Threshold dynamics for the piecewise constant Mumford–Shah functional

We propose an efficient algorithm for minimizing the piecewise constant Mumford–Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding.