The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces

Conference paper

DOI: 10.1007/978-3-319-18461-6_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)
Cite this paper as:
Schmidt M., Weickert J. (2015) The Morphological Equivalents of Relativistic and Alpha-Scale-Spaces. In: Aujol JF., Nikolova M., Papadakis N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science, vol 9087. Springer, Cham


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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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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