%0 Journal Article
%A Kahra, Marvin
%A Breuß, Michael
%A Kleefeld, Andreas
%A Welk, Martin
%T Matrix-Valued LogSumExp Approximation for Colour Morphology
%J Journal of mathematical imaging and vision
%V 67
%N 5
%@ 0924-9907
%C Dordrecht [u.a.]
%I Springer Science + Business Media B.V
%M FZJ-2025-03812
%P 52
%D 2025
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:001574657700001
%R 10.1007/s10851-025-01267-5
%U https://juser.fz-juelich.de/record/1046459