7,724 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
Cosmic velocity--gravity relation in redshift space
We propose a simple way to estimate the parameter beta = Omega_m^(0.6)/b from
three-dimensional galaxy surveys. Our method consists in measuring the relation
between the cosmological velocity and gravity fields, and thus requires
peculiar velocity measurements. The relation is measured *directly in redshift
space*, so there is no need to reconstruct the density field in real space. In
linear theory, the radial components of the gravity and velocity fields in
redshift space are expected to be tightly correlated, with a slope given, in
the distant observer approximation, by g / v = (1 + 6 beta / 5 + 3 beta^2 /
7)^(1/2) / beta. We test extensively this relation using controlled numerical
experiments based on a cosmological N-body simulation. To perform the
measurements, we propose a new and rather simple adaptive interpolation scheme
to estimate the velocity and the gravity field on a grid. One of the most
striking results is that nonlinear effects, including `fingers of God', affect
mainly the tails of the joint probability distribution function (PDF) of the
velocity and gravity field: the 1--1.5 sigma region around the maximum of the
PDF is *dominated by the linear theory regime*, both in real and redshift
space. This is understood explicitly by using the spherical collapse model as a
proxy of nonlinear dynamics. Applications of the method to real galaxy catalogs
are discussed, including a preliminary investigation on homogeneous (volume
limited) `galaxy' samples extracted from the simulation with simple
prescriptions based on halo and sub-structure identification, to quantify the
effects of the bias between the galaxy and the total matter distibution, and of
shot noise (ABRIDGED).Comment: 24 pages, 10 figures. Matches the version accepted for publication in
MNRAS. The definitive version is available at
http://www.blackwell-synergy.co
BLADE: Filter Learning for General Purpose Computational Photography
The Rapid and Accurate Image Super Resolution (RAISR) method of Romano,
Isidoro, and Milanfar is a computationally efficient image upscaling method
using a trained set of filters. We describe a generalization of RAISR, which we
name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable
edge-adaptive filtering framework that is general, simple, computationally
efficient, and useful for a wide range of problems in computational
photography. We show applications to operations which may appear in a camera
pipeline including denoising, demosaicing, and stylization
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