Abstract
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/s10851-006-8372-2Citationsformater
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Alternative 2D Shape Representations using the Symmetry Set. / Kuijper, Arjan; Olsen, Ole Fogh; Giblin, Peter; Nielsen, Mads.
I: Journal of Mathematical Imaging and Vision, Bind 26, Nr. 1-2, 2006, s. 127-147.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review
}
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 -