656 research outputs found
S2LET: A code to perform fast wavelet analysis on the sphere
We describe S2LET, a fast and robust implementation of the scale-discretised
wavelet transform on the sphere. Wavelets are constructed through a tiling of
the harmonic line and can be used to probe spatially localised, scale-depended
features of signals on the sphere. The scale-discretised wavelet transform was
developed previously and reduces to the needlet transform in the axisymmetric
case. The reconstruction of a signal from its wavelets coefficients is made
exact here through the use of a sampling theorem on the sphere. Moreover, a
multiresolution algorithm is presented to capture all information of each
wavelet scale in the minimal number of samples on the sphere. In addition S2LET
supports the HEALPix pixelisation scheme, in which case the transform is not
exact but nevertheless achieves good numerical accuracy. The core routines of
S2LET are written in C and have interfaces in Matlab, IDL and Java. Real
signals can be written to and read from FITS files and plotted as Mollweide
projections. The S2LET code is made publicly available, is extensively
documented, and ships with several examples in the four languages supported. At
present the code is restricted to axisymmetric wavelets but will be extended to
directional, steerable wavelets in a future release.Comment: 8 pages, 6 figures, version accepted for publication in A&A. Code is
publicly available from http://www.s2let.or
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
Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation
Copyright @ 2011 Shadi AlZubi et al. This article has been made available through the Brunel Open Access Publishing Fund.The experimental study presented in this paper is aimed at the development of an automatic image segmentation system for classifying region of interest (ROI) in medical images which are obtained from different medical scanners such as PET, CT, or MRI. Multiresolution analysis (MRA) using wavelet, ridgelet, and curvelet transforms has been used in the proposed segmentation system. It is particularly a challenging task to classify cancers in human organs in scanners output using shape or gray-level information; organs shape changes throw different slices in medical stack and the gray-level intensity overlap in soft tissues. Curvelet transform is a new extension of wavelet and ridgelet transforms which aims to deal with interesting phenomena occurring along curves. Curvelet transforms has been tested on medical data sets, and results are compared with those obtained from the other transforms. Tests indicate that using curvelet significantly improves the classification of abnormal tissues in the scans and reduce the surrounding noise
Decomposition of Integral Self-Affine Multi-Tiles
In this paper, we propose a method to decompose an integral self-affine
-tiling set into measure disjoint pieces satisfying
in such a way that the collection of sets
forms an integral self-affine collection associated with the matrix and
this with a minimum number of pieces . When used on a given measurable
-tiling set , this decomposition terminates
after finitely many steps if and only if the set is an integral self-affine
multi-tile. Furthermore, we show that the minimal decomposition we provide is
unique.Comment: 15pages, 5figures, added references, typo correction
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