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

Department of Computer Science

4 Citations (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.

Original language	English
Title of host publication	20th International Conference on Pattern Recogniction - ICPR 2010
Number of pages	5
Publisher	IEEE
Publication date	2010
Pages	2089-2093
ISBN (Print)	978-1-4244-7542-1
ISBN (Electronic)	978-1-4244-7541-4
DOIs	https://doi.org/10.1109/ICPR.2010.513
Publication status	Published - 2010
Event	20th International Conference on Pattern Recognition - Istanbul, Turkey Duration: 23 Aug 2010 → 26 Aug 2010

Conference

Conference	20th International Conference on Pattern Recognition
Country/Territory	Turkey
City	Istanbul
Period	23/08/2010 → 26/08/2010

Access to Document

10.1109/ICPR.2010.513

Cite this

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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. ",

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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.

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