“One, Two, Three,... Infinity”

  • J. Serra
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 23)

Abstract

This famous title remarkably summarizes the recent evolution of the ideas in quantitative image analysis, and the impact of mathematical morphology on it. “One”, for the case of basic stereological measurements. In fact, they all involve an implicit image transformation. “Two” appears when this transformation is preceded by another one, as a linear erosion (laws of intercepts) or a covariance. With “Three”, we iterate two transformations before the measurements : bi-dimensional openings, for instance. And immediately after, one jumps to infinity with the pattern recognition algorithms, as the Skeletton.

In this evolution, the train of thoughts is given by the conditions that the transforms have to satisfy. The quantization is associated with four basic principles: invariance under the translations, compatibility with homothetics, local knowledge, semi-continuity. Moreover, each criterion corresponds to new logical constraints, like the granulometric axioms for example.

Keywords

Covariance Hexagonal Coherence Hull Paral 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • J. Serra
    • 1
  1. 1.Centre de Morphologie MathématiqueEcole Nationale Supérieure des Mines de ParisFontainebleauFrance

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