Joint graph cut and relative fuzzy connectedness image segmentation algorithm.

We introduce an image segmentation algorithm, called GC(sum)(max), which combines, in novel manner, the strengths of two popular algorithms: Relative Fuzzy Connectedness (RFC) and (standard) Graph Cut (GC). We show, both theoretically and experimentally, that GC(sum)(max) preserves robustness of RFC with respect to the seed choice (thus, avoiding "shrinking problem" of GC), while keeping GC's stronger control over the problem of "leaking though poorly defined boundary segments." The analysis of GC(sum)(max) is greatly facilitated by our recent theoretical results that RFC can be described within the framework of Generalized GC (GGC) segmentation algorithms.

A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks.

In the current vast image segmentation literature, there seems to be considerable redundancy among algorithms, while there is a serious lack of methods that would allow their theoretical comparison to establish their similarity, equivalence, or distinctness. In this paper, we make an attempt to fill this gap. To accomplish this goal, we argue that: (1) every digital segmentation algorithm [Formula: see text] should have a well defined continuous counterpart [Formula: see text], referred to as its model, which constitutes an asymptotic of [Formula: see text] when image resolution goes to infinity; (2) the equality of two such models [Formula: see text] and [Formula: see text] establishes a theoretical (asymptotic) equivalence of their digital counterparts [Formula: see text] and [Formula: see text].

Iterative Relative Fuzzy Connectedness for Multiple Objects with Multiple Seeds.

In this paper we present a new theory and an algorithm for image segmentation based on a strength of connectedness between every pair of image elements. The object definition used in the segmentation algorithm utilizes the notion of iterative relative fuzzy connectedness, IRFC. In previously published research, the IRFC theory was developed only for the case when the segmentation was involved with just two segments, an object and a background, and each of the segments was indicated by a single seed.