Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Journal of Mathematical Imaging and Vision
Quasi-Linear Algorithms for the Topological Watershed
Journal of Mathematical Imaging and Vision
Watersheds, mosaics, and the emergence paradigm
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
International Journal of Computer Vision
A Metric Approach to Vector-Valued Image Segmentation
International Journal of Computer Vision
Fusion Graphs: Merging Properties and Watersheds
Journal of Mathematical Imaging and Vision
Constrained Connectivity for Hierarchical Image Decomposition and Simplification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Weighted fusion graphs: Merging properties and watersheds
Discrete Applied Mathematics
Watershed Cuts: Minimum Spanning Forests and the Drop of Water Principle
IEEE Transactions on Pattern Analysis and Machine Intelligence
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Building the Component Tree in Quasi-Linear Time
IEEE Transactions on Image Processing
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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We study hierachical 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 edge-segmentations.