New Characterizations of Minimum Spanning Trees and of Saliency Maps Based on Quasi-flat Zones

  • Jean Cousty
  • Laurent Najman
  • Yukiko Kenmochi
  • Silvio Guimarães
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9082)

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.

Keywords

Hierarchy Saliency map Minimum spanning tree 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jean Cousty
    • 1
  • Laurent Najman
    • 1
  • Yukiko Kenmochi
    • 1
  • Silvio Guimarães
    • 1
    • 2
  1. 1.LIGM, A3SI, ESIEE ParisUniversité Paris-EstParisFrance
  2. 2.PUC Minas - ICEI - DCC - VIPLABBelo HorizonteFrance

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