Contribution to a conference proceedings/Contribution to a book

FZJ-2024-02761

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation

Kahra, M. (Corresponding author) ; Breuß, M. ; Kleefeld, A.FZJ* ; Welk, M.

2024
Springer Cham
ISBN: 978-3-031-57792-5 (print), 978-3-031-57793-2 (electronic)

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Please use a persistent id in citations: doi:10.1007/978-3-031-57793-2_25  doi:10.34734/FZJ-2024-02761

Abstract: Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations.In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2024

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Database coverage:
; Nationallizenz ; SCOPUS

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