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Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships

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Mathematical Morphology and Its Application to Signal and Image Processing (ISMM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5720))

Abstract

In this paper the relationship of hyperconnected filters with path openings and attribute-space connected filters is studied. Using a recently developed axiomatic framework based on hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings, it is shown that path openings are a special case of hyperconnected area openings. The new axiomatics also yield insight into the relationship between hyperconnectivity and attribute-space connectivity. It is shown any hyperconnectivity is an attribute-space connectivity, but that the reverse is not true.

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Author information

Authors and Affiliations

  1. Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 407, 9700, AK, Groningen, The Netherlands

    Michael H. F. Wilkinson

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  1. Michael H. F. Wilkinson
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Editors and Affiliations

  1. Institute of Mathematics and Computing Science, University of Groningen, P. O. Box 407, 9700, Groningen, AK, The Netherlands

    Michael H. F. Wilkinson

  2. Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700, Groningen, AK, The Netherlands

    Jos B. T. M. Roerdink

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© 2009 Springer-Verlag Berlin Heidelberg

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Wilkinson, M.H.F. (2009). Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds) Mathematical Morphology and Its Application to Signal and Image Processing. ISMM 2009. Lecture Notes in Computer Science, vol 5720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03613-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-03613-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03612-5

  • Online ISBN: 978-3-642-03613-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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