TY  - CONF
AU  - Kahra, Marvin
AU  - Breuß, Michael
AU  - Kleefeld, Andreas
AU  - Welk, Martin
TI  - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation
VL  - 14605
CY  - Cham
PB  - Springer
M1  - FZJ-2024-02761
SN  - 978-3-031-57792-5 (print)
T2  - Lecture Notes in Computer Science
SP  - 325-337
PY  - 2024
AB  - 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.
T2  - IAPR Third International Conference on Discrete Geometry and Mathematical Morphology
CY  - 15 Apr 2024 - 18 Apr 2024, Florence (Italy)
Y2  - 15 Apr 2024 - 18 Apr 2024
M2  - Florence, Italy
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
UR  - <Go to ISI:>//WOS:001280284700025
DO  - DOI:10.1007/978-3-031-57793-2_25
UR  - https://juser.fz-juelich.de/record/1025193
ER  -