We study three representations of hierarchies of partitions: dendrograms (direct representations), saliency maps, and minimum spanning trees. We provide a newbijection between saliencymaps and hierarchies based on quasi-flat zones as used in image processing and characterize saliency maps and minimumspanning 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.
CITATION STYLE
Cousty, J., Najman, L., Kenmochi, Y., & Guimarães, S. (2015). New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 9082, 205–216. https://doi.org/10.1007/978-3-319-18720-4_18
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