315,177 research outputs found
k-dimensional Size Functions for shape description and comparison
This paper advises the use of k-dimensional size functions for comparison and retrieval in the context of multidimensional shapes, where by shape we mean something in two or higher dimensions having a visual appearance. The attractive feature of k-dimensional size functions is that they allow to readily establish a similarity measure between shapes of arbitrary dimension, taking into account different properties expressed by a multivalued real function defined on the shape. This task is achieved through a particular projection of k-dimensional size functions into the
1-dimensional case. Therefore, previous results on the stability for matching purposes become applicable to a wider range of data. We outline the potential of our approach in a series of experiments
Formenvergleich in höheren Dimensionen
Cover and Contents
1 Introduction
1.1 Overview
1.2 Credits
2 Preliminaries
2.1 Representation of Shapes
2.2 Distance Measures
2.3 Miscellaneous
3 Hausdorff Distance Under Translations
3.1 Overview
3.2 Basic Properties of \delta;->H
3.3 Matching Points to Sites
3.4 Matching Two Sets of Sites
3.5 Approximate Algorithms
4 Matching Special Shape Classes Under Translations
4.1 Matching Terrains
4.2 Matching Convex Polyhedra
5 Matching Curves with respect to the Fréchet Distance
5.1 Basic Properties of the Fréchet Distance
5.2 Polygonal Curves Under Translations
5.3 Polygonal Curves Under Affine Transformations
5.4 Variants
6 Matching a Polygonal Curve in a Graph of Curves
6.1 Problem Statement
6.2 Algorithm
6.3 Variants
Bibliography
Index
A Zusammenfassung
B LebenslaufThe comparison of geometric shapes is a task which naturally arises in many
applications, such as in computer vision, computer aided design, robotics,
medical imaging, etc. Usually geometric shapes are represented by a number of
simple objects (sites) that either describe the boundary of the shape, or the
whole shape itself. Sites are often chosen to be linear objects, such as line
segments, triangles, or simplices in general, since linear objects are easier
to handle in algorithms. But sometimes also patches of algebraic curves or
surfaces, such as circular arcs or portions of spheres or cylinders are of
interest. In order to compare two shapes we need to have a notion of
similarity or dissimilarity, which arises from the desired application. There
is a large variety of different similarity measures. Popular similarity
notions are, for example, the Hausdorff distance, the area of symmetric
difference, or especially for curves the turn-angle distance, or the Fréchet
distance. The application usually supplies a distance measure, and furthermore
a set of allowed transformations, and the task is to find a transformation
that, when applied to the first object, minimizes the distance to the second
one. Typical transformation classes are translations, rotations, and rigid
motions (which are combinations of translations and rotations).
The contribution of this thesis consists of several algorithms for matching
simplicial shapes in dimensions d >= 2. The shapes are either represented as
sets of simplicial objects or as polygonal curves with a given
parametrization. The considered distance measures are mainly the Hausdorff
distance and the Fréchet distance. In the literature most matching algorithms
either attack two-dimensional problems, or consider finite point sets in
higher dimensions. In the first half of this thesis we present results for the
Hausdorff distance in d >= 2 dimensions under translations, for a rather
general notion of simplicial shapes, as well as for some special shape classes
which allow to speed up the computations. In the second half of this thesis we
investigate the Fréchet distance for polygonal curves. The Fréchet distance is
a natural distance measure for curves, but has not been investigated much in
the literature. We present the first algorithms to optimize the Fréchet
distance under various transformation classes for polygonal curves in
arbitrary dimensions. In the last chapter we consider a partial matching
variant in which a geometric graph and another curve are given, and we show
how to find a polygonal path in the graph which minimizes the Fréchet distance
to the curve.Das Vergleichen zweier geometrischer Formen ist eine Aufgabe, die aus
vielerlei Anwendungen natĂĽrlich hervorgeht. Einige Anwendungen sind Computer
Vision, Computer Graphik, Computer Aided Design, Robotics, medizinische
Bilderverarbeitung, etc. Normalerweise werden geometrische Formen aus
einfacheren Objekten zusammengesetzt, die entweder den Rand der Form oder die
ganze Form ansich beschreiben. Oft verwendet werden lineare Objekte wie
Strecken, Dreicke, oder Simplizes in höheren Dimensionen. Um zwei Formen zu
vergleichen braucht man zunächst einen Ähnlichkeits- oder Abstandsbegriff
zwischen zwei Formen, der in der Regel aus der jeweiligen Anwendung
hervorgeht. Naturgemäß gibt es eine große Vielfalt solcher Abstandsmaße; eines
der natĂĽrlichsten ist der Hausdorff-Abstand. Weiterhin gibt die Anwendung in
der Regel eine Menge von Transformationen vor, und möchte eine Transformation
finden, die, angewandt auf die erste Form, den Abstand zur zweiten Form
minimiert. Diese Aufgabe wird als Matching bezeichnet. Oft verwendete
Transformationsklassen sind zum Beispiel Translationen, Rotationen und starre
Bewegungen (Kombinationen von Translationen und Rotationen).
