Advertisement

On a nonlocal model of image segmentation

  • Herbert GajewskiEmail author
  • Klaus Gärtner
Original Paper

Abstract.

We understand an image as binary grey ‘alloy’ of a black and a white component and use a nonlocal phase separation model to describe image segmentation. The model consists in a degenerate nonlinear parabolic equation with a nonlocal drift term additionally to the familiar Perona-Malik model. We formulate conditions for the model parameters to guarantee global existence of a unique solution that tends exponentially in time to a unique steady state. This steady state is solution of a nonlocal nonlinear elliptic boundary value problem and allows a variational characterization. Numerical examples demonstrate the properties of the model.

Mathematics Subject Classification (2000).

35K45 35K65 35B40 80A22 74N25 

Keywords.

Cahn-Hilliard equation initial boundary value problem Perona-Malik model a priori estimates Lyapunov function equilibria asymptotic behaviour classical thermodynamics nonlocal phase separation model image reconstruction and separation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

Personalised recommendations