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(FG 3) Description: Understanding an image as binary grey ``alloy'' of a black and a white component, we use a nonlocal phase separation model [1], [3], [4] to describe image segmentation and noise reduction.
The model consists in a degenerate nonlinear parabolic equation with a nonlocal drift term additionally to the familiar PeronaMalik model:
where is a convex function, the kernel represents nonlocal attracting forces, and v may be interpreted as chemical potential.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.
The application of the model to noise reduction is related to model parameters guaranteeing a unique steady state. Image segmentation is related to parameters where a unique steady state may not exist.
Figure 1 demonstrates some properties of the model applied to the noise reduction problem.
References:




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