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

Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

Échantillonnage basé sur les Tuiles de Penrose et applications en infographie

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Chirplet approximation of band-limited, real signals made easy

In this paper we present algorithms for approximating real band-limited signals by multiple Gaussian Chirps. These algorithms do not rely on matching pursuit ideas. They are hierarchial and, at each stage, the number of terms in a given approximation depends only on the number of positive-valued maxima and negative-valued minima of a signed amplitude function characterizing part of the signal. Like the algorithms used in \cite{gre2} and unlike previous methods, our chirplet approximations require neither a complete dictionary of chirps nor complicated multi-dimensional searches to obtain suitable choices of chirp parameters

Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models

In regression models with many potential predictors, choosing an appropriate subset of covariates and their interactions at the same time as determining whether linear or more flexible functional forms are required is a challenging and important task. We propose a spike-and-slab prior structure in order to include or exclude single coefficients as well as blocks of coefficients associated with factor variables, random effects or basis expansions of smooth functions. Structured additive models with this prior structure are estimated with Markov Chain Monte Carlo using a redundant multiplicative parameter expansion. We discuss shrinkage properties of the novel prior induced by the redundant parameterization, investigate its sensitivity to hyperparameter settings and compare performance of the proposed method in terms of model selection, sparsity recovery, and estimation error for Gaussian, binomial and Poisson responses on real and simulated data sets with that of component-wise boosting and other approaches