Towards Processing Fields of General Real-Valued Square Matrices

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

In this paper, a general framework is presented that allows for the fundamental morphological operations such as dilation and erosion for real-valued square matrix fields. Hence, it is also possible to process any field consisting of a subgroup of general matrices with examples like the general linear, symmetric, skew-symmetric, Hermitian, and orthonormal group. Therefore, from the theoretical point of view it is possible to process any field with entries consisting of the aforementioned groups. Extended examples illustrated the different conversion processes and the definition of corresponding pseudo-suprema and pseudo-infima. Furthermore, some possible applications are illustrated.

Notes

Acknowledgements

The authors would like to thank the two anonymous referees for their useful comments and valuable insights that helped to improve this work.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Forschungszentrum Jülich GmbH, Institute for Advanced SimulationJülich Supercomputing CentreJülichGermany

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