Nonlinear image labeling for multivalued segmentation

We describe a framework for multivalued segmentation and demonstrate that some of the problems affecting common region-based algorithms can be overcome by integrating statistical and topological methods in a nonlinear fashion. We address the sensitivity to parameter setting, the difficulty with handling global contextual information, and the dependence of results on analysis order and on initial conditions. We develop our method within a theoretical framework and resort to the definition of image segmentation as an estimation problem. We show that, thanks to an adaptive image scanning mechanism, there is no need of iterations to propagate a global context efficiently. The keyword multivalued refers to a result property, which spans over a set of solutions. The advantage is twofold: first, there is no necessity for setting a priori input thresholds; secondly, we are able to cope successfully with the problem of uncertainties in the signal model. To this end, we adopt a modified version of fuzzy connectedness, which proves particularly useful to account for densitometric and topological information simultaneously. The algorithm was tested on several synthetic and real images. The peculiarities of the method are assessed both qualitatively and quantitatively.