Image Sampling with Quasicrystals

Mark Grundland

Web: www.Eyemaginary.com
Email: Mark@Eyemaginary.com

 


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


Citation:

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).

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.

Online:

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

Examples:

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

 

 


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