On the equivalence between hierarchical segmentations and ultrametric watersheds

Abstract

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice in the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.

19 pages, double-column

References in corpus (1)

• Enhanced computation method of topological smoothing on shared memory parallel machines

Cited by in corpus (8)

• The Mutex Watershed and its Objective: Efficient, Parameter-Free Graph Partitioning
• A graph-based mathematical morphology reader
• On morphological hierarchical representations for image processing and spatial data clustering
• Rethinking Interactive Image Segmentation: Feature Space Annotation
• An efficient hierarchical graph based image segmentation
• New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
• Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection
• A Contrario Selection of Optimal Partitions for Image Segmentation