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New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones

Abstract : We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a new bijection between saliency maps and hierarchies based on quasi-flat zones as used in image processing and characterize saliency maps and minimum spanning trees as solutions to constrained minimization problems where the constraint is quasi-flat zones preservation. In practice, these results form a toolkit for new hierarchical methods where one can choose the most convenient representation. They also invite us to process non-image data with morphological hierarchies.
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https://hal.archives-ouvertes.fr/hal-01148958
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Submitted on : Tuesday, May 26, 2015 - 3:21:02 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:07 PM
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Jean Cousty, Laurent Najman, Yukiko Kenmochi, Silvio Guimarães. New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones. 12th International Symposium on Mathematical Morphology (ISMM), Benediktsson, J.A.; Chanussot, J.; Najman, L.; Talbot,, May 2015, Reykjavik, Iceland. pp.205-216, ⟨10.1007/978-3-319-18720-4_18⟩. ⟨hal-01148958⟩

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