On a nonlocal model of image segmentation
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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
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