Alternative 2D Shape Representations using the Symmetry Set

Arjan Kuijper; Ole Fogh Olsen; Peter Giblin; Mads Nielsen

Alternative 2D Shape Representations using the Symmetry Set

Arjan Kuijper, Ole Fogh Olsen, Peter Giblin, Mads Nielsen

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

9 Citationer (Scopus)

Abstract

Udgivelsesdato: November

Originalsprog	Engelsk
Tidsskrift	Journal of Mathematical Imaging and Vision
Vol/bind	26
Udgave nummer	1-2
Sider (fra-til)	127-147
ISSN	0924-9907
Status	Udgivet - 2006
Udgivet eksternt	Ja

Bibliografisk note

Paper id:: 10.1007/s10851-006-8372-2

Citationsformater

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title = "Alternative 2D Shape Representations using the Symmetry Set",

abstract = "Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set . This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane. In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons. Second, alternative ways to visualize the are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure. Example shapes from a data base are shown and their data structures derived. ",

author = "Arjan Kuijper and Olsen, {Ole Fogh} and Peter Giblin and Mads Nielsen",

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TY - JOUR

T1 - Alternative 2D Shape Representations using the Symmetry Set

AU - Kuijper, Arjan

AU - Olsen, Ole Fogh

AU - Giblin, Peter

AU - Nielsen, Mads

N1 - Paper id:: 10.1007/s10851-006-8372-2

PY - 2006

Y1 - 2006

N2 - Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set . This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane. In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons. Second, alternative ways to visualize the are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure. Example shapes from a data base are shown and their data structures derived.

AB - Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set . This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane. In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons. Second, alternative ways to visualize the are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure. Example shapes from a data base are shown and their data structures derived.

M3 - Journal article

VL - 26

SP - 127

EP - 147

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 1-2

ER -