567 research outputs found
Measuring linearity of open planar curve segments
In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure
Improving polygonal hybrid systems reachability analysis through the use of the phase portrait
Polygonal hybrid systems (SPDI) are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. The computation of certain objects of the phase portrait of an SPDI, namely the viability, controllability, invariance kernels and semi-separatrix curves have been shown to be eciently decidable. On the other hand, although the reachability problem for SPDIs is known to be decidable, its complexity makes it unfeasible on large systems. We summarise our recent results on the use of the SPDI phase portraits for improving reachability analysis by (i) state-space reduction and (ii) decomposition techniques of the state space, enabling compositional parallelisation of the analysis. Both techniques contribute to increasing the feasability of reachability analysis on large SPDI systems.peer-reviewe
Static analysis of SPDIs for state-space reduction
Polygonal hybrid systems (SPDI) are a subclass of planar hybrid
automata which can be represented by piecewise constant differential
inclusions. The reachability problem as well as the computation of certain objects of the phase portrait, namely the viability, controllability
and invariance kernels, for such systems is decidable. In this paper
we show how to compute another object of an SPDI phase portrait,
namely semi-separatrix curves and show how the phase portrait can
be used for reducing the state-space for optimizing the reachability
analysis.peer-reviewe
Turning function and shape recognition
The technique of turning function is a powerful method for measuring similarity between two dimensional shapes. The method works well when the boundary of the shape does not contain noise edges. We propose an algorithm for smoothing noise edges by decomposing the boundary into monotone components and smoothing the noise edges in each component. We also present an implementation of the proposed smoothing algorithm
Trends in Mathematical Imaging and Surface Processing
Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments
Semiclassical Treatment of Diffraction in Billiard Systems with a Flux Line
In billiard systems with a flux line semiclassical approximations for the
density of states contain contributions from periodic orbits as well as from
diffractive orbits that are scattered on the flux line. We derive a
semiclassical approximation for diffractive orbits that are scattered once on a
flux line. This approximation is uniformly valid for all scattering angles. The
diffractive contributions are necessary in order that semiclassical
approximations are continuous if the position of the flux line is changed.Comment: LaTeX, 17 pages, 4 figure
The semiclassical tool in mesoscopic physics
Semiclassical methods are extremely valuable in the study of transport and
thermodynamical properties of ballistic microstructures. By expressing the
conductance in terms of classical trajectories, we demonstrate that quantum
interference phenomena depend on the underlying classical dynamics of
non-interacting electrons. In particular, we are able to calculate the
characteristic length of the ballistic conductance fluctuations and the weak
localization peak in the case of chaotic dynamics. Integrable cavities are not
governed by single scales, but their non-generic behavior can also be obtained
from semiclassical expansions (over isolated trajectories or families of
trajectories, depending on the system). The magnetic response of a
microstructure is enhanced with respect to the bulk (Landau) susceptibility,
and the semiclassical approach shows that this enhancement is the largest for
integrable geometries, due to the existence of families of periodic orbits. We
show how the semiclassical tool can be adapted to describe weak residual
disorder, as well as the effects of electron-electron interactions. The
interaction contribution to the magnetic susceptibility also depends on the
nature of the classical dynamics of non-interacting electrons, and is
parametrically larger in the case of integrable systems.Comment: Latex, Cimento-varenna style, 82 pages, 21 postscript figures;
lectures given in the CXLIII Course "New Directions in Quantum Chaos" on the
International School of Physics "Enrico Fermi"; Varenna, Italy, July 1999; to
be published in Proceeding
Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
Investigations of emergent symmetry breaking phenomena occurring in small
finite-size systems are reviewed, with a focus on the strongly correlated
regime of electrons in two-dimensional semicoductor quantum dots and trapped
ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize
universal aspects and similarities of symmetry breaking found in these systems,
as well as in more traditional fields like nuclear physics and quantum
chemistry, which are characterized by very different interparticle forces. A
unified description of strongly correlated phenomena in finite systems of
repelling particles (whether fermions or bosons) is presented through the
development of a two-step method of symmetry breaking at the unrestricted
Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock
projection techniques. Quantitative and qualitative aspects of the two-step
method are treated and validated by exact diagonalization calculations.
Strongly-correlated phenomena emerging from symmetry breaking include: (I)
Chemical bonding, dissociation, and entanglement (at zero and finite magnetic
fields) in quantum dot molecules and in pinned electron molecular dimers formed
within a single anisotropic quantum dot. (II) Electron crystallization, with
particle localization on the vertices of concentric polygonal rings, and
formation of rotating electron molecules (REMs) in circular quantum dots. (III)
At high magnetic fields, the REMs are described by parameter-free analytic wave
functions, which are an alternative to the Laughlin and composite-fermion
approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating
traps and in analogy with the REMs, such repelling bosons form rotating boson
molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4.
95 pages with 37 color figures. To download a copy with high-quality figures,
go to publication #82 in http://www.prism.gatech.edu/~ph274cy
Correspondence of three-dimensional objects
First many thanks go to Prof. Hans du Buf, for his supervision based
on his experience, for providing a stimulating and cheerful research environment
in his laboratory, for letting me participate in the projects that
produced results for papers, thus made me more aware of the state of the
art in Computer Vision, especially in the area of 3D recognition. Also for
his encouraging support and his way to always nd time for discussions,
and last but not the least for the cooking recipes...
Many thanks go also to my laboratory fellows, to Jo~ao Rodrigues, who
invited me to participate in FCT and QREN projects, Jaime Carvalho
Martins and Miguel Farrajota, for discussing scienti c and technical
problems, but also almost all problems in the world.
To all persons, that worked in, or visited the Vision Laboratory, especially
those with whom I have worked with, almost on a daily basis.
A special thanks to the Instituto Superior de Engenharia at UAlg and
my colleagues at the Department of Electrical Engineering, for allowing
me to suspend lectures in order to be present at conferences.
To my family, my wife and my kids
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