On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric

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Standard

On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric. / Tatu, Aditya Jayant; Lauze, Francois Bernard; Sommer, Stefan Horst; Nielsen, Mads.

I: Journal of Mathematical Imaging and Vision, Bind 38, Nr. 3, 2010, s. 226-240.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Tatu, AJ, Lauze, FB, Sommer, SH & Nielsen, M 2010, 'On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric', Journal of Mathematical Imaging and Vision, bind 38, nr. 3, s. 226-240. https://doi.org/10.1007/s10851-010-0218-2

APA

Tatu, A. J., Lauze, F. B., Sommer, S. H., & Nielsen, M. (2010). On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric. Journal of Mathematical Imaging and Vision, 38(3), 226-240. https://doi.org/10.1007/s10851-010-0218-2

Vancouver

Tatu AJ, Lauze FB, Sommer SH, Nielsen M. On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric. Journal of Mathematical Imaging and Vision. 2010;38(3):226-240. https://doi.org/10.1007/s10851-010-0218-2

Author

Tatu, Aditya Jayant ; Lauze, Francois Bernard ; Sommer, Stefan Horst ; Nielsen, Mads. / On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric. I: Journal of Mathematical Imaging and Vision. 2010 ; Bind 38, Nr. 3. s. 226-240.

Bibtex

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title = "On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric",
abstract = "This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L 2-metric.We first show how to solve differential equations on a finite dimensional Riemannian manifold defined implicitly as a submanifold of a parameterized one, which in turn may be a Riemannian submanifold of an infinite dimensional one, using some optimal control techniques.We give an elementary example of the technique on a spherical submanifold of a 3-sphere and then a series of examples on a highly non-linear subspace of the space of closed spline curves, where we have restricted mean curvature motion, Geodesic Active contours and compute geodesic between two curves.",
keywords = "Faculty of Science",
author = "Tatu, {Aditya Jayant} and Lauze, {Francois Bernard} and Sommer, {Stefan Horst} and Mads Nielsen",
year = "2010",
doi = "10.1007/s10851-010-0218-2",
language = "English",
volume = "38",
pages = "226--240",
journal = "Journal of Mathematical Imaging and Vision",
issn = "0924-9907",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - On restricting planar curve evolution to finite dimensional implicit subspaces with non-Euclidean metric

AU - Tatu, Aditya Jayant

AU - Lauze, Francois Bernard

AU - Sommer, Stefan Horst

AU - Nielsen, Mads

PY - 2010

Y1 - 2010

N2 - This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L 2-metric.We first show how to solve differential equations on a finite dimensional Riemannian manifold defined implicitly as a submanifold of a parameterized one, which in turn may be a Riemannian submanifold of an infinite dimensional one, using some optimal control techniques.We give an elementary example of the technique on a spherical submanifold of a 3-sphere and then a series of examples on a highly non-linear subspace of the space of closed spline curves, where we have restricted mean curvature motion, Geodesic Active contours and compute geodesic between two curves.

AB - This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L 2-metric.We first show how to solve differential equations on a finite dimensional Riemannian manifold defined implicitly as a submanifold of a parameterized one, which in turn may be a Riemannian submanifold of an infinite dimensional one, using some optimal control techniques.We give an elementary example of the technique on a spherical submanifold of a 3-sphere and then a series of examples on a highly non-linear subspace of the space of closed spline curves, where we have restricted mean curvature motion, Geodesic Active contours and compute geodesic between two curves.

KW - Faculty of Science

U2 - 10.1007/s10851-010-0218-2

DO - 10.1007/s10851-010-0218-2

M3 - Journal article

VL - 38

SP - 226

EP - 240

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 3

ER -

ID: 23090366