Abstract
This paper presents a fast digital stippling algorithm, which makes a fair balance on result quality and computational efficiency. The algorithm is based on precomputed blue noise point sets constructed by incremental Voronoi sets (IVS) and a real-time parallelized rejection strategy. The proposed technique is readily extended to generate multi-tone-level or multi-nib-size stippling results of increased pleasure visual impressions with smooth tone transition. The IVS can also be regressed to generate blue noise masks for digital halftoning.
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Ahmed, A., Guo, J., Yan, D.M., Franceschi, J.Y., Zhang, X., Deussen, O.: A simple push-pull algorithm for blue-noise sampling. IEEE Trans. Vis. Comput. Graph. 23(12), 2496–2508 (2017)
Ahmed, A., Niese, T., Huang, H., Deussen, O.: An adaptive point sampler on a regular lattice. ACM Trans. Graph. 36(4), 4138:1–138:13 (2017)
Ahmed, A., Perrier, H., Coeurjolly, D., Ostromoukhov, V., Guo, J., Yan, D., Huang, H., Deussen, O.: Low-discrepancy blue noise sampling. ACM Trans. Graph. 35(6), 247:1–247:13 (2016)
Ahmed, A.G.M., Huang, H., Deussen, O.: AA patterns for point sets with controlled spectral properties. ACM Trans. Graph. 34(6), 212:1–212:8 (2015)
Ascencio-Lopez, I., Meruvia-Pastor, O., Hidalgo-Silva, H.: Adaptive incremental stippling using the Poisson-disk distribution. J. Graph. GPU Game Tools 15(1), 29–47 (2010)
Balzer, M., Schlömer, T., Deussen, O.: Capacity-constrained point distributions: a variant of Lloyd’s method. ACM Trans. Graph. (Proc. SIGGRAPH) 28(6), 86:1–86:8 (2009)
Bayer, B.E.: An optimum method for two-level rendition of continuous-tone pictures. IEEE Int. Conf. Commun. 26, 11–15 (1973)
Chen, J., Ge, X., Wei, L.Y., Wang, B., Wang, Y., Wang, H., Fei, Y., Qian, K.L., Yong, J.H., Wang, W.: Bilateral blue noise sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 32(6), 216:1–216:11 (2013)
Chen, R., Gotsman, C.: Parallel blue-noise sampling by constrained farthest point optimization. Comput. Graph. Forum (Proc. SGP) 31(5), 1775–1785 (2012)
Chen, Z., Yuan, Z., Choi, Y.K., Liu, L., Wang, W.: Variational blue noise sampling. IEEE Trans. Vis. Comput. Graph. 18(10), 1784–1796 (2012)
Cline, D., Jeschke, S., Razdan, A., White, K., Wonka, P.: Dart throwing on surfaces. Comput. Graph. Forum (Proc. EGSR) 28(4), 1217–1226 (2009)
Cohen, M.F., Shade, J., Hiller, S., Deussen, O.: Wang tiles for image and texture generation. Int. Conf. Comput. Graph. Interact. Tech. 22(3), 287–294 (2003)
Cook, R.L.: Stochastic sampling in computer graphics. ACM Trans. Graph. 5(1), 69–78 (1986)
Deussen, O., Hiller, S., Van Overveld, C., Strothotte, T.: Floating points: a method for computing stipple drawings. Comput. Graph. Forum 19(3), 41–50 (2000)
Deussen, O., Hiller, S., Van Overveld, C., Strothotte, T.: Floating points: a method for computing stipple drawings. Comput. Graph. Forum 19, 41–50 (2000). Wiley Online Library
Du, Q., Faber, V., Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41, 637–676 (1999)
Ebeida, M.S., Mitchell, S.A., Patney, A., Davidson, A.A., Owens, J.D.: A simple algorithm for maximal Poisson-disk sampling in high dimensions. Comput. Graph. Forum (Proc. EUROGRAPHICS) 31(2), 785–794 (2012)
Ebeida, M.S., Patney, A., Mitchell, S.A., Andrew Davidson, P.M.K., Owens, J.D.: Efficient maximal Poisson-disk sampling. ACM Trans. Graph. (Proc. SIGGRAPH) 30(4), 49:1–49:12 (2011)
Eldar, Y., Lindenbaum, M., Porat, M., Zeevi, Y.Y.: The farthest point strategy for progressive image sampling. IEEE Trans. Image Process. 6(9), 1305–1315 (1997)
Fattal, R.: Blue-noise point sampling using kernel density model. ACM Trans. Graph. (Proc. SIGGRAPH) 28(3), 48:1–48:10 (2011)
Georgiev, I., Fajardo, M.: Blue-noise dithered sampling. In: ACM SIGGRAPH 2016 Talks, SIGGRAPH ’16. ACM, New York, NY, USA, pp. 35:1–35:1 (2016)
de Goes, F., Breeden, K., Ostromoukhov, V., Desbrun, M.: Blue noise through optimal transport. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 171:1–171:12 (2012)
Gwosdek, P., Schmaltz, C., Weickert, J., Teuber, T.: Electrostatic halftoning. J. Real-Time Image Proc. 9(2), 379–392 (2014)
Kang, H.R.: Digital color halftoning, 1st edn. Society of Photo-Optical Instrumentation Engineers (SPIE), Bellingham, WA, USA (1999)
Kopf, J., Cohen-Or, D., Deussen, O., Lischinski, D.: Recursive Wang tiles for real-time blue noise. ACM Trans. Graph. (Proc. SIGGRAPH) 11(2), 509–518 (2006)
