Duality between the Watershed by Image Foresting Transform and the Fuzzy Connectedness Segmentation Approaches

This paper makes a rereading of two successful image segmentation approaches, the fuzzy connectedness (FC) and the watershed (WS) approaches, by analyzing both by means of the image foresting transform (IFT). This graph-based transform provides a sound framework for analyzing and implementing these methods. This paradigm allows to show the duality existing between the WS by IFT and the FC segmentation approaches. Both can be modeled by an optimal forest computation in a dual form (maximization of the similarities or minimization of the dissimilarities), the main difference being the input parameters: the weights associated to each arc of the graph representing the image. In the WS approach, such weights are based on the (possibly filtered) image gradient values whereas they are based on much more complex affinity values in the FC theory. An efficient algorithm for both FC and IFT-WS computation is proposed. Segmentation robustness issue is also discussed