On a nonlocal model of image segmentation

  • Herbert GajewskiEmail author
  • Klaus Gärtner
Original Paper


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 


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 


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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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