A formal $\Gamma$-convergence approach for the detection of points in $2$-D images

Daniele Graziani (1) , Laure Blanc-Féraud (1) , Gilles Aubert (2)

1 ARIANA - Inverse problems in earth monitoring
2 JAD - Laboratoire Jean Alexandre Dieudonné

We propose a new variational model to isolate points in a $2$-dimensional image. To this purpose we introduce a suitable functional whose minimizers are given by the points we want to detect. In order to provide numerical experiments we replace this energy with a sequence of a more treatable functionals by means of the notion of $\Gamma$-convergence.

Mots clés: points detection; curvature-depending functionals; divergence-measure fields; $\Gamma$-convergence; biological $2$-D images.; biological $2$-D images

Domaines: Traitement des images [eess.IV]

Daniele Graziani, Laure Blanc-Féraud, Gilles Aubert. A formal $\Gamma$-convergence approach for the detection of points in $2$-D images. [Research Report] RR-7038, INRIA. 2009, pp.25. ⟨inria-00418526⟩