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The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces

  • Martin Schmidt
  • Joachim Weickert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)

Abstract

The relations between linear system theory and mathematical morphology are mainly understood on a pure convolution / dilation level. A formal connection on the level of differential or pseudo-differential equations is still missing. In our paper we close this gap. We establish the sought relation by means of infinitesimal generators, exploring essential properties of the slope and a modified Cramér transform. As an application of our general theory, we derive the morphological counterparts of relativistic scale-spaces and of \(\alpha \)-scale-spaces for \(\alpha \in [\frac{1}{2}, \infty )\). Our findings are illustrated by experiments.

Keywords

Mathematical morphology Alpha-scale-spaces Relativistic scale-spaces Cramér transform Slope transform 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany

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