Search results for "total variation"
showing 6 items of 26 documents
Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere
2013
Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.
THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE
2014
We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…
Regularization of chattering phenomena via bounded variation controls
2018
In control theory, the term chattering is used to refer to strong oscillations of controls, such as an infinite number of switchings over a compact interval of times. In this paper we focus on three typical occurences of chattering: the Fuller phenomenon, referring to situations where an optimal control switches an infinite number of times over a compact set; the Robbins phenomenon, concerning optimal control problems with state constraints, meaning that the optimal trajectory touches the boundary of the constraint set an infinite number of times over a compact time interval; the Zeno phenomenon, referring as well to an infinite number of switchings over a compact set, for hybrid optimal co…
Modified total variation regularization using fuzzy complement for image denoising
2015
In this paper, we propose a denoising algorithm based on the Total Variation (TV) model. Specifically, we associate to the regularization term of the Rodin-Osher-Fatimi (ROF) functional a small weight whenever denoising is performed in edge and texture regions, which means less regularization and more details preservation. On the other hand, a large weight is associated if the region being filtered is smooth which means noise will be well suppressed. The weight computation is inspired from the fuzzy edge complement. Experiments on well-known images and comparison with state of the art denoising algorithms demonstrate that the proposed method not only presents good denoising performance but …
Broglie and Young, visionaries who shed light in the polar topology that grounds our reality: a hypothesis
2020
Una observación matemática que relaciona los patrones fractales y la operación de convolución en el contexto del procesamiento de imágenes digitales interrumpió una investigación que nos lleva a plantear la hipótesis de que el concepto de onda de materia (o dualidad onda-partícula) se encuentra en la dicotomía entre el par débil y un topología fuerte en el ámbito del marco de atractores singulares continuos en ninguna parte diferenciables y el concepto de fotón-solitón de Vigier. Tal inferencia parece ser más evidente en la interpretación de Broglie-Bohm de la mecánica cuántica en el cruce de características locales x globales. De esto se deduce también que la relación de los fenómenos natu…
On elliptic equations involving the 1-Laplacian operator
2018
El objetivo de esta tesis doctoral es dar a conocer los resultados obtenidos sobre existencia, unicidad y regularidad de las soluciones de diferentes ecuaciones elípticas regidas por el operador 1-laplaciano. El primer capítulo está dedicado al estudio de la ecuación - div (Du/|Du|) + g(u) |Du| = f(x) en un subconjunto abierto y acotado U de R^N con frontera Lipschitz, con la condición de Dirichlet u=0 en la frontera, tomando una función f positiva y siendo g una función real, continua y positiva. Por un lado, obtenemos soluciones no acotadas cuando el dato f pertenece al espacio de Marcinkiewicz L^{N,\infty}(U), por lo que debemos introducir la definición apropiada para este tipo de soluci…