Variational approximation for detecting point-like target problems*
Laboratoire J.A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France. firstname.lastname@example.org
2 Ariana CNRS/INRIA/UNSA Sophia Antipolis, Inria, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. Daniele.Graziani@sophia.inria.fr
Revised: 16 November 2009
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.
Mathematics Subject Classification: 49J45 / 49Q20
Key words: Points detection / biological images / divergence-measure fields / p-capacity / Γ-convergence
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