Perona-Malik equation and its numerical properties

Abstract

This work concerns the Perona-Malik equation, which plays essential role in image processing. The first part gives a survey of results on existance, uniqueness and stability of solutions, the second part introduces discretisations of equation and deals with an analysis of discrete problem. In the last part I present some numerical results, in particular with algorithms applied to real images.

My bachelor thesis, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, 2010