We continue the analysis of some modifications of the total variation image inpainting method formulated on the space BV (Ω) in the sense that we generalize some of the main results of [13] to the case of vectorvalued images where now we do not impose any structure condition on our density F and the dimension of the domain Ω is arbitrary. Precisely we discuss existence of generalized solutions ...

The relation between quasiconvexity and k-quasiconvexity, k ≥ 2, is investigated. It is shown that every smooth strictly k-quasiconvex integrand with p-growth at infinity, p > 1, is the restriction to k-th order symmetric tensors of a quasiconvex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semi...

The main aim of this talk is to discuss a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transfo...

Facular emission is one of the major contributors to long-term solar irradiance variations. Reconstructions of past facular variations, however, are strongly hampered by the lack of reliable proxies, particularly on time-scales longer than a solar cycle. We consider the five potential facular proxies with records covering more than 40 years. By suitably weighting and combining them we create a ...

We present a new vectorial total variation (VTV) method that addresses the problem of color consistent image filtering. Our approach combines insights based on the double-opponent cell representation in the visual cortex with state-of-the-art variational modelling using VTV regularization. Existing methods of vectorial total variation regularizers have insufficient (even no) coupling between th...

in  cite{gl}, b. gerla and i. leuc{s}tean introduced the notion of similarity on mv-algebra. a similarity mv-algebra is an mv-algebra endowed with a binary operation $s$ that verifies certain additional properties. also, chirtec{s} in cite{c}, study the notion of similarity on l ukasiewicz-moisil algebras. in particular, strong similarity l ukasiewicz-moisil algebras were defined. in this paper...

We investigate a modification of the total variation image inpainting method in higher dimensions, i.e. we assume n ≥ 3 and discuss existence as well as smoothness of corresponding solutions to the underlying variational problem. Precisely, we are going to establish that our type of a linear growth regularization admits a unique solution in the Sobolev space W 1,1(Ω), i.e. we do not need to con...

S(u) denotes the interfacial area associated with the surfaces upon which u jumps, and G(x, y) denotes the Green’s function for − on QL with Neumann boundary conditions. The variational problem consists of competing short-range (S(u)) and long-range (the nonlocal Green’s function term) contributions. The former term is attractive, favoring large domains of pure phases with boundaries of minimal...

Abstract. Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna, Fonseca, Malý & Trivisa [18]. For energies with superlinear or linear growth, a Γ-convergence result is established i...

Occlusion—how the teeth fit together within and between the arches—has important consequences functionally and especially esthetically. Occlusal variation is considerable in modern westernized societies, but the occurrence and extent of the variation appear to be lower in the past and lower in non-westernized groups. This methodological paper describes several commonly-used variables that, coll...