Image Sampling with Quasicrystals

Mark Grundland



Quasicrystal Delaunay GraphQuasicrystal Delaunay GraphQuasicrystal Delaunay Graph
Quasicrystal Delaunay GraphQuasicrystal Delaunay GraphQuasicrystal Delaunay Graph


Image Sampling with Quasicrystals
Mark Grundland, Jiri Patera, Zuzana Masakova, and Neil A. Dodgson
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 5, pp. 075:1-23, (2009). ISSN 1815-0659.
Presented also as a poster at the International Congress on Mathematical Physics (Prague, Czech Republic, 3-8 August, 2009).


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.


Paper  +  Experiments  +  Poster

Sampling Data:     Periodic  +  Quasicrystal  +  Farthest Point  +  Jittered  +  Quasirandom  +  Random 

Animations:     Voronoi Diagram  +  Delaunay Graph  +  Delaunay Graph: The Sequel

Related Research  +  More Publications


Periodic Sampling Quasicrystal Sampling Farthest Point Sampling
 Image Sampling Techniques
Jittered Sampling Quasirandom Sampling Random Sampling



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