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)


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.


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


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© 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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