In this paper, we study topological watersheds on perfect fusion graphs, an ideal framework for region merging. An important result is that contrarily to the general case, in this framework, any topological watershed is thin.Then we investigate a new image transformation called C-watershed and we show that, on perfect fusion graphs, the segmentations obtained by C-watershed correspond to segmentations obtained by topological watersheds. Compared to topological watershed, a major advantage of this transformation is that, on perfect fusion graph, it can be computed thanks to a simple linear-time immersion-like algorithm. Finally, we derive characterizations of perfect fusion graphs based on thinness properties of both topological watersheds and C-watersheds.
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