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
A connected component approach to the watershed segmentation
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
IFT-Watershed from Gray-Scale Marker
SIBGRAPI '02 Proceedings of the 15th Brazilian Symposium on Computer Graphics and Image Processing
The Image Foresting Transform: Theory, Algorithms, and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tie-Zone Watershed, Bottlenecks, and Segmentation Robustness Analysis
SIBGRAPI '05 Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing
An improved watershed algorithm based on efficient computation of shortest paths
Pattern Recognition
Uniquely-Determined Thinning of the Tie-Zone Watershed Based on Label Frequency
Journal of Mathematical Imaging and Vision
Comparison between immersion-based and toboggan-based watershed image segmentation
IEEE Transactions on Image Processing
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To better understand the numerous solutions related to watershed transform (WT), this paper shows the relationships between some discrete definitions of the WT, especially those based on image foresting transform (IFT) with/without lexicographic cost function, topographic distance (TD), local condition (LC), flooding (F), and minimum spanning forest (MSF). Some of these paradigms allow multiple solutions. The tie-zone (TZ) transform returns a unique solution from a set of multiple solutions of a given WT. We demonstrate that the TZ transform applied to the IFT-WT includes all the solutions predicted by the other paradigms. More precisely, the watershed line of TD-WT and F-WT are contained in the TZ of the IFT-WT, while the catchment basins of TD-WT or F-WT contain the basins of the TZ-IFT-WT. In addition, the TD-WT can be seen as the tie-zone transform of the LC-WT. Furthermore, any solution of LC-WT or MSF-WT is also solution of the IFT-WT. Finally, MSF-WT and IFT-WT have the same tie-zone transform.