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Minimal Component-Hypertrees

  • Alexandre MorimitsuEmail author
  • Wonder Alexandre Luz Alves
  • Dennis Jose Silva
  • Charles Ferreira Gobber
  • Ronaldo Fumio HashimotoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)

Abstract

Component trees are interesting structures of nested connected components, efficiently represented by max-trees, used to implement fast algorithms in Image Processing. In these structures, connected components are constructed using a single neighborhood. In recent years, an extension of component trees, called component-hypertrees, was introduced. It consists of a sequence of component trees, generated from a sequence of increasing neighborhoods, in which their connected components are also hierarchically organized. Although this structure could be useful in applications dealing with clusters of objects, not much attention has been given to component-hypertrees. A naive implementation can be costly both in terms of time and memory. So, in this paper, we present algorithms and data structures to efficiently compute and store these structures without redundancy obtaining a minimal representation of component-hypertrees. Experimental results using our efficient algorithm show that the number of nodes is reduced by approximately 70% in comparison to a naive implementation.

Keywords

Mathematical Morphology Component-hypertree Component tree Connected component Connected operators 

Notes

Acknowledgements

This study was financed in part by the CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Finance Code 001); FAPESP - Fundação de Amparo a Pesquisa do Estado de São Paulo (Proc. 2018/15652-7); CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Proc. 428720/2018-8).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexandre Morimitsu
    • 1
    Email author
  • Wonder Alexandre Luz Alves
    • 2
  • Dennis Jose Silva
    • 1
  • Charles Ferreira Gobber
    • 2
  • Ronaldo Fumio Hashimoto
    • 1
    Email author
  1. 1.Department of Computer Science, Institute of Mathematics and StatisticsUniversidade de São PauloSão PauloBrazil
  2. 2.Informatics and Knowledge Management Graduate ProgramUniversidade Nove de JulhoSão PauloBrazil

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