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Sampling with polyominoes

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Victor OstromoukhovAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 26, Issue 3

Pages 78 - es

https://doi.org/10.1145/1276377.1276475

Published: 29 July 2007 Publication History

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Abstract

We present a new general-purpose method for fast hierarchical importance sampling with blue-noise properties. Our approach is based on self-similar tiling of the plane or the surface of a sphere with rectifiable polyominoes. Sampling points are associated with polyominoes, one point per polyomino. Each polyomino is recursively subdivided until the desired local density of samples is reached. A numerical code generated during the subdivision process is used for thresholding to accept or reject the sample. The exact position of the sampling point within the polyomino is determined according to a structural index, which indicates the polyomino's local neighborhood. The variety of structural indices and associated sampling point positions are computed during the offline optimization process, and tabulated. Consequently, the sampling itself is extremely fast. The method allows both deterministic and pseudo-non-deterministic sampling. It can be successfully applied in a large variety of graphical applications, where fast sampling with good spectral and visual properties is required. The prime application is rendering.

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Bærentzen JFrisvad JMartínez J(2023)Curl Noise JitteringSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618163(1-11)Online publication date: 10-Dec-2023
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Index Terms

Sampling with polyominoes
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
      2. Image and video acquisition
  2. Computer graphics
    1. Image manipulation

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 26, Issue 3

July 2007

976 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1276377

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 July 2007

Published in TOG Volume 26, Issue 3

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Cited By

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Ahmed ASkopenkov MHadwiger MWonka P(2023)Analysis and Synthesis of Digital Dyadic SequencesACM Transactions on Graphics10.1145/361830842:6(1-17)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618308
Ahmed APharr MWonka P(2023)ART-Owen ScramblingACM Transactions on Graphics10.1145/361830742:6(1-11)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618307
Bærentzen JFrisvad JMartínez J(2023)Curl Noise JitteringSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618163(1-11)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618163
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
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
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Fabarisova AKartak V(2021)Solving Irregular Polyomino Tiling Problem Using Simulated Annealing and Integer ProgrammingMathematical Optimization Theory and Operations Research: Recent Trends10.1007/978-3-030-86433-0_12(175-183)Online publication date: 21-Sep-2021
https://doi.org/10.1007/978-3-030-86433-0_12
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
Xu HHui KFu CZhang H(2020)TilinGNNACM Transactions on Graphics10.1145/3386569.339238039:4(129:1-129:16)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392380
Öztireli A(2020)A Comprehensive Theory and Variational Framework for Anti‐aliasing Sampling PatternsComputer Graphics Forum10.1111/cgf.1405939:4(133-148)Online publication date: 20-Jul-2020
https://doi.org/10.1111/cgf.14059
Lanaro MPerrier HCoeurjolly DOstromoukhov VRizzi A(2020)Blue-noise sampling for human retinal cone spatial distribution modelingJournal of Physics Communications10.1088/2399-6528/ab80644:3(035013)Online publication date: 30-Mar-2020
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