Image Sampling with Quasicrystals

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Authors: Grundland, M., Patera, J., Masáková, Z., Dodgson, N.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149141
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Image Sampling with Quasicrystals / M. Grundland, J. Patera, Z. Masáková, N.A. Dodgson // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 51 назв. — англ.

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.