Summary: TIME-DELAYED PERONA-MALIK TYPE PROBLEMS
HERBERT AMANN
Abstract. We propose time regularizations for ill posed evolution equations of the
type of the Perona-Malik equation of image processing, prove that they are well
posed, and give numerical evidence for their superiority to the widely used space
regularizations.
1. Introduction
Nonlinear diffusion filters are used in image processing to simultaneously smoothen
noisy pictures and enhance sharp contrasts in brightness, This approach was ini-
tiated by the pioneering work of P. Perona and J. Malik [23]. These authors
proposed a scale space technique based on the evolution problem
tu - · g(| u|2
) u = 0 on × (0, ),
u(·, 0) = u0
on ,
(1.1)
which has to be complemented by boundary conditions, no-flux conditions being
the most appropriate choice. Here u0
is the grey level distribution of a given
(distorted) picture occupying a bounded domain in Rn

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

Collections: Mathematics