Article

Fast hierarchical importance sampling with blue noise properties

Authors:

Victor Ostromoukhov,

Charles Donohue,

Pierre-Marc JodoinAuthors Info & Claims

SIGGRAPH '04: ACM SIGGRAPH 2004 Papers

Pages 488 - 495

https://doi.org/10.1145/1186562.1015750

Published: 01 August 2004 Publication History

Abstract

This paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Pre-computed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importance-based environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.

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References

[1]

AGARWAL, S., RAMAMOORTHI, R., BELONGIE, S., AND JENSEN, H. 2003. Structured importance sampling of environment maps. ACM Trans. on Graphics 22, 3 (July), 605--612.

Digital Library

[2]

ALLIEZ, P., MEYER, M., AND DESBRUN, M. 2002. Interactive geometry remeshing. ACM Trans. on Graphics 21, 3, 347--354.

Digital Library

[3]

BAYER, B. 1973. An optimum method for two-level rendition of continuous-tone pictures. In IEEE Int. Conf. on Communications, 11--15.

[4]

COHEN, J., AND DEBEVEC, P. 2001. LightGen, HDRShop plugin. http://www.ict.usc.edu/~jcohen/lightgen/lightgen.html.

[5]

COHEN, M., SHADE, J., HILLER, S., AND DEUSSEN, O. 2003. Wang tiles for image and texture generation. ACM Trans. on Graphics 22, 3 (July), 287--294.

Digital Library

[6]

COOK, R. 1986. Stochastic sampling in computer graphics. ACM Trans. on Graphics 5, 1 (Jan.), 51--72.

Digital Library

[7]

DEBEVEC, P. 1998. Rendering synthetic objects into real scenes: Bridging traditional and image-based graphics with global illumination and high dynamic range photography. In Proc. SIGGRAPH '98, 189--198.

Digital Library

[8]

DU, Q., FABER, V., AND GUNZBURGER, M. 1999. Centroidal Voronoi tessellations: Applications and algorithms. SIAM Review 41, 4 (Dec.), 637--676.

Digital Library

[9]

FOLEY, J., VAN DAM, A., FEINER, S., AND HUGHES, J. 1990. Computer Graphics, Principles and Practice, 2nd ed. Addison-Wesley.

Digital Library

[10]

GARDNER, M. 1977. Extraordinary nonperiodic tiling that enriches the theory of tiles. Scientific American 236, 110--121.

[11]

GLASSNER, A. 1995. Principles of Digital Image Synthesis. Morgan Kaufmann.

Digital Library

[12]

GLASSNER, A. 1998. Andrew Glassner's notebook: Penrose tiling. IEEE Computer Graphics & Applications 18, 4, 78--86.

Digital Library

[13]

GRAHAM, R., KNUTH, D., AND PATASHNIK, O. 1994. Concrete Mathematics: a foundation for Computer Science, 2nd ed. Chapter 6.6. Addison-Wesley.

Digital Library

[14]

GRÜNBAUM, B., AND SHEPHARD, G. 1986. Tilings and Patterns. W. H. Freeman.

Digital Library

[15]

HILLER, S., DEUSSEN, O., AND KELLER, A. 2001. Tiled blue noise samples. In Proc. Vision Modeling and Visualization, 265--272.

Digital Library

[16]

HOFF, K., CULVER, T., KEYSER, J., LIN, M., AND MANOCHA, D. 1999. Fast computation of generalized voronoi diagrams using graphics hardware. In Proc. SIGGRAPH '99, 277--286.

Digital Library

[17]

KNUTH, D. 1997. The Art of Computer Programming, Volume 1, Fundamental Algorithms, 3rd ed. page 86. Addison-Wesley.

Digital Library

[18]

KOLLIG, T., AND KELLER, A. 2001. Efficient bidirectional path tracing by randomized quasi-monte carlo integration. Niederreiter, K. Fang, and F. Hickernell, Eds., Monte Carlo and Quasi-Monte Carlo Methods 2000, 290--305.

[19]

KOLLIG, T., AND KELLER, A. 2002. Efficient multidimensional sampling. Computer Graphics Forum 21, 3, 557--564.

[20]

KOLLIG, T., AND KELLER, A. 2003. Efficient illumination by high dynamic range images. In Eurographics Symposium on Rendering: 14th Eurographics Workshop on Rendering, 45--51.

Digital Library

[21]

LLOYD, S. 1983. An optimization approach to relaxation labeling algorithms. Image and Vision Computing 1, 2, 85--91.

[22]

MACKAY, A. 1982. Crystallography and the Penrose pattern. Physica 114A, 609--613.

[23]

MCCOOL, M., AND FIUME, E. 1992. Hierarchical poisson disk sampling distributions. In Proc. Graphics Interface '92, 94--105.

Digital Library

[24]

MITCHELL, D. 1991. Spectrally optimal sampling for distributed ray tracing. In Proc. SIGGRAPH '91, vol. 25, 157--164.

Digital Library

[25]

NIEDERREITER, H. 1992. Random Number Generation and Quasi-Monte-Carlo Methods. Soc. for Industrial and Applied Mathematics.

Digital Library

[26]

OSTROMOUKHOV, V., HERSCH, R., AND AMIDROR, I. 1994. Rotated dispersion dither: a new technique for digital halftoning. In Proc. SIGGRAPH '94, 123--130.

Digital Library

[27]

OSTROMOUKHOV, V. 2001. A simple and efficient error-diffusion algorithm. In Proc. SIGGRAPH 2001, 567--572.

