Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …

Image segmentation is a hot topic of research given its applicability as a pre-processing
technique in many image understanding applications. This paper describes the Mumford …

We study the action minimization problem that is formally associated to phase transformation
in the stochastically perturbed Allen‐Cahn equation. The sharp‐interface limit is related to …

The higher order total variation-based model for image restoration proposed by Chan,
Marquina, and Mulet in [SIAM J. Sci. Comput., 22 (2000), pp. 503–516] is analyzed in one …

Partial localization is the phenomenon of self-aggregation of mass into highdensity
structures that are thin in one direction and extended in the others. We give a detailed study …

We consider, in an open subset Ω of, energies depending on the perimeter of a subset (or
some equivalent surface integral) and on a function u which is defined only on. We compute …

Segmentation with depth is the challenging problem of obtaining three dimensional
information from a single two dimensional image. Unlike the standard segmentation …

We analyze the sharp-interface limit of the action minimization problem for the stochastically
perturbed Allen-Cahn equation in one space dimension. The action is a deterministic …

We introduce and study a two-dimensional variational model for the reconstruction of a
smooth generic solid shape E, which may handle the self-occlusions and that can be …

We establish some new results about the Γ-limit, with respect to the L1-topology, of two
different (but related) phase-field approximations\hbox {$\{\mathcal E_\eps\} …