Diese Arbeit beschäftigt sich mit dem Matching von geometrischen Formen in
Dimensionen d >= 2, die aus stĂĽckweise linearen Objekten bestehen. Die Formen
sind entweder als Mengen solcher Objekte, oder als PolygonzĂĽge, die als
parametrisierte Kurven aufgefaĂźt werden, beschrieben. Als AbstandsmaĂźe werden
hauptsächlich der Hausdorff-Abstand und der Fréchet-Abstand betrachtet.
Bisherige Ergebnisse fĂĽr das Matching von Formen behandeln in der Regel
entweder zweidimensionale Formen, oder Punktmengen in höheren Dimensionen. Die
erste Hälfte dieser Dissertation präsentiert Ergebnisse für den Hausdorff-
Abstand in d >= 2 Dimensionen unter Translationen fĂĽr einen allgemein
gehaltenen Formenbegriff, sowie fĂĽr einige spezielle Klassen geometrischer
Formen, die eine schnellere Berechnung erlauben. Die zweite Hälfte der
Dissertation beschäftigt sich mit dem Matching von parametrisierten Kurven
bezüglich des Fréchet-Abstandes. Obwohl der Fréchet-Abstand ein natürliches
AbstandsmaĂź fĂĽr Kurven darstellt, gibt es bisher diesbezĂĽglich wenig
Ergebnisse in der Literatur. FĂĽr parametrisierte Kurven in d >= 2 Dimensionen
wird in dieser Dissertation ein Matching-Algorithmus vorgestellt, der unter
Translationen und relativ allgemein gehaltenen Teilmengen der affinen
Abbildungen den Fréchet-Abstand minimiert. Als letztes Ergebnis wird eine
weitere Matching-Variante bezüglich des Fréchet-Abstandes vorgestellt, in der
eine Teilkurve in in einem eingebetteten planaren Graphens gefunden werden
soll, die den Fréchet-Abstand zu einer gegebenen Kurve minimiert
SPIDA: Abstracting and generalizing layout design cases
Abstraction and generalization of layout design cases generate new knowledge that is more widely applicable to use than specific design cases. The abstraction and generalization of design cases into hierarchical levels of abstractions provide the designer with the flexibility to apply any level of abstract and generalized knowledge for a new layout design problem. Existing case-based layout learning (CBLL) systems abstract and generalize cases into single levels of abstractions, but not into a hierarchy. In this paper, we propose a new approach, termed customized viewpoint - spatial (CV-S), which supports the generalization and abstraction of spatial layouts into hierarchies along with a supporting system, SPIDA (SPatial Intelligent Design Assistant)
Wideband P-Shaped Dielectric Resonator Antenna
A novel P-shaped dielectric resonator antenna (DRA) is presented and investigated for wideband wireless application. By using P-shaped resonator, a wideband impedance bandwidth of 80% from 3.5 to 8.2 GHz is achieved. The antenna covers all of wireless systems like C-band, 5.2, 5.5 & 5.8 GHz-WLAN & WiMax. The proposed antenna has a low profile and the thickness of the resonator is only 5.12 mm, which is 0.06-0.14 free space wavelength. A parametric study is presented. The proposed DRA is built and the characteristics of the antenna are measured. Very good agreement between numerical and measured results is obtained
Kaluza-Klein States versus Winding States: Can Both Be Above the String Scale?
When closed strings propagate in extra compactified dimensions, a rich
spectrum of Kaluza-Klein states and winding states emerges. Since the masses of
Kaluza-Klein states and winding states play a reciprocal role, it is often
believed that either the lightest Kaluza-Klein states or the lightest winding
states must be at or below the string scale. In this paper, we demonstrate that
this conclusion is no longer true for compactifications with non-trivial shape
moduli. Specifically, we demonstrate that toroidal compactifications exist for
which all Kaluza-Klein states as well as all winding states are heavier than
the string scale. This observation could have important phenomenological
implications for theories with reduced string scales, suggesting that it is
possible to cross the string scale without detecting any states associated with
spacetime compactification.Comment: 8 pages, LaTeX, no figure
A precise determination of alpha_s from LEP thrust data using effective field theory
Starting from a factorization theorem in Soft-Collinear Effective Theory, the
thrust distribution in e+e- collisions is calculated including resummation of
the next-to-next-to-next-to leading logarithms. This is a significant
improvement over previous calculations which were only valid to next-to-leading
logarithmic order. The fixed-order expansion of the resummed result approaches
the exact fixed-order distribution towards the kinematic endpoint. This close
agreement provides a verification of both the effective field theory expression
and recently completed next-to-next-to-leading fixed order event shapes. The
resummed distribution is then matched to fixed order, resulting in a
distribution valid over a large range of thrust. A fit to ALEPH and OPAL data
from LEP 1 and LEP 2 produces alpha_s(m_Z)= 0.1172 +/- 0.0010 +/- 0.0008
+/-0.0012 +/- 0.0012, where the uncertainties are respectively statistical,
systematic, hadronic, and perturbative. This is one of the world's most precise
extractions of alpha_s to date.Comment: 37 pages, 12 figures; v2: hadronization discussion and appendices
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