Digital Library

[28]

PENROSE, R. 1974. The role of aesthetics in pure and applied mathematical research. Bull. Inst. Math. & its Applns. 10, 266--271.

[29]

PENROSE, R. 1979. Pentaplexity, a class of non-periodic tilings of the plane. The Mathematical Intelligencer 2, 32--37.

[30]

SECORD, A., HEIDRICH, W., AND STREIT, L. 2002. Fast primitive distribution for illustration. In 13th Eurographics Workshop on Rendering, 215--226.

Digital Library

[31]

SHIRLEY, P. 1991. Discrepancy as a quality measure for sample distributions. In Proc. Eurographics '91, 183--194.

[32]

SOCOLAR, J. 1989. Simple octagonal and dodecagonal quasicrystals. Physical Revue B39, 10519--10551.

[33]

STEINHARDT, P., AND OSTLUND, S. 1987. The Physics of Quasicrystals. World Scientific.

[34]

SURAZHSKY, V., ALLIEZ, P., AND GOTSMAN, C. 2003. Isotropic remeshing of surfaces: a local parameterization approach. In Proc. of 12th Int. Meshing Roundtable.

[35]

ULICHNEY, R. 1987. Digital Halftoning. MIT Press.

Digital Library

[36]

ULICHNEY, R. A. 1988. Dithering with blue noise. Proc. of the IEEE 76, 56--79.

[37]

VEACH, E. 1997. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis. Stanford University.

Digital Library

[38]

ZHOU, B., AND FANG, X. 2003. Improving mid-tone quality of variable-coefficient error diffusion using threshold modulation. ACM Trans. on Graphics 22, 3 (July), 437--444.

Digital Library

Cited By

Ahmed ARen JWonka P(2022)Gaussian Blue NoiseACM Transactions on Graphics10.1145/3550454.355551941:6(1-15)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555519
Paulin LCoeurjolly DIehl JBonneel NKeller AOstromoukhov V(2021)Cascaded Sobol' samplingACM Transactions on Graphics10.1145/3478513.348048240:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480482
Ma LShi JChen YShen HZhuang YSmith JYang YCesar PMetze FPrabhakaran B(2021)Milliseconds Color StipplingProceedings of the 29th ACM International Conference on Multimedia10.1145/3474085.3475427(2539-2548)Online publication date: 17-Oct-2021
https://dl.acm.org/doi/10.1145/3474085.3475427
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Index Terms

Fast hierarchical importance sampling with blue noise properties
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
    2. Rendering

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cover image ACM Conferences

SIGGRAPH '04: ACM SIGGRAPH 2004 Papers

August 2004

684 pages

ISBN:9781450378239

DOI:10.1145/1186562

Editor:
Joe Marks
Mitsubishi Electric Research Laboratories (MERL)

Copyright © 2004 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 August 2004

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SIGGRAPH04: Special Interest Group on Computer Graphics and Interactive Techniques

August 8 - 12, 2004

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SIGGRAPH '04 Paper Acceptance Rate 83 of 478 submissions, 17%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

Ahmed ARen JWonka P(2022)Gaussian Blue NoiseACM Transactions on Graphics10.1145/3550454.355551941:6(1-15)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555519
Paulin LCoeurjolly DIehl JBonneel NKeller AOstromoukhov V(2021)Cascaded Sobol' samplingACM Transactions on Graphics10.1145/3478513.348048240:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480482
Ma LShi JChen YShen HZhuang YSmith JYang YCesar PMetze FPrabhakaran B(2021)Milliseconds Color StipplingProceedings of the 29th ACM International Conference on Multimedia10.1145/3474085.3475427(2539-2548)Online publication date: 17-Oct-2021
https://dl.acm.org/doi/10.1145/3474085.3475427
Ahmed AWonka P(2020)Screen-space blue-noise diffusion of monte carlo sampling error via hierarchical ordering of pixelsACM Transactions on Graphics10.1145/3414685.341788139:6(1-15)Online publication date: 27-Nov-2020
https://dl.acm.org/doi/10.1145/3414685.3417881
Marques RBouville CBouatouch K(2018)Optimal Sample Weights for Hemispherical Integral QuadraturesComputer Graphics Forum10.1111/cgf.1339238:1(59-72)Online publication date: 10-Apr-2018
https://doi.org/10.1111/cgf.13392
Wong KWong T(2017)Blue noise sampling using an N-body simulation-based methodThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-017-1382-933:6-8(823-832)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s00371-017-1382-9
Reinert BRitschel TSeidel HGeorgiev I(2016)Projective Blue-Noise SamplingComputer Graphics Forum10.1111/cgf.1272535:1(285-295)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1111/cgf.12725
Sampaio AChaine RVidal CCavalcante-Neto J(2016)Temporally coherent sculpture of composite objectsComputers and Graphics10.1016/j.cag.2016.05.01158:C(118-127)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.cag.2016.05.011
Ahmed AHuang HDeussen O(2015)AA patterns for point sets with controlled spectral propertiesACM Transactions on Graphics10.1145/2816795.281813934:6(1-8)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2816795.2818139
Ebeida MAwad MGe XMahmoud AMitchell SKnupp PWei L(2014)Improving spatial coverage while preserving the blue noise of point setsComputer-Aided Design10.1016/j.cad.2013.08.01546(25-36)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1016/j.cad.2013.08.015
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