TY  - CONF
A1  - Kahra, Marvin
A1  - Breuß, Michael
A1  - Kleefeld, Andreas
A1  - Welk, Martin
A2  - Brunetti, Sara
A2  - Frosini, Andrea
A2  - Rinaldi, Simone
T1  - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation
T2  - Discrete Geometry and Mathematical Morphology
N2  - 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 2x2 matrices. 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.
Y1  - 2024
UR  - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/11495
SN  - 978-3-031-57793-2
N1  - Third International Joint Conference, DGMM 2024, Florence, Italy, April 15–18, 2024
SP  - 325
EP  - 337
PB  - Springer
CY  - Cham
ER  -