Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Graphical Models 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
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)
Quasi-Linear Algorithms for the Topological Watershed
Journal of Mathematical Imaging and Vision
Image and Vision Computing
Uniquely-Determined Thinning of the Tie-Zone Watershed Based on Label Frequency
Journal of Mathematical Imaging and Vision
Fusion Graphs: Merging Properties and Watersheds
Journal of Mathematical Imaging and Vision
Weighted fusion graphs: Merging properties and watersheds
Discrete Applied Mathematics
Uniqueness of the Perfect Fusion Grid on Zd
Journal of Mathematical Imaging and Vision
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Collapses and Watersheds in Pseudomanifolds
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Topological Properties of Thinning in 2-D Pseudomanifolds
Journal of Mathematical Imaging and Vision
On watershed cuts and thinnings
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Segmentation of 4D cardiac MRI: Automated method based on spatio-temporal watershed cuts
Image and Vision Computing
Topology-preserving thinning in 2-D pseudomanifolds
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Some links between extremum spanning forests, watersheds and min-cuts
Image and Vision Computing
Parallel image thinning through topological operators on shared memory parallel machines
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Artwork 3D model database indexing and classification
Pattern Recognition
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Towards a parallel topological watershed: first results
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
General Adaptive Neighborhood-Based Pretopological Image Filtering
Journal of Mathematical Imaging and Vision
Fusion graphs, region merging and watersheds
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Algorithms for the topological watershed
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Grayscale watersheds on perfect fusion graphs
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
An unbiased and intervoxel watershed algorithm for 3d image segmentation
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
Segmentation of three phase micrograph: an automated approach
Proceedings of the CUBE International Information Technology Conference
Morphological filtering on graphs
Computer Vision and Image Understanding
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In this paper, we investigate topological watersheds (Couprie and Bertrand, 1997). One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension. A consequence of the theorem is that there exists a (greedy) polynomial time algorithm to decide whether a map G is a watershed of a map F or not. We introduce a notion of "separation between two points" of an image which leads to a second necessary and sufficient condition. We also show that, given an arbitrary total order on the minima of a map, it is possible to define a notion of "degree of separation of a minimum" relative to this order. This leads to a third necessary and sufficient condition for a map G to be a watershed of a map F. At last we derive, from our framework, a new definition for the dynamics of a minimum.