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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Communication dans un congrès
12th International Symposium on Mathematical Morphology (ISMM), May 2015, Reykjavik, Iceland. Lecture Notes in Computer Science (LNCS), 9082, pp.205-216, Mathematical Morphology and Its Applications to Signal and Image Processing. 〈10.1007/978-3-319-18720-4_18〉
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Soumis le : mardi 26 mai 2015 - 15:21:02
Dernière modification le : jeudi 5 juillet 2018 - 14:29:17
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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), May 2015, Reykjavik, Iceland. Lecture Notes in Computer Science (LNCS), 9082, pp.205-216, Mathematical Morphology and Its Applications to Signal and Image Processing. 〈10.1007/978-3-319-18720-4_18〉. 〈hal-01148958〉

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