A simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law

Guillaume Noyel (1, 2, 3) , Michel Jourlin (1, 4)

1 IPRI - International Prevention Research Institute
2 University of Strathclyde [Glasgow]
3 SIGPH@iPRI - University of Strathclyde Institute of Global Public Health
4 LHC - Laboratoire Hubert Curien

We introduce a simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law. It is a difference between a morphological dilation and a morphological erosion with an additive structuring function which corresponds to a morphological gradient.

Mots clés: Double-sided probing; Map of Asplund's distances; Erosion; Dilation; Logarithmic Image Processing; Mathematical Morphology; Asplund's metric; Morphological gradient; Additive structuring functions; Pattern recognition; Multiplicative structuring functions

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Topologie générale [math.GN]; Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]

Guillaume Noyel, Michel Jourlin. A simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law. 12th European Congress for Stereology and Image Analysis 2017 (ECSIA 2017), University of Kaiserslautern; Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM), Sep 2017, Kaiserslautern, Germany. ⟨hal-01576183v2⟩