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 di?erent 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 deŽnitions designed to answer the following fundamental questions: What is the relation between an idealized image and its digital representation? What properties a segmentation algorithm must satisfy 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 prove that the FP algorithm is weakly model-equivalent with the absolute fuzzy connectedness algorithm of Udupa and Samarasekera used with gradient based a?nity. Experimental evidence of this equivalence is also provided. The presented theoretical framework can be used to analyze any arbitrary segmentation algorithm. This line of investigation is a sub ject of our forthcoming work.
Conference Proceeding reprint.
Last modified May 24, 2010.