Goes, F., Breeden, K., Ostromoukhov, V., Desbrun, M.: Blue noise through optimal transport. ACM Trans. Graph. (Proc. SIGGRAPH Asia 2012) 31(6), 171:1–171:11 (2012)

    Google Scholar 

  13. Hiller, S., Deussen, O., Keller, A.: Tiled blue noise samples. In: Proceedings of the vision modeling and visualization conference 2001, pp. 265–272. Aka GmbH (2001)

  14. Huang, H.d., Chen, Y., Tong, X., Wang, W.c.: Incremental wavelet importance sampling for direct illumination. In: Proceedings of the 2007 ACM symposium on virtual reality software and technology, pp. 149–152. ACM (2007)

  15. Kajiya, J.T.: The rendering equation. In: Proceedings of the 13th annual conference on computer graphics and interactive techniques, pp. 143–150. ACM (1986)

  16. Kopf, J., Cohen-Or, D., Deussen, O., Lischinski, D.: Recursive Wang tiles for real-time blue noise. ACM Trans. Graph. (Proc. SIGGRAPH 2006) 25(3), 509–518 (2006)

    Article  Google Scholar 

  17. Lagae, A., Dutré, P.: A procedural object distribution function. ACM Trans. Graph. 24(4), 1442–1461 (2005)

    Article  Google Scholar 

  18. Lagae, A., Dutré, P.: An alternative for Wang tiles: colored edges versus colored corners. ACM Trans. Graph. 25(4), 1442–1459 (2006)

    Article  Google Scholar 

  19. Lagae, A., Dutré, P.: A comparison of methods for generating Poisson disk distributions. Comput. Graph. Forum 27(1), 114–129 (2008)

    Article  Google Scholar 

  20. McCool, M., Fiume, E.: Hierarchical Poisson disk sampling distributions. In: Proceedings of the conference on graphics interface ’92, pp. 94–105. Morgan Kaufmann Publ. Inc. (1992)

  21. Mitsa, T., Parker, K.J.: Digital halftoning technique using a blue-noise mask. J. Opt. Soc. Am. A 9(11), 1920–1929 (1992)

    Article  Google Scholar 

  22. Newbern, J.L., Bove Jr., V.M.: Generation of blue noise arrays by genetic algorithm. Proc. SPIE Hum. Vis. Electron. Imaging II 3016, 441–450 (1997)

    Article  Google Scholar 

  23. Ostromoukhov, V.: Sampling with polyominoes. ACM Trans. Graph. (Proc. SIGGRAPH 2007) 26(3), 1–6 (2007)

  24. Ostromoukhov, V., Donohue, C., Jodoin, P.M.: Fast hierarchical importance sampling with blue noise properties. ACM Trans. Graph. (Proc. SIGGRAPH 2004) 23(3), 488–495 (2004)

    Article  Google Scholar 

  25. Purgathofer, W., Tobler, R.F., Geiler, M.: Forced random dithering: improved threshold matrices for ordered dithering. Proc. 1st IEEE Int. Conf. Image Process. 2, 1032–1035 (1994)

    Article  Google Scholar 

  26. Schmaltz, C., Gwosdek, P., Bruhn, A., Weickert, J.: Electrostatic halftoning. Comput. Graph. Forum 29(8), 2313–2327 (2010)

    Article  Google Scholar 

  27. Shade, J., Cohen, M.F., Mitchell, D.P.: Tiling layered depth images. Technical report 02-12-07, University of Washington, Department of Computer Science and Engineering (2002)

  28. Ulichney, R.: Digital halftoning. MIT Press, Cambridge (1987)

    Google Scholar 

  29. Ulichney, R.: Dithering with blue noise. Proc. IEEE 76(1), 56–79 (1988)

    Article  Google Scholar 

  30. Ulichney, R.: The void-and-cluster method for dither array generation. Proc. of SPIE, Hum. Vis. Vis. Process. Digit. Disp IV 1913, 332–343 (1993)

    Article  Google Scholar 

  31. Wachtel, F., Pilleboue, A., Coeurjolly, D., Breeden, K., Singh, G., Cathelin, G., de Goes, F., Desbrun, M., Ostromoukhov, V.: Fast tile-based adaptive sampling with user-specified Fourier spectra. ACM Trans. Graph. (Proc. SIGGRAPH 2014) 33(4), 56:1–56:11 (2014)

    Google Scholar 

  32. Wei, L.Y.: Parallel Poisson disk sampling. ACM Trans. Graph. (Proc. SIGGRAPH 2008) 27(3), 20:1–20:9 (2008)

    MathSciNet  Google Scholar 

  33. Wei, L.Y.: Public SVN repository of Li-Yi Wei, Revision 13 (2011). https://github.com/1iyiwei/noise/ (accessed February 19, 2017)

  34. Wei, L.Y., Wang, R.: Differential domain analysis for non-uniform sampling. ACM Trans. Graph. (Proc. SIGGRAPH 2011) 30(4), 50:1–50:10 (2011)

    Google Scholar 

  35. Weinzierl-Heigl, C.: Efficient VAL-based real-time global illumination. In: Proceedings of the 17th Central European Seminar on Computer Graphics (2013)

  36. Xiang, Y., Xin, S.Q., Sun, Q., He, Y.: Parallel and accurate Poisson disk sampling on arbitrary surfaces. In: SIGGRAPH Asia 2011 Sketches, pp. 18:1–18:2. ACM (2011)

  37. Yellott Jr., J.I.: Spectral consequences of photoreceptor sampling in the rhesus retina. Science 221, 382–385 (1983)

    Article  Google Scholar 

  38. Yuksel, C.: Sample elimination for generating Poisson disk sample sets. Comput. Graph. Forum (Proc. Eurograph. 2015) 34(2), 25–32 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

The competence center VRVis is funded by BMVIT, BMWFW and City of Vienna (ZIT) within the scope of COMET Competence Centers for Excellent Technologies. The program COMET is managed by FFG. Hiroyuki Sakai is partly supported by the Austrian Science Fund (FWF), project no. P 27974. We thank Christoph Weinzierl-Heigl for providing us access to his implementation of reflective shadow mapping.

Author information

Authors and Affiliations

  1. VRVis Research Center, Vienna, Austria

    Daniel Cornel, Robert F. Tobler & Christian Luksch

  2. TU Wien, Vienna, Austria

    Hiroyuki Sakai & Michael Wimmer

Authors
  1. Daniel Cornel
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Robert F. Tobler
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hiroyuki Sakai
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Christian Luksch
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Michael Wimmer
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Daniel Cornel.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (rar 17210 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cornel, D., Tobler, R.F., Sakai, H. et al. Forced Random Sampling: fast generation of importance-guided blue-noise samples. Vis Comput 33, 833–843 (2017). https://doi.org/10.1007/s00371-017-1392-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-017-1392-7

Keywords