The University of Montana
Department of Mathematical Sciences

Technical report #36/2008

A Fixed Point Formulation of the k-Means Algorithm for Image Segmentation and a Connection to Mumford-Shah

J. M. Bardsley
Department of Mathematical Sciences
University of Montana
Missoula, Montana 59812, USA

Aaron Luttman
Division of Mathematics and Computer Science
Clarkson University, Science Center
Potsdam, New York, 13699

Abstract

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 k-phase Mumford-Shah energy functional.

Keywords:Mumford-Shah segmentation, fixed point methods, k-means

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