Piecewise constant level set methods and image segmentation

Authors:
Johan Lie;Marius Lysaker;Xue-Cheng Tai
Affiliations:
Department of Mathematics, University of Bergen, Bergen, Norway;Simula Research Laboratory, Lysaker, Norway;Department of Mathematics, University of Bergen, Bergen, Norway
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface problems, we minimize a smooth locally convex functional under a constraint. We show numerical results using the methods for image segmentation.