Fundamental geodesic deformations in spaces of treelike shapes

Aasa Feragen; Francois Bernard Lauze; Mads Nielsen

doi:10.1109/ICPR.2010.513

Fundamental geodesic deformations in spaces of treelike shapes

Aasa Feragen, Francois Bernard Lauze, Mads Nielsen

Datalogisk Institut

4 Citationer (Scopus)

Abstract

This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees.

Originalsprog	Engelsk
Titel	20th International Conference on Pattern Recogniction - ICPR 2010
Antal sider	5
Forlag	IEEE
Publikationsdato	2010
Sider	2089-2093
ISBN (Trykt)	978-1-4244-7542-1
ISBN (Elektronisk)	978-1-4244-7541-4
DOI	https://doi.org/10.1109/ICPR.2010.513
Status	Udgivet - 2010
Begivenhed	20th International Conference on Pattern Recognition - Istanbul, Tyrkiet Varighed: 23 aug. 2010 → 26 aug. 2010

Konference

Konference	20th International Conference on Pattern Recognition
Land/Område	Tyrkiet
By	Istanbul
Periode	23/08/2010 → 26/08/2010

Adgang til dokumentet

10.1109/ICPR.2010.513

Citationsformater

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title = "Fundamental geodesic deformations in spaces of treelike shapes",

abstract = "This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees. ",

author = "Aasa Feragen and Lauze, {Francois Bernard} and Mads Nielsen",

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doi = "10.1109/ICPR.2010.513",

language = "English",

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AU - Lauze, Francois Bernard

AU - Nielsen, Mads

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AB - This paper presents a new geometric framework for analysis of planar treelike shapes for applications such as shape matching, recognition and morphology, using the geometry of the space of treelike shapes. Mathematically, the shape space is given the structure of a stratified set which is a quotient of a normed vector space with a metric inherited from the vector space norm. We give examples of geodesic paths in tree-space corresponding to fundamental deformations of small trees, and discuss how these deformations are key building blocks for understanding deformations between larger trees.

U2 - 10.1109/ICPR.2010.513

DO - 10.1109/ICPR.2010.513

M3 - Article in proceedings

SN - 978-1-4244-7542-1

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BT - 20th International Conference on Pattern Recogniction - ICPR 2010

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