A Fixed Point Formulation Of The k-Means Algorithm And A Connection To Mumford-Shah

In this note, we present a fixed point formulation of the k-means segmentation algorithm and show that the iteration’s fixed points are solutions of the Euler-Lagrange equation for the unregularized k-phase Mumford-Shah energy functional. This short note illustrates a connection between the k-means algorithm and MumfordShah segmentation via a fixed point formulation of k-means. This connection is explicitly mentioned in [3, 10], but is made theoretically concrete here. However, since k-means itself has been extensively studied, any further analysis of the method would be redundant, hence the shortness of the discussion. ~