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In this paper, a new method for the segmentation of natural images is proposed. Original images g(x,y) are first regularized by using a self-adaptive implementation of the Mumford-Shah functional so that the two parameters α and γ controlling the smoothness and fidelity, automatically adapt to the local scale and contrast of g(x,y). From the regularized image u(x,y) which is piecewise smooth, it is possible to obtain a piecewise constant image sN(x,y) representing a segmentation of the original image g(x,y). Indeed, sN(x,y) is the union of N closed regions, having a constant grey level, preserving thin bars and trihedral junctions present in the original image g(x,y). If the number N of closed regions is too high, closed regions can be merged by minimizing a functional which depends on a parameter n. When n is set equal to 1, a coarse segmentation is obtained with a few tens of distinct regions. With larger values of n, finer segmentations are obtained with about a hundred distinct regions. Therefore, by selecting the value of n it is possible to obtain segmentations at different resolutions. The proposed method for image segmentation was evaluated in two cases where a ground truth segmentation is available. The proposed procedure for image segmentation is rather versatile and depends on only one parameter n and seems suitable for higher level processing, such as categorization, recognition, and scene understanding.