118,380 research outputs found
Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image
Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm
Methods for characterising microphysical processes in plasmas
Advanced spectral and statistical data analysis techniques have greatly
contributed to shaping our understanding of microphysical processes in plasmas.
We review some of the main techniques that allow for characterising fluctuation
phenomena in geospace and in laboratory plasma observations. Special emphasis
is given to the commonalities between different disciplines, which have
witnessed the development of similar tools, often with differing terminologies.
The review is phrased in terms of few important concepts: self-similarity,
deviation from self-similarity (i.e. intermittency and coherent structures),
wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres
Continuous Self-Similarity Breaking in Critical Collapse
This paper studies near-critical evolution of the spherically symmetric
scalar field configurations close to the continuously self-similar solution.
Using analytic perturbative methods, it is shown that a generic growing
perturbation departs from the critical Roberts solution in a universal way. We
argue that in the course of its evolution, initial continuous self-similarity
of the background is broken into discrete self-similarity with echoing period
, reproducing the symmetries of the critical
Choptuik solution.Comment: RevTeX 3.1, 28 pages, 5 figures; discussion rewritten to clarify
several issue
Long's Vortex Revisited
The conical self-similar vortex solution of Long (1961) is reconsidered, with
a view toward understanding what, if any, relationship exists between Long's
solution and the more-recent similarity solutions of Mayer and Powell (1992),
which are a rotational-flow analogue of the Falkner-Skan boundary-layer flows,
describing a self-similar axisymmetric vortex embedded in an external stream
whose axial velocity varies as a power law in the axial (z) coordinate, with
phi=r/z^n being the radial similarity coordinate and n the core growth rate
parameter. We show that, when certain ostensible differences in the
formulations and radial scalings are properly accounted for, the Long and
Mayer-Powell flows in fact satisfy the same system of coupled ordinary
differential equations, subject to different kinds of outer-boundary
conditions, and with Long's equations a special case corresponding to conical
vortex core growth, n=1 with outer axial velocity field decelerating in a 1/z
fashion, which implies a severe adverse pressure gradient. For pressure
gradients this adverse Mayer and Powell were unable to find any
leading-edge-type vortex flow solutions which satisfy a basic physicality
criterion based on monotonicity of the total-pressure profile of the flow, and
it is shown that Long's solutions also violate this criterion, in an extreme
fashion. Despite their apparent nonphysicality, the fact that Long's solutions
fit into a more general similarity framework means that nonconical analogues of
these flows should exist. The far-field asymptotics of these generalized
solutions are derived and used as the basis for a hybrid spectral-numerical
solution of the generalized similarity equations, which reveal the existence of
solutions for more modestly adverse pressure gradients than those in Long's
case, and which do satisfy the above physicality criterion.Comment: 30 pages, including 16 figure
The Similarity Hypothesis in General Relativity
Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
Self-Similarity in General Relativity \endtitle
The different kinds of self-similarity in general relativity are discussed,
with special emphasis on similarity of the ``first'' kind, corresponding to
spacetimes admitting a homothetic vector. We then survey the various classes of
self-similar solutions to Einstein's field equations and the different
mathematical approaches used in studying them. We focus mainly on spatially
homogenous and spherically symmetric self-similar solutions, emphasizing their
possible roles as asymptotic states for more general models. Perfect fluid
spherically symmetric similarity solutions have recently been completely
classified, and we discuss various astrophysical and cosmological applications
of such solutions. Finally we consider more general types of self-similar
models.Comment: TeX document, 53 page
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