Image Sampling with Quasicrystals

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.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

A Real-Time Adaptive Sampling Strategy Optimized by Uncertainty for Spatial Data Analysis on Complex Domains

Environmental monitoring is used to reveal the state of the environment, to inform experts and help them to prioritise actions in the context of environmental policies. Environmental sampling is the way the environment is interrogated to get measures of environmental (e.g., physical, chemical) parameters in a limited set of locations (samples). The environmental properties varies from place to place in continuum and there are infinitely many places at which we might record what they are like, but practically we can measure them at only a finite number by sampling. The role of the location in which samples are collected is very crucial. The focus of the thesis is the study of a mathematical framework that supports a reasoned and non-random sampling of environmental variables, with the aim of defining a methodological approach to optimise the number of sampling required while maintaining a target precision. The arrangement of points is not selected or known a priori; conversely, we propose an iterative process where the next-sample location is determined on-the-fly on the basis of the environmental scenario that is delineated more and more accurately at each iteration. At each iteration, the distribution map is updated with the new incoming data. The geostatistical analysis we implement provides a predicted value and the related uncertainty about that value, actually providing an uncertainty map beside the predicted distribution. The system responds to the current state by requiring a measurement in the area with highest uncertainty, to reduce uncertainty and increase accuracy. Environmental survey areas to monitor are often characterised by very complex boundaries. Unstructured grids are more flexible to faithfully represent complex geometries compared to structured grids. The usage of unstructured grids introduces another innovation aspect studied in the thesis, which is the change of support model

Mode transitions in a model reaction-diffusion system driven by domain growth and noise

Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns