6,509 research outputs found
Detecting Rotational Symmetries
Abstract We present an algorithm for detecting multiple rotational symmetries in natural images. Give
Involutions of polynomially parametrized surfaces
We provide an algorithm for detecting the involutions leaving a surface
defined by a polynomial parametrization invariant. As a consequence, the
symmetry axes, symmetry planes and symmetry center of the surface, if any, can
be determined directly from the parametrization, without computing or making
use of the implicit representation. The algorithm is based on the fact, proven
in the paper, that any involution of the surface comes from an involution of
the parameter space (the real plane, in our case); therefore, by determining
the latter, the former can be found. The algorithm has been implemented in the
computer algebra system Maple 17. Evidence of its efficiency for moderate
degrees, examples and a complexity analysis are also given
Symmetries in Images on Ancient Seals
We discuss the presence of symmetries in images engraved on ancient seals, in
particular on stamp seals. Used to stamp decorations, to secure the containers
from tampering and for owner's identification, we can find seals that can be
dated from Neolithic times. Earliest seals were engraved with lines, dots and
spirals. Nevertheless, these very ancient stamp seals, in the small circular or
ovoid space of their bases, possess bilateral and rotational symmetries. The
shape of the base seems to determine the symmetries of images engraved on it.
We will also discuss what could be the meaning of antisymmetry and broken
symmetry for images on seals.Comment: CogPrints, University of Southampton, ID6221, 16 October 200
Geometric and form feature recognition tools applied to a design for assembly methodology
The paper presents geometric tools for an automated Design for Assembly (DFA) assessment system. For each component in an assembly a two step features search is performed: firstly (using the minimal bounding box) mass, dimensions and symmetries are identified allowing the part to be classified, according to DFA convention, as either rotational or prismatic; secondly form features are extracted allowing an effective method of mechanised orientation to be determined. Together these algorithms support the fuzzy decision support system, of an assembly-orientated CAD system known as FuzzyDFA
Digital spiral object identification using random light
Photons that are entangled or correlated in orbital angular momentum have
been extensively used for remote sensing, object identification and imaging. It
has recently been demonstrated that intensity fluctuations give rise to the
formation of correlations in the orbital angular momentum components and
angular positions of random light. Here, we demonstrate that the spatial
signatures and phase information of an object, with rotational symmetries, can
be identified using classical orbital angular momentum correlations in random
light. The Fourier components imprinted in the digital spiral spectrum of the
object, measured through intensity correlations, unveil its spatial and phase
information. Sharing similarities with conventional compressive sensing
protocols that exploit sparsity to reduce the number of measurements required
to reconstruct a signal, our technique allows sensing of an object with fewer
measurements than other schemes that use pixel-by-pixel imaging. One remarkable
advantage of our technique is the fact that it does not require the preparation
of fragile quantum states of light and works at both low- and high-light
levels. In addition, our technique is robust against environmental noise, a
fundamental feature of any realistic scheme for remote sensing.Comment: 5 pages, 4 figure
Beyond basis invariants
Physical observables cannot depend on the basis one chooses to describe
fields. Therefore, all physically relevant properties of a model are, in
principle, expressible in terms of basis-invariant combinations of the
parameters. However, in many cases it becomes prohibitively difficult to
establish key physical features exclusively in terms of basis invariants. Here,
we advocate an alternative route in such cases: the formulation of
basis-invariant statements in terms of basis-covariant objects. We give several
examples where the basis-covariant path is superior to the traditional approach
in terms of basis invariants. In particular, this includes the formulation of
necessary and sufficient basis-invariant conditions for various physically
distinct forms of CP conservation in two- and three-Higgs-doublet models.Comment: 20 pages, no figure
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