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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
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001046459 520__ $$aMathematical morphology is a part of image processing that employs a moving window to modify pixel values through the application of specific operations. The supremum and infimum are pivotal concepts, yet defining them in a general sense for high-dimensional data such as colour is a challenging endeavour. As a result, a number of different approaches have been taken to try to find a solution, with certain compromises being made along the way. In this paper, we present an analysis of a novel approach that replaces the supremum within a morphological operation with the LogExp approximation of the maximum for matrix-valued colours. This approach has the advantage of extending the associativity of dilation from the one-dimensional to the higher-dimensional case. Furthermore, the minimality property is investigated and a relaxation specified to ensure that the approach is continuously dependent on the