The results we present are based on integer programming and graph cut methods. They were specially proposed to solve practical problems of image processing and Bayes estimation. Often such problems can be formulated finally as problems of minimization of specific functions, for instance, modular or submodullar polynomials of many integer variables. We propose a new technique that allows the application of a multiresolution approach to minimize mentioned functions. The technique enables to find parts of an exact solution of the problem by minimizations of parts of the functions consisting only selected groups of variables until the whole solution will be computed.
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