12,439 research outputs found
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
Fourier Analysis of Stochastic Sampling Strategies for Assessing Bias and Variance in Integration
Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image.
We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.</jats:p
Imfit: A Fast, Flexible New Program for Astronomical Image Fitting
I describe a new, open-source astronomical image-fitting program called
Imfit, specialized for galaxies but potentially useful for other sources, which
is fast, flexible, and highly extensible. A key characteristic of the program
is an object-oriented design which allows new types of image components (2D
surface-brightness functions) to be easily written and added to the program.
Image functions provided with Imfit include the usual suspects for galaxy
decompositions (Sersic, exponential, Gaussian), along with Core-Sersic and
broken-exponential profiles, elliptical rings, and three components which
perform line-of-sight integration through 3D luminosity-density models of disks
and rings seen at arbitrary inclinations.
Available minimization algorithms include Levenberg-Marquardt, Nelder-Mead
simplex, and Differential Evolution, allowing trade-offs between speed and
decreased sensitivity to local minima in the fit landscape. Minimization can be
done using the standard chi^2 statistic (using either data or model values to
estimate per-pixel Gaussian errors, or else user-supplied error images) or
Poisson-based maximum-likelihood statistics; the latter approach is
particularly appropriate for cases of Poisson data in the low-count regime. I
show that fitting low-S/N galaxy images using chi^2 minimization and
individual-pixel Gaussian uncertainties can lead to significant biases in
fitted parameter values, which are avoided if a Poisson-based statistic is
used; this is true even when Gaussian read noise is present.Comment: pdflatex, 27 pages, 19 figures. Revised version, accepted by ApJ.
Programs, source code, and documentation available at:
http://www.mpe.mpg.de/~erwin/code/imfit
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
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