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Partial Differential Equations for Morphological Operators

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Space, Structure and Randomness

Part of the book series: Lecture Notes in Statistics ((LNS,volume 183))

Abstract

Two of G. Matheron’s seminal contributions have been his development of size distributions (else called ‘granulometries’) and his kernel representation theory. The first deals with semigroups of multiscale openings and closings of binary images (shapes) by compact convex sets, a basic ingredient of which are the multiscale Minkowski dilations and erosions. The second deals with representing increasing and translation-invariant set operators as union of erosions by its kernel sets or as an intersection of dilations.

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Author information

Authors and Affiliations

  1. DO Labs, 3 rue Nationale, 92100, Boulogne, France

    Frederic Guichard

  2. School of ECE, National Technical University of Athens, 15773, Athens, Greece

    Petros Maragos

  3. CMLA, Ecole Normale Superieure de Cachan, 94235, Cachan, France

    Jean-Michel Morel

Authors
  1. Frederic Guichard
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  2. Petros Maragos
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  3. Jean-Michel Morel
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Editor information

Editors and Affiliations

  1. Centre de Morphologie Mathématique, Ecole des Mines de Paris, 35 rue Saint Honoré, 77305, Fontainebleau, France

    Michel Bilodeau  & Fernand Meyer  & 

  2. Direction des recherches, Ecole des Mines de Paris, 60 Boulevard Saint Michel, 75272, Paris Cedex 06, France

    Michel Schmitt

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Guichard, F., Maragos, P., Morel, JM. (2005). Partial Differential Equations for Morphological Operators. In: Bilodeau, M., Meyer, F., Schmitt, M. (eds) Space, Structure and Randomness. Lecture Notes in Statistics, vol 183. Springer, New York, NY. https://doi.org/10.1007/0-387-29115-6_15

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