TY  - JOUR
AU  - Kahra, Marvin
AU  - Breuß, Michael
AU  - Kleefeld, Andreas
AU  - Welk, Martin
TI  - Matrix-Valued LogSumExp Approximation for Colour Morphology
JO  - Journal of mathematical imaging and vision
VL  - 67
IS  - 5
SN  - 0924-9907
CY  - Dordrecht [u.a.]
PB  - Springer Science + Business Media B.V
M1  - FZJ-2025-03812
SP  - 52
PY  - 2025
AB  - Mathematical morphology is a part of image processing that employs a moving window to modify pixel values through the application of specific operations. The supremum and infimum are pivotal concepts, yet defining them in a general sense for high-dimensional data such as colour is a challenging endeavour. As a result, a number of different approaches have been taken to try to find a solution, with certain compromises being made along the way. In this paper, we present an analysis of a novel approach that replaces the supremum within a morphological operation with the LogExp approximation of the maximum for matrix-valued colours. This approach has the advantage of extending the associativity of dilation from the one-dimensional to the higher-dimensional case. Furthermore, the minimality property is investigated and a relaxation specified to ensure that the approach is continuously dependent on the input data.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001574657700001
DO  - DOI:10.1007/s10851-025-01267-5
UR  - https://juser.fz-juelich.de/record/1046459
ER  -