The main subject of this paper is a theoretical study of image segmentation algorithms in the multiregion competition setting. In particular, we investigate such segmentations when the competition is based on a value of the gradient magnitude of the image. The idealized model for such segmentation is placed in the theoretical segmentation framework from our earlier work. We show that this model is represented by the gradient based relative fuzzy connectedness, RFC, algorithm. We also show that the model is weakly represented by a level set multiregion competition algorithm and that both algorithms are weakly model-equivalent. A particular consequence of this theoretical result is that the difficulties attributed to the level set multiregion competition algorithms could be avoided by using the gradient based RFC algorithm. We also describe a natural model for the fuzzy connectedness algorithm used with the homogeneity based affinity in the RFC setting and also for absolute fuzzy connectedness algorithms.

MIPG Technical Report
**# 338 version.**

**Last modified September 21, 2007.**