The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme.
We propose a new variational model to locate points in 2-dimensional biological images. 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 more treatable functionals by means of the notion of Γ-convergence.
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.Mathematics Subject Classification. 49J45, 49Q20.
In this paper we address a relaxation theorem for a new integral functional of the calculus of variations defined on the space of functions in [Formula: see text] whose gradient is an Lp-vector field with distributional divergence given by a Radon measure. The result holds for integrand of type f(x, Δu) without any coerciveness condition, with respect to the second variable, and C1-continuity assumptions with respect to the spatial variable x.
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