Dissertationen online der Freien Universität Berlin


Shape Matching With Reference Points
Klein, Oliver

HaupttitelShape Matching With Reference Points
TitelvarianteGeometrische Mustererkennung mit Hilfe von Referenzpunkten
AutorKlein, Oliver
Geburtsort: Bergisch Gladbach
GutachterProf. Dr. Guenter Rote
weitere GutachterDr. Remco C. Veltkamp
Freie Schlagwörtercomputational geometry, shape matching, reference point
DDC006 Spezielle Methoden der Informatik
516 Geometrie
ZusammenfassungShape matching is an important topic in computational geometry,
computer vision, image retrieval, object recognition and robotics. For a fixed
distance measure D and a class of transformations T we can describe the
problem as follows: Given two shapes A and B in R^d, find a
transformation T^* in T, such that the distance between A and T^*(B) is
minimal among all transformations in T. Usually finding such a transformation
is computationally expensive, if at all possible. Thus we concentrate on
approximation algorithms. We follow an approach by Alt, Behrends and Blömer,
and Alt, Aichholzer and Rote. They use mappings called reference points to fix
the relative position between the two sets. A reference point is a
Lipschitz continuous mapping from the set of shapes into R^d which is
equivariant under the considered class of transformations.
This approach reduces the degrees of freedom of the underlying problem
by the dimension d.

In this thesis we study approximation algorithms for shape matching
with respect to various metrics, e.g., the Hausdorff distance, the
Earth Mover's Distance, the Monge-Kantorovich Distance and the
bottleneck distance. We investigate translations, rigid motions,
i.e., combinations of translations and rotations, and similarities,
i.e., combinations of rigid motions and scalings.

The basic structure of the approximation algorithms is the same for all
metrics and we describe our approach in an abstract reference point
framework. We first determine the relative position of the two shapes
to each other by computing their reference points. We then translate
the shapes such that the reference points coincide. Next we
determine a rotation for one of the shapes such that the distance of
the two shapes is at most a constant times
their optimal distance. Similarities can always
be dealt with by finding an approximate scaling before finding the
Dataobject from FUDISS_thesis_000000004258
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SeitenzahlXI, 133 S.
Fachbereich/EinrichtungFB Mathematik und Informatik
Rechte Nutzungsbedingungen
Tag der Disputation21.04.2008
Erstellt am10.07.2008 - 07:27:22
Letzte Änderung19.02.2010 - 10:41:37
Statische URLhttp://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000004258