Geodesic
Level set driven smooth curve approximation from unorganized or noisy point set
A. Claisse1 ; P. Frey1, 2
1 UPMC Univ Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005 Paris, France.
2 Universidad de Chile, UMI 2807, Centro de Modelamiento Matemático, Santiago, Chile.
ESAIM. Proceedings, Tome 27 (2009), pp. 254-271 Cet article a éte moissonné depuis la source EDP Sciences

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In this paper, we propose a curve construction method for a non uniform point data set based on a minimal curve approximation model. Numerically, the level set method is used for curve reconstruction. We represent the shape of the curve through its distance function and formulate curve reconstruction as a constrained minimization problem. We solve the minimization problem on a highly anisotropic triangulation to improve the accuracy of the numerical scheme. This method can handle complex geometries and deal with arbitrary topologies as well as with noisy data sets. Several numerical examples are provided to show the efficiency of the proposed approach.
DOI : 10.1051/proc/2009031

A. Claisse 1 ; P. Frey 1, 2

1 UPMC Univ Paris 06, UMR 7598, Laboratoire J.-L. Lions, F-75005 Paris, France.
2 Universidad de Chile, UMI 2807, Centro de Modelamiento Matemático, Santiago, Chile. 
@article{EP_2009_27_a14,
     author = {A. Claisse and P. Frey},
     title = {Level set driven smooth curve approximation from unorganized or noisy point set},
     journal = {ESAIM. Proceedings},
     pages = {254--271},
     year = {2009},
     volume = {27},
     doi = {10.1051/proc/2009031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009031/}
}
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A. Claisse; P. Frey. Level set driven smooth curve approximation from unorganized or noisy point set. ESAIM. Proceedings, Tome 27 (2009), pp. 254-271. doi: 10.1051/proc/2009031

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