Watershed by image foresting transform, tie-zone, and theoretical relationships with other watershed definitions

To better understand the numerous solutions related to watershed transform (WT), this paper shows the relationships between some discrete de nitions of the WT: the watersheds based on image foresting transform (IFT), topographic distance (TD), local condition (LC), and minimum spanning forest (MSF). We demonstrate that the tie-zone (TZ) concept, that uni es the multiple solutions of a given WT, when applied to the IFT-WT, includes all the solutions predicted by the other paradigms: the watershed line of TD-WT is contained in the TZ of the IFT-WT, while the catchment basins of the former contain the basins of the latter; any solution of LCWT or MSF-WT is also solution of the IFT-WT. Furthermore, the TD-WT can be seen as the TZ transform of the LC-WT.

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