Incremental Algorithm for Hierarchical Minimum Spanning Forests and Saliency of Watershed Cuts

We study hierarchical segmentations that are optimal in the sense of minimal spanning forests of the original image. We introduce a region-merging operation called uprooting, and we prove that optimal hierarchical segmentations are equivalent to the ones given by uprooting a watershed-cut based segmentation. Based on those theoretical results, we propose an efficient algorithm to compute such hierarchies, as well as the first saliency map algorithm compatible with the morphological filtering framework.