In the current vast image segmentation literature, there is a serious lack of methods that would allow theoretical comparison of the algorithms introduced by using different mathematical methodologies. The main goal of this article is to introduce a general theoretical framework for image segmentation that would allow such comparison. The framework is based on the formal definitions designed to answer the following fundamental questions: What is the relation between an idealized image and its digital representation? What properties a segmentation algorithm satisfy have to be acknowledged as acceptable? What does it mean that a digital image segmentation algorithm truly approximates an idealized segmentation model?

We use the formulated framework to analyze the front propagation (FP) level set algorithm of Malladi, Sethian, and Vemuri and compare it with the fuzzy connectedness family of algorithms. In particular, we show that the FP algorithm is model-equivalent with the absolute fuzzy connectedness algorithm used with gradient based affinity. Experimental evidence of this equivalence is also provided.

The presented theoretical framework can be used to analyze an arbitrary segmentation algorithm and this line of investigation is a subject of our forthcoming work.

MIPG Technical Report # 335 version.

SPIE Conference Proc. version.

Last modified April 9, 2007.