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Variational approach to image segmentation

This paper deals with a class of variational problems rising from image segmentation. After introducing the mathematical model of this question, we analysis it's rationality in details. At the same time, two numerical methods will be proposed to solve it. Furthermore, the equivalence of these two equations will be proved briefly. At last, we shall apply this result to approximate a minimum problem that was introduced by D.Mumford and J.Shah to Study image Segmentation.