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

Disk Loss and Disk Renewal Phases in Classical Be Stars I: Analysis of Long-Term Spectropolarimetric Data

(Abridged) Classical Be stars occasionally transition from having a gaseous circumstellar disk (''Be phase'') to a state in which all observational evidence for the presence of these disks disappears (''normal B-star phase''). We present one of the most comprehensive spectropolarimetric views to date of such a transition for two Be stars, pi Aquarii and 60 Cygni. 60 Cyg's disk loss episode was characterized by a monotonic decrease in emission strength over a time-scale of 1000 days, consistent with the viscous time-scale of the disk, assuming alpha is 0.14. pi Aqr's disk loss was episodic in nature and occurred over a time-scale of 2440 days. An observed time lag between the behavior of the polarization and H-alpha in both stars indicates the disk clearing proceeded in an ''inside-out'' manner. We determine the position angle of the intrinsic polarization to be 166.7 +/- 0.1 degrees for pi Aqr and 107.7 +/- 0.4 degrees for 60 Cyg, and model the observed polarization during the quiescent diskless phase of each star to determine the interstellar polarization along the line of sight. Minor outbursts observed during the quiescent phase of each star shared similar lifetimes as those previously reported for mu Cen, suggesting that the outbursts represent the injection and subsequent viscous dissipation of individual blobs of material into the inner circumstellar environments of these stars. We also observe deviations from the mean intrinsic polarization position angle during polarization outbursts in each star, indicating deviations from axisymmetry. We propose that these deviations might be indicative of the injection (and subsequent circularization) of new blobs into the inner disk, either in the plane of the bulk of the disk material or in a slightly inclined (non-coplanar) orbit.Comment: 30 pages, 14 figures; accepted in Ap

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

Autocalibrating and Calibrationless Parallel Magnetic Resonance Imaging as a Bilinear Inverse Problem

Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming Fourier-encoding steps by undersampling. The receive sensitivities are a priori unknown and influenced by geometry and electric properties of the (moving) subject. For optimal results, they need to be estimated jointly with the image from the same undersampled measurement data. Formulated as an inverse problem, this leads to a bilinear reconstruction problem related to multi-channel blind deconvolution. In this work, we will discuss some recently developed approaches for the solution of this problem.Comment: 3 pages, 3 figures, 12th International Conference on Sampling Theory and Applications, Tallinn 201