Image Sampling with Quasicrystals

TL;DR

This paper explores the use of quasicrystals for image sampling, leveraging their non-periodic, space-filling properties and self-similar symmetry to improve image reconstruction and rendering techniques.

Contribution

It introduces the algebraic theory of cut-and-project quasicrystals for image sampling and evaluates their practical effectiveness in photorealistic and non-photorealistic image rendering.

Findings

Quasicrystal sampling produces evenly spread, visually appealing patterns.

The approach enhances image reconstruction quality.

A novel mosaic rendering technique visualizes quasicrystal point sets.

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.