Kriss, Michael: Handbook of Digital Imaging. Wiley, New York (2015)
Lagae, A., Dutré, P.: An alternative for wang tiles: colored edges versus colored corners. ACM Trans. Graph. 25(4), 1442–1459 (2006)
Lagae, A., Dutré, P.: A comparison of methods for generating Poisson disk distributions. Comput. Graph. Forum 27(1), 114–129 (2008)
Lloyd, S.A.: Least squares quantization in PCM. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)
Lu, A., Morris, C.J., Taylor, J., Ebert, D.S., Hansen, C., Rheingans, P., Hartner, M.: Illustrative interactive stipple rendering. IEEE Trans. Vis. Comput. Graph. 9(2), 127–138 (2003)
Martín, D., Arroyo, G., Rodríguez, A., Isenberg, T.: A survey of digital stippling. Comput. Graph. 67, 24–44 (2017)
Mitsa, T., Parker, K.J.: Digital halftoning technique using a blue-noise mask. J. Opt. Soc. Am. A 9(11), 1920–1929 (1992)
Niederreiter, H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51–70 (1988)
Niederreiter, H.: Random number generation and quasi-Monte Carlo methods. J. Am. Stat. Assoc. 88(89), 147153 (1992)
Ostromoukhov, V., Donohue, C., Jodoin, P.M.: Fast hierarchical importance sampling with blue noise properties. ACM Trans. Graph. (Proc. SIGGRAPH) 23(3), 488–495 (2004)
Ostromoukhov, V., Donohue, C., Jodoin, P.M.: Sampling with polyominoes. ACM Trans. Graph. (Proc. SIGGRAPH) 26(3), 78:1–78:6 (2007)
Pang, W.M., Qu, Y., Wong, T.T., Cohen-Or, D., Heng, P.A.: Structure-aware halftoning. ACM Trans. Graph. 27(3), 89:1–89:8 (2008)
Pnueli, Y., Bruckstein, A.M.: Gridless halftoning: a reincarnation of the old method. Graph. Models Image Process. 58(1), 38–64 (1996)
Purgathofer, W., Tobler, R.F., Geiler, M.: Forced random dithering: improved threshold matrices for ordered dithering, Vol. 2. In: Proceedings of 1st International Conference on Image Processing, pp. 1032–1035 (1994)
Schlömer, T., Heck, D., Deussen, O.: Farthest-point optimized point sets with maximized minimum distance. In: High Performance Graphics Proceedings, pp. 135–142 (2011)
Schretter, C., Kobbelt, L., Dehaye, P.: Golden ratio sequences for low-discrepancy sampling. J. Graph. Tools 16(2), 95–104 (2012)
Secord, A.: Weighted Voronoi stippling. In: Proceedings of the Second International Symposium on Non-photorealistic Animation and Rendering—NPAR ’02, 1, 37 (2002)
Spicker, M., Hahn, F., Lindemeier, T., Saupe, D., Deussen, O.: Quantifying visual abstraction quality for stipple drawings. In: Proceedings of the Symposium on Non-photorealistic Animation and Rendering, NPAR ’17. ACM, New York, NY, USA, pp. 8:1–8:10 (2017)
Ulichney, R.: Digital Halftoning. MIT Press, Cambridge (1987)
Ulichney, R.: Dithering with Blue Noise. MIT Press, Cambridge (1987)
Ulichney, R.: Void-and-cluster method for dither array generation. In: Proceedings of SPIE - The International Society for Optical Engineering, pp. 332–343 (1993)
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. 33(4), 56:1–56:11 (2014)
Wei, L.Y.: Multi-class blue noise sampling. ACM Trans. Graph. (Proc. SIGGRAPH) 29(4), 79:1–79:8 (2010)
Wong, T.T., Luk, W.S., Heng, P.A.: Sampling with hammersley and halton points. J. Graph. Tools 2(2), 9–24 (1997)
Xu, Y., Liu, L., Gotsman, C., Gortler, S.J.: Capacity-constrained Delaunay triangulation for point distributions. Comput. Graph. 35(3), 510–516 (2011)
Yan, D.M., Guo, J., Jia, X., Zhang, X., Wonka, P.: Blue-noise remeshing with farthest point optimization. Comput. Graph. Forum (Proc. SGP) 33(5), 167–176 (2014)
Yan, D.M., Guo, J., Wang, B., Zhang, X., Wonka, P.: A survey of blue-noise sampling and its applications. J. Comput. Sci. Technol. 30(3), 439–452 (2015)
Yan, D.M., Wonka, P.: Gap processing for adaptive maximal Poisson-disk sampling. ACM Trans. Graph. 32(5), 148:1–148:15 (2013)
Yuksel, C.: Sample elimination for generating Poisson disk sample sets. Comput. Graph. Forum 34(2), 25–32 (2015)
Zhou, B., Fang, X.: Improving mid-tone quality of variable-coefficient error diffusion using threshold modulation. ACM Trans. Graph. 22(3), 437–444 (2003)
Acknowledgements
This study is funded by UGC (Grant number 4055060), joint NSFC grants (no. 61379087, 61602183).
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Special thanks to Wenjuan Shen.
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Ma, L., Chen, Y., Qian, Y. et al. Incremental Voronoi sets for instant stippling. Vis Comput 34, 863–873 (2018). https://doi.org/10.1007/s00371-018-1541-7
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DOI: https://doi.org/10.1007/s00371-018-1541-7