31,253 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
New Optimised Estimators for the Primordial Trispectrum
Cosmic microwave background studies of non-Gaussianity involving higher-order
multispectra can distinguish between early universe theories that predict
nearly identical power spectra. However, the recovery of higher-order
multispectra is difficult from realistic data due to their complex response to
inhomogeneous noise and partial sky coverage, which are often difficult to
model analytically. A traditional alternative is to use one-point cumulants of
various orders, which collapse the information present in a multispectrum to
one number. The disadvantage of such a radical compression of the data is a
loss of information as to the source of the statistical behaviour. A recent
study by Munshi & Heavens (2009) has shown how to define the skew spectrum (the
power spectra of a certain cubic field, related to the bispectrum) in an
optimal way and how to estimate it from realistic data. The skew spectrum
retains some of the information from the full configuration-dependence of the
bispectrum, and can contain all the information on non-Gaussianity. In the
present study, we extend the results of the skew spectrum to the case of two
degenerate power-spectra related to the trispectrum. We also explore the
relationship of these power-spectra and cumulant correlators previously used to
study non-Gaussianity in projected galaxy surveys or weak lensing surveys. We
construct nearly optimal estimators for quick tests and generalise them to
estimators which can handle realistic data with all their complexity in a
completely optimal manner. We show how these higher-order statistics and the
related power spectra are related to the Taylor expansion coefficients of the
potential in inflation models, and demonstrate how the trispectrum can
constrain both the quadratic and cubic terms.Comment: 19 pages, 2 figure
Multilinear Wavelets: A Statistical Shape Space for Human Faces
We present a statistical model for D human faces in varying expression,
which decomposes the surface of the face using a wavelet transform, and learns
many localized, decorrelated multilinear models on the resulting coefficients.
Using this model we are able to reconstruct faces from noisy and occluded D
face scans, and facial motion sequences. Accurate reconstruction of face shape
is important for applications such as tele-presence and gaming. The localized
and multi-scale nature of our model allows for recovery of fine-scale detail
while retaining robustness to severe noise and occlusion, and is
computationally efficient and scalable. We validate these properties
experimentally on challenging data in the form of static scans and motion
sequences. We show that in comparison to a global multilinear model, our model
better preserves fine detail and is computationally faster, while in comparison
to a localized PCA model, our model better handles variation in expression, is
faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201
3D weak lensing with spin wavelets on the ball
We construct the spin flaglet transform, a wavelet transform to analyze spin
signals in three dimensions. Spin flaglets can probe signal content localized
simultaneously in space and frequency and, moreover, are separable so that
their angular and radial properties can be controlled independently. They are
particularly suited to analyzing of cosmological observations such as the weak
gravitational lensing of galaxies. Such observations have a unique 3D
geometrical setting since they are natively made on the sky, have spin angular
symmetries, and are extended in the radial direction by additional distance or
redshift information. Flaglets are constructed in the harmonic space defined by
the Fourier-Laguerre transform, previously defined for scalar functions and
extended here to signals with spin symmetries. Thanks to various sampling
theorems, both the Fourier-Laguerre and flaglet transforms are theoretically
exact when applied to bandlimited signals. In other words, in numerical
computations the only loss of information is due to the finite representation
of floating point numbers. We develop a 3D framework relating the weak lensing
power spectrum to covariances of flaglet coefficients. We suggest that the
resulting novel flaglet weak lensing estimator offers a powerful alternative to
common 2D and 3D approaches to accurately capture cosmological information.
While standard weak lensing analyses focus on either real or harmonic space
representations (i.e., correlation functions or Fourier-Bessel power spectra,
respectively), a wavelet approach inherits the advantages of both techniques,
where both complicated sky coverage and uncertainties associated with the
physical modeling of small scales can be handled effectively. Our codes to
compute the Fourier-Laguerre and flaglet transforms are made publicly
available.Comment: 24 pages, 4 figures, version accepted for publication in PR
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