Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
type: Item
instance of: scholarly article
title: Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
zbMATH Open document ID: 1084.49003
DOI: 10.4171/IFB/112
author: Antonin Chambolle
author: François Alter
author: V. Caselles
published in: Interfaces and Free Boundaries
publication date: 2005-04-18T00:00:00Z
review text: The authors compute the explicit solution of the minimizing total variation flow in \(\mathbb{R}^2\) given by the equation \[ {\partial u\over\partial t}= \text{div}\Biggl({Du\over|Du|}\Biggr)\quad\text{in }Q_T= (0,T)\times \mathbb{R}^2 \] together with the initial datum \(u(0,x)= \sum^m_{i=1} b_i\chi_{C_i}(x)\), where \(b_i\in\mathbb{R}\) and \(C_i\) are bounded convex sets in \(\mathbb{R}^2\), which are sufficiently far apart. The paper also contains numerical examples of evolutions.
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 2157848
zbMATH Keywords: BV functions
zbMATH Keywords: total variation flow
zbMATH Keywords: convex set
zbMATH Keywords: denoising
reviewed by: M. Fuchs
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/112
OpenAlex ID: W2043380148
description: scientific article; zbMATH DE number 2157848