Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 075, 23 pages      arXiv:0907.3604      http://dx.doi.org/10.3842/SIGMA.2009.075

Image Sampling with Quasicrystals

Mark Grundland a, Jirí Patera b, Zuzana Masáková c and Neil A. Dodgson a
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

Received December 15, 2008, in final form July 06, 2009; Published online July 20, 2009

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.

Key words: computer graphics; image sampling; image representation; cut-and-project quasicrystal; non-periodic tiling; golden ratio; mosaic rendering.

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