  We proposed an efficient iterative thresholding method for multi-phase image
segmentation. The algorithm is based on minimizing piecewise constant
Mumford-Shah functional in which the contour length (or perimeter) is
approximated by a non-local multi-phase energy. The minimization problem is
solved by an iterative method. Each iteration consists of computing simple
convolutions followed by a thresholding step. The algorithm is easy to
implement and has the optimal complexity $O(N \log N)$ per iteration. We also
show that the iterative algorithm has the total energy decaying property. We
present some numerical results to show the efficiency of our method.
