Mathematical morphology has traditionally been grounded in lattice theory. For non-scalar data lattices often prove too restrictive, however. In this paper we present a more general alternative, sponges, that still allows useful definitions of various properties and concepts from morphological theory. It turns out that some of the existing work on “pseudo-morphology” for non-scalar data can in fact be considered “proper” mathematical morphology in this new framework, while other work cannot, and that this correlates with how useful/intuitive some of the resulting operators are.


Mathematical morphology Pseudo-morphology Weakly associative lattices Sponges 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jasper J. van de Gronde
    • 1
    Email author
  • Jos B. T. M. Roerdink
    • 1
  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningen AKThe Netherlands

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