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PDE-Based Color Morphology Using Matrix Fields

  • In this work, we propose a novel way for performing operations of mathematical morphology on color images. To this end, we convert pixelwise the rgb-values into symmetric 2x2 matrices. The new color space can be interpreted geometrically as a biconal color space structure. Motivated by the formulation of the fundamental morphological operations dilation and erosion in terms of partial differential equations (PDEs), we show how to define finite difference schemes making use of the matrix field formulation. The computation of a pseudo supremum and a pseudo infimum of three color matrices is a crucial step for setting up advanced PDE-based methods. We show that this can be achieved for our goal by an algebraic technique. We investigate our approach by dedicated experiments and confirm useful properties of the new PDE-based color morphology operations.

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Metadaten
Author: Ali Sharifi Boroujerdi, Michael BreußGND, Bernhard Burgeth, Andreas Kleefeld
DOI:https://doi.org/10.1007/978-3-319-18461-6_37
ISBN:978-3-319-18460-9
Title of the source (English):Scale Space and Variational Methods in Computer Vision, 5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings
Publisher:Springer
Place of publication:Berlin
Editor: Jean-François Aujol, Mila Nikolova, Nicolas Papadakis
Document Type:Conference Proceeding
Language:English
Year of publication:2015
Tag:Color morphology; FCT scheme; Finite difference schemes; Matrix fields; PDE-based morphology; Pseudo infimum; Pseudo supremum
First Page:461
Last Page:473
Series ; volume number:Lecture Notes in Computer Science ; 9087
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Angewandte Mathematik
Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Numerische Mathematik und Wissenschaftliches Rechnen
Institution name at the time of publication:Fakultät für Mathematik, Naturwissenschaften und Informatik (eBTU) / LS Mathematik, insbesondere Numerische Mathematik und Wissenschaftliches Rechnen
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