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 alpha and gamma 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.