2013
DOI: 10.1007/978-3-642-38294-9_8
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Constructive Links between Some Morphological Hierarchies on Edge-Weighted Graphs

Abstract: Abstract. In edge-weighted graphs, we provide a unified presentation of a family of popular morphological hierarchies such as component trees, quasi flat zones, binary partition trees, and hierarchical watersheds. For any hierarchy of this family, we show if (and how) it can be obtained from any other element of the family. In this sense, the main contribution of this paper is the study of all constructive links between these hierarchies.

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Cited by 37 publications
(81 citation statements)
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“…Note that statement 1 appeared in [14] but Theorem 4 completes the result of [14]. Indeed, Theorem 4 indicates that there is no proper subgraph of a MST that induces the same quasi-flat zone hierarchy as the initial weighted graph.…”
Section: Minimum Spanning Treesmentioning
confidence: 76%
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“…Note that statement 1 appeared in [14] but Theorem 4 completes the result of [14]. Indeed, Theorem 4 indicates that there is no proper subgraph of a MST that induces the same quasi-flat zone hierarchy as the initial weighted graph.…”
Section: Minimum Spanning Treesmentioning
confidence: 76%
“…In particular, in [20], an extensive assessment based on the framework of [4] shows that the hierarchical method performs at least as well as its non-hierarchical counterpart while providing at once all the possible scales. The results of this article constitute the theoretical basis of the methods presented in the aforementioned references [12,14,35,19,21,22]. It also opens the door towards new hierarchical image analysis.…”
Section: Introductionmentioning
confidence: 72%
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“…This definition has been formalized in the context of minimum spanning forests that already enabled to define watershed cuts as an optimal solution to a combinatorial problem related to minimum spanning tree [21]. It has also been shown that hierarchies of watersheds are linked to the quasiflat zones hierarchies [22], to the single-linkage clustering problem [23], and to connective segmentation [14], [24].…”
Section: Introductionmentioning
confidence: 99%