8,331 research outputs found
A Novel Active Contour Model for Texture Segmentation
Texture is intuitively defined as a repeated arrangement of a basic pattern
or object in an image. There is no mathematical definition of a texture though.
The human visual system is able to identify and segment different textures in a
given image. Automating this task for a computer is far from trivial. There are
three major components of any texture segmentation algorithm: (a) The features
used to represent a texture, (b) the metric induced on this representation
space and (c) the clustering algorithm that runs over these features in order
to segment a given image into different textures. In this paper, we propose an
active contour based novel unsupervised algorithm for texture segmentation. We
use intensity covariance matrices of regions as the defining feature of
textures and find regions that have the most inter-region dissimilar covariance
matrices using active contours. Since covariance matrices are symmetric
positive definite, we use geodesic distance defined on the manifold of
symmetric positive definite matrices PD(n) as a measure of dissimlarity between
such matrices. We demonstrate performance of our algorithm on both artificial
and real texture images
Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
In this paper, we review our novel information geometrodynamical approach to
chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of
our information-geometrodynamical entropy (IGE) as an indicator of chaoticity
in a simple application. Furthermore, knowing that integrable and chaotic
quantum antiferromagnetic Ising chains are characterized by asymptotic
logarithmic and linear growths of their operator space entanglement entropies,
respectively, we apply our IGAC to present an alternative characterization of
such systems. Remarkably, we show that in the former case the IGE exhibits
asymptotic logarithmic growth while in the latter case the IGE exhibits
asymptotic linear growth. At this stage of its development, IGAC remains an
ambitious unifying information-geometric theoretical construct for the study of
chaotic dynamics with several unsolved problems. However, based on our recent
findings, we believe it could provide an interesting, innovative and
potentially powerful way to study and understand the very important and
challenging problems of classical and quantum chaos.Comment: 21 page
Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference
Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page
Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
In this Letter, we propose a novel information-geometric characterization of
chaotic (integrable) energy level statistics of a quantum antiferromagnetic
Ising spin chain in a tilted (transverse) external magnetic field. Finally, we
conjecture our results might find some potential physical applications in
quantum energy level statistics.Comment: 9 pages, added correct journal referenc
Scale relativity and fractal space-time: theory and applications
In the first part of this contribution, we review the development of the
theory of scale relativity and its geometric framework constructed in terms of
a fractal and nondifferentiable continuous space-time. This theory leads (i) to
a generalization of possible physically relevant fractal laws, written as
partial differential equation acting in the space of scales, and (ii) to a new
geometric foundation of quantum mechanics and gauge field theories and their
possible generalisations. In the second part, we discuss some examples of
application of the theory to various sciences, in particular in cases when the
theoretical predictions have been validated by new or updated observational and
experimental data. This includes predictions in physics and cosmology (value of
the QCD coupling and of the cosmological constant), to astrophysics and
gravitational structure formation (distances of extrasolar planets to their
stars, of Kuiper belt objects, value of solar and solar-like star cycles), to
sciences of life (log-periodic law for species punctuated evolution, human
development and society evolution), to Earth sciences (log-periodic
deceleration of the rate of California earthquakes and of Sichuan earthquake
replicas, critical law for the arctic sea ice extent) and tentative
applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the
Evolution and Development of the Universe,8th - 9th October 2008, Paris,
Franc
The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models
We present an analytical computation of the asymptotic temporal behavior of
the information geometric complexity (IGC) of finite-dimensional Gaussian
statistical manifolds in the presence of microcorrelations (correlations
between microvariables). We observe a power law decay of the IGC at a rate
determined by the correlation coefficient. It is found that microcorrelations
lead to the emergence of an asymptotic information geometric compression of the
statistical macrostates explored by the system at a faster rate than that
observed in absence of microcorrelations. This finding uncovers an important
connection between (micro)-correlations and (macro)-complexity in Gaussian
statistical dynamical systems.Comment: 12 pages; article in press, Physica A (2010)
Vlasov moments, integrable systems and singular solutions
The Vlasov equation for the collisionless evolution of the single-particle
probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian
system. Remarkably, the operation of taking the moments of the Vlasov PDF
preserves the Lie-Poisson structure. The individual particle motions correspond
to singular solutions of the Vlasov equation. The paper focuses on singular
solutions of the problem of geodesic motion of the Vlasov moments. These
singular solutions recover geodesic motion of the individual particles.Comment: 16 pages, no figures. Submitted to Phys. Lett.
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