Matrix valued images, so-called matrix fields, represent a data type frequently encountered, for instance, in medical imaging and engineering sciences. For symmetric matrices the Loewner order may be utilised to establish many useful morphological operations for these fields, both order- and PDE-based. This talk is about the basic mathematical background of the framework and its extension to non-symmetric matrices, such as rotation matrices. Numerical results will indicate the potential of the proposed approach.

This presentation is part of Minisymposium “MS48 - Recent Advances in Mathematical Morphology: Algebraic and PDE-based Approaches”
organized by: Martin Welk (Private University for Health Sciences, Medical Informatics and Technology (UMIT)) , Michael Breuss (Brandenburg University of Technology) .

Authors:

Bernhard Burgeth (Saarland University, Saarbrücken)

Keywords:

loewner order, matrix field