A Seeded Image Segmentation Framework Unifying Graph Cuts And Random Walker Which Yields A New Algorithm

Abstract

In this work, we present a common framework for seeded image segmentation algorithms that yields two of the leading methods as special cases - The Graph Cuts and the Random Walker algorithms. The formulation of this common framework naturally suggests a new, third, algorithm that we develop here. Specifically, the former algorithms may be shown to minimize a certain energy with respect to either an 𝓁 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> or an 𝓁 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm. Here, we explore the segmentation algorithm defined by an 𝓁 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm, provide a method for the optimization and show that the resulting algorithm produces an accurate segmentation that demonstrates greater stability with respect to the number of seeds employed than either the Graph Cuts or Random Walker methods.

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