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Flat Morphological Operators on Arbitrary Power Lattices

  • Christian Ronse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2616)

Abstract

We give here the basis for a general theory of flat morphological operators for functions defined on a space E and taking their values in an arbitrary complete lattice V . Contrarily to Heijmans [4], [6], we make no assumption on the complete lattice V , and in contrast with Serra [18], we rely exclusively on the usual construction of flat operators by thresholding and stacking.

Some known properties of flat operators for numerical functions (V = \( \overline Z \) or \( \overline R \) ) extend to this general framework: flat dilations and erosions, flat extension of a union of operators or of a composition of an operator by a dilation. Others don’t, unless V is completely distributive: flat extension of an intersection or of a composition of operators; for these we give counterexamples with V being the non-distributive lattice of labels. In another paper [15], we will consider the commutation of flat operators with anamorphoses (contrast functions) and thresholdings, duality by inversion, as well as related questions of continuity.

Keywords

Complete Lattice Mathematical Morphology Morphological Operator Contrast Function Complete Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Christian Ronse
    • 1
  1. 1.LSIIT UMR 7005 CNRS-ULPIllkirchFrance

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