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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 075, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.075
(Mi sigma420)
 

This article is cited in 3 scientific papers (total in 3 papers)

Image Sampling with Quasicrystals

Mark Grundlanda, Jirí Paterab, Zuzana Masákovác, Neil A. Dodgsona

a Computer Laboratory, University of Cambridge, UK
b Centre de Recherches Mathématiques, Université de Montréal, Canada
c Department of Mathematics FNSPE, Czech Technical University in Prague, Czech Republic
References:
Abstract: We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.
Keywords: computer graphics; image sampling; image representation;cut-and-project quasicrystal; non-periodic tiling; golden ratio;mosaic rendering.
Received: December 15, 2008; in final form July 6, 2009; Published online July 20, 2009
Bibliographic databases:
Document Type: Article
Language: English
Citation: Mark Grundland, Jirí Patera, Zuzana Masáková, Neil A. Dodgson, “Image Sampling with Quasicrystals”, SIGMA, 5 (2009), 075, 23 pp.
Citation in format AMSBIB
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\paper Image Sampling with Quasicrystals
\jour SIGMA
\yr 2009
\vol 5
\papernumber 075
\totalpages 23
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
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