Geodesic
Shape deformation and optimal control
Sylvain Arguillère1 ; Emmanuel Trélat2 ; Alain Trouvé3 ; Laurent Younès4
1 Université Pierre et Marie Curie (Univ. Paris 6), CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
2 Université Pierre et Marie Curie (Univ. Paris 6) and Institut Universitaire de France and Team GECO Inria Saclay, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
3 Ecole Normale Supérieure de Cachan, Centre de Mathématiques et Leurs Applications, CMLA, 61 av. du Pdt Wilson, F-94235 Cachan Cedex, France
4 Johns Hopkins University, Center for Imaging Science, Department of Applied Mathematics and Statistics, Clark 324C, 3400 N. Charles st. Baltimore, MD 21218, USA
ESAIM. Proceedings, Tome 45 (2014), pp. 300-307.

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Shape deformation analysis is concerned with determining a deformation of a given shape into another one, which is optimal for a certain cost. We provide the main ideas for a new general approach to shape deformation analysis, using the framework of optimal control theory. This point of view can be made independent from the parametrization of the shape, and allows to model general constrained shape analysis problems. The use of a infinite dimensional variant of the constrained Pontryagin Maximum Principle characterizes the optimal solutions of the shape deformation problem in a very general way.
DOI : 10.1051/proc/201445031

Sylvain Arguillère 1 ; Emmanuel Trélat 2 ; Alain Trouvé 3 ; Laurent Younès 4

1 Université Pierre et Marie Curie (Univ. Paris 6), CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
2 Université Pierre et Marie Curie (Univ. Paris 6) and Institut Universitaire de France and Team GECO Inria Saclay, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France
3 Ecole Normale Supérieure de Cachan, Centre de Mathématiques et Leurs Applications, CMLA, 61 av. du Pdt Wilson, F-94235 Cachan Cedex, France
4 Johns Hopkins University, Center for Imaging Science, Department of Applied Mathematics and Statistics, Clark 324C, 3400 N. Charles st. Baltimore, MD 21218, USA 
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     title = {Shape deformation and optimal control},
     journal = {ESAIM. Proceedings},
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Sylvain Arguillère; Emmanuel Trélat; Alain Trouvé; Laurent Younès. Shape deformation and optimal control. ESAIM. Proceedings, Tome 45 (2014), pp. 300-307. doi : 10.1051/proc/201445031. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445031/

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