Journal Article

FZJ-2025-03812

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Matrix-Valued LogSumExp Approximation for Colour Morphology

Kahra, M. (Corresponding author) ; Breuß, M. ; Kleefeld, A.FZJ* ; Welk, M.

2025
Springer Science + Business Media B.V Dordrecht [u.a.]

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Please use a persistent id in citations: doi:10.1007/s10851-025-01267-5  doi:10.34734/FZJ-2025-03812

Abstract: 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2025

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Engineering, Computing and Technology ; DEAL Springer ; Essential Science Indicators ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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