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Variational approximation for detecting point-like target problems*

Published online by Cambridge University Press:  06 August 2010

Gilles Aubert  and
Daniele Graziani
Gilles Aubert
Affiliation:
Laboratoire J.A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France. gaubert@unice.fr
Daniele Graziani
Affiliation:
Ariana CNRS/INRIA/UNSA Sophia Antipolis, Inria, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. Daniele.Graziani@sophia.inria.fr
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Abstract

The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the Γ-convergence to the initial one.

Keywords

Points detectionbiological imagesdivergence-measure fieldsp-capacityΓ-convergence
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 909 - 930
Copyright
© EDP Sciences, SMAI, 2010

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