Abstract
This work is settled in the framework of abstract simplicial complexes. We propose a definition of a watershed and of a collapse for maps defined on pseudomanifolds of arbitrary dimension. Through an equivalence theorem, we establish a deep link between these two notions: any watershed can be obtained by collapse iterated until idempotence, and conversely any collapse iterated until idempotence induces a watershed. We also state an equivalence result which links the notions of a watershed and of a collapse with the one of a minimum spanning forest.
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Cousty, J., Bertrand, G., Couprie, M., Najman, L. (2009). Collapses and Watersheds in Pseudomanifolds. In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_31
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DOI: https://doi.org/10.1007/978-3-642-10210-3_31
Publisher Name: Springer, Berlin, Heidelberg
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