001046459 001__ 1046459 001046459 005__ 20260122125235.0 001046459 0247_ $$2doi$$a10.1007/s10851-025-01267-5 001046459 0247_ $$2ISSN$$a0924-9907 001046459 0247_ $$2ISSN$$a1573-7683 001046459 0247_ $$2datacite_doi$$a10.34734/FZJ-2025-03812 001046459 0247_ $$2WOS$$aWOS:001574657700001 001046459 037__ $$aFZJ-2025-03812 001046459 041__ $$aEnglish 001046459 082__ $$a510 001046459 1001_ $$0P:(DE-HGF)0$$aKahra, Marvin$$b0$$eCorresponding author 001046459 245__ $$aMatrix-Valued LogSumExp Approximation for Colour Morphology 001046459 260__ $$aDordrecht [u.a.]$$bSpringer Science + Business Media B.V$$c2025 001046459 3367_ $$2DRIVER$$aarticle 001046459 3367_ $$2DataCite$$aOutput Types/Journal article 001046459 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1764239145_6908 001046459 3367_ $$2BibTeX$$aARTICLE 001046459 3367_ $$2ORCID$$aJOURNAL_ARTICLE 001046459 3367_ $$00$$2EndNote$$aJournal Article 001046459 520__ $$aMathematical morphology is a part of image processing that employs a moving window to modify pixel values through the application of specific operations. The supremum and infimum are pivotal concepts, yet defining them in a general sense for high-dimensional data such as colour is a challenging endeavour. As a result, a number of different approaches have been taken to try to find a solution, with certain compromises being made along the way. In this paper, we present an analysis of a novel approach that replaces the supremum within a morphological operation with the LogExp approximation of the maximum for matrix-valued colours. This approach has the advantage of extending the associativity of dilation from the one-dimensional to the higher-dimensional case. Furthermore, the minimality property is investigated and a relaxation specified to ensure that the approach is continuously dependent on the input data. 001046459 536__ $$0G:(DE-HGF)POF4-5112$$a5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511)$$cPOF4-511$$fPOF IV$$x0 001046459 588__ $$aDataset connected to CrossRef, Journals: juser.fz-juelich.de 001046459 7001_ $$0P:(DE-HGF)0$$aBreuß, Michael$$b1 001046459 7001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b2$$ufzj 001046459 7001_ $$0P:(DE-HGF)0$$aWelk, Martin$$b3 001046459 773__ $$0PERI:(DE-600)1479363-5$$a10.1007/s10851-025-01267-5$$gVol. 67, no. 5, p. 52$$n5$$p52$$tJournal of mathematical imaging and vision$$v67$$x0924-9907$$y2025 001046459 8564_ $$uhttps://juser.fz-juelich.de/record/1046459/files/s10851-025-01267-5.pdf$$yOpenAccess 001046459 909CO $$ooai:juser.fz-juelich.de:1046459$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire 001046459 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a Brandenburg University of Technology Cottbus-Senftenberg$$b0 001046459 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a Brandenburg University of Technology Cottbus-Senftenberg$$b1 001046459 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)169421$$aForschungszentrum Jülich$$b2$$kFZJ 001046459 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a UMIT TIROL$$b3 001046459 9131_ $$0G:(DE-HGF)POF4-511$$1G:(DE-HGF)POF4-510$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5112$$aDE-HGF$$bKey Technologies$$lEngineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action$$vEnabling Computational- & Data-Intensive Science and Engineering$$x0 001046459 9141_ $$y2025 001046459 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)1160$$2StatID$$aDBCoverage$$bCurrent Contents - Engineering, Computing and Technology$$d2024-12-10 001046459 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 001046459 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bJ MATH IMAGING VIS : 2022$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)3002$$2StatID$$aDEAL Springer$$d2024-12-10$$wger 001046459 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)9900$$2StatID$$aIF < 5$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 001046459 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2024-12-10 001046459 915__ $$0StatID:(DE-HGF)0420$$2StatID$$aNationallizenz$$d2024-12-10$$wger 001046459 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2024-12-10 001046459 920__ $$lno 001046459 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0 001046459 980__ $$ajournal 001046459 980__ $$aVDB 001046459 980__ $$aUNRESTRICTED 001046459 980__ $$aI:(DE-Juel1)JSC-20090406 001046459 9801_ $$aFullTexts