On Canonical Parameterizations of 2D-Shapes
Document type :
Direction scientifique d'une publication (ouvrage, numéro spécial de revue, proceedings): Proceedings
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Title :
On Canonical Parameterizations of 2D-Shapes
Author(s) :
Tumpach, Alice Barbora [Directeur de publication]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut CNRS-PAULI [ICP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut CNRS-PAULI [ICP]
Conference title :
Geometric Science of Information
Journal title :
Lecture Notes in Computer Science
Publisher :
Springer Nature Switzerland
Publication place :
Cham
Publication date :
2023-08-01
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterization of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider ...
Show more >This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterization of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider other natural parameterizations like the parameterization proportional to the curvature of the curve. Both aforementionned parameterizations are very natural and correspond to a natural physical movement: the arc-length parameterization corresponds to travelling along the curve at constant speed, whereas parameterization proportional to curvature corresponds to a constant-speed moving frame. Since the curvature function of a curve is a geometric invariant of the unparameterized curve, a parameterization using the curvature function is a canonical parameterization. The main idea is that to any physically meaningful strictly increasing function is associated a natural parameterization of 2D-curves, which gives an optimal sampling, and which can be used to compare unparameterized curves in an efficient and pertinent way. An application to point correspondence in medical imaging is given.Show less >
Show more >This paper is devoted to the study of unparameterized simple curves in the plane. We propose diverse canonical parameterization of a 2D-curve. For instance, the arc-length parameterization is canonical, but we consider other natural parameterizations like the parameterization proportional to the curvature of the curve. Both aforementionned parameterizations are very natural and correspond to a natural physical movement: the arc-length parameterization corresponds to travelling along the curve at constant speed, whereas parameterization proportional to curvature corresponds to a constant-speed moving frame. Since the curvature function of a curve is a geometric invariant of the unparameterized curve, a parameterization using the curvature function is a canonical parameterization. The main idea is that to any physically meaningful strictly increasing function is associated a natural parameterization of 2D-curves, which gives an optimal sampling, and which can be used to compare unparameterized curves in an efficient and pertinent way. An application to point correspondence in medical imaging is given.Show less >
Language :
Anglais
Audience :
Internationale
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Source :
Submission date :
2025-01-24T14:06:43Z
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