  We study the existence and uniqueness of solutions of a nonlinear
integro-differential problem which we reformulate introducing the notion of the
decreasing rearrangement of the solution. A dimensional reduction of the
problem is obtained and a detailed analysis of the properties of the solutions
of the model is provided. Finally, a fast numerical method is devised and
implemented to show the performance of the model when typical image processing
tasks such as filtering and segmentation are performed.
