Iterative relative fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation

The notion of fuzzy connectedness captures the idea of “hanging-togetherness” of image elements in an object by assigning a strength of connectedness to every possible path between every possible pair of image elements. In a previous framework the authors presented, a fuzzy connected object was defined with a threshold on the strength of connectedness. Relative fuzzy connectedness provides a framework in which objects compete among each other and an image element is grabbed by the object within which the element has the largest fuzzy connectedness strength. Here, the authors introduce the notion of iterative relative fuzzy connectedness that leads to more effective segmentations using relative connectedness. The idea here is to identify the “core” of the object through relative connectedness in the first iteration. Subsequently this region is excluded from being considered by other co-objects for tracking their connectivity paths through. This effectively minimizes moderately strong paths seeping through the object of interest. The authors present a theoretical and algorithmic framework for defining objects via iterative relative fuzzy connectedness and demonstrate that the objects defined are independent of reference elements chosen as long as they are not in the fuzzy boundary between objects. Effectiveness of the method is demonstrated using both qualitative examples and a quantitative phantom analysis