2,049 research outputs found
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
Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
The typical goal of surface remeshing consists in finding a mesh that is (1)
geometrically faithful to the original geometry, (2) as coarse as possible to
obtain a low-complexity representation and (3) free of bad elements that would
hamper the desired application. In this paper, we design an algorithm to
address all three optimization goals simultaneously. The user specifies desired
bounds on approximation error {\delta}, minimal interior angle {\theta} and
maximum mesh complexity N (number of vertices). Since such a desired mesh might
not even exist, our optimization framework treats only the approximation error
bound {\delta} as a hard constraint and the other two criteria as optimization
goals. More specifically, we iteratively perform carefully prioritized local
operators, whenever they do not violate the approximation error bound and
improve the mesh otherwise. In this way our optimization framework greedily
searches for the coarsest mesh with minimal interior angle above {\theta} and
approximation error bounded by {\delta}. Fast runtime is enabled by a local
approximation error estimation, while implicit feature preservation is obtained
by specifically designed vertex relocation operators. Experiments show that our
approach delivers high-quality meshes with implicitly preserved features and
better balances between geometric fidelity, mesh complexity and element quality
than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization
and Computer Graphic
Structure in the 3D Galaxy Distribution: I. Methods and Example Results
Three methods for detecting and characterizing structure in point data, such
as that generated by redshift surveys, are described: classification using
self-organizing maps, segmentation using Bayesian blocks, and density
estimation using adaptive kernels. The first two methods are new, and allow
detection and characterization of structures of arbitrary shape and at a wide
range of spatial scales. These methods should elucidate not only clusters, but
also the more distributed, wide-ranging filaments and sheets, and further allow
the possibility of detecting and characterizing an even broader class of
shapes. The methods are demonstrated and compared in application to three data
sets: a carefully selected volume-limited sample from the Sloan Digital Sky
Survey redshift data, a similarly selected sample from the Millennium
Simulation, and a set of points independently drawn from a uniform probability
distribution -- a so-called Poisson distribution. We demonstrate a few of the
many ways in which these methods elucidate large scale structure in the
distribution of galaxies in the nearby Universe.Comment: Re-posted after referee corrections along with partially re-written
introduction. 80 pages, 31 figures, ApJ in Press. For full sized figures
please download from: http://astrophysics.arc.nasa.gov/~mway/lss1.pd
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd
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