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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.
@article{COCV_2011__17_4_909_0,
author = {Aubert, Gilles and Graziani, Daniele},
title = {Variational approximation for detecting point-like target problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {909--930},
publisher = {EDP-Sciences},
volume = {17},
number = {4},
year = {2011},
doi = {10.1051/cocv/2010029},
mrnumber = {2859858},
zbl = {1238.49024},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010029/}
}
TY - JOUR AU - Aubert, Gilles AU - Graziani, Daniele TI - Variational approximation for detecting point-like target problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 909 EP - 930 VL - 17 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010029/ DO - 10.1051/cocv/2010029 LA - en ID - COCV_2011__17_4_909_0 ER -
%0 Journal Article %A Aubert, Gilles %A Graziani, Daniele %T Variational approximation for detecting point-like target problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 909-930 %V 17 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010029/ %R 10.1051/cocv/2010029 %G en %F COCV_2011__17_4_909_0
Aubert, Gilles; Graziani, Daniele. Variational approximation for detecting point-like target problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 909-930. doi: 10.1051/cocv/2010029
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