An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation

Kahra, Marvin; Kleefeld, Andreas; Welk, Martin; Breuß, Michael

doi:10.1007/978-3-031-57793-2_25

Contribution to a conference proceedings/Contribution to a book

FZJ-2024-02761

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)

Discrete Geometry and Mathematical Morphology
IAPR Third International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2024, Florence, Italy, 15 Apr 2024 - 18 Apr 2024 Cham : Springer, Lecture Notes in Computer Science 14605, 325-337 (2024) [10.1007/978-3-031-57793-2_25]

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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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