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arXiv · 0907.3604

Image Sampling with Quasicrystals

Mark Grundland·Jiri Patera·Zuzana Masakova·Neil A. Dodgson
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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.

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Mark Grundland, Jiri Patera, Zuzana Masakova, Neil A. Dodgson. 2009-07-21. Image Sampling with Quasicrystals. https://doi.org/10.3842/sigma.2009.075

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