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

• Main Authors: Cousty, Jean, Najman, Laurent, Kenmochi, Yukiko, Guimarães, Silvio
• Other Authors: Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Audio-visual Information Processing Lab Sao Gabriel (VIPLAB), Pontifical Catholic University of Minas Gerais Belo Horizonte, CAPES/PVE 064965/2014-01, CAPES/COFECUB 592/08, Benediktsson, J.A.; Chanussot, J.; Najman, L.; Talbot, ANR-10-BLAN-0205,KIDICO,Intégration des connaissances pour la convolution discrète, la segmentation et la reconstruction d'informations dans les images digitales(2010)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: Hierarchy; saliency map; minimum spanning tree; [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]; [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]; [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]; Iceland
• Online Access: https://hal.archives-ouvertes.fr/hal-01148958; https://hal.archives-ouvertes.fr/hal-01148958/document; https://hal.archives-ouvertes.fr/hal-01148958/file/JC.pdf; https://doi.org/10.1007/978-3-319-18720-4_18

International audience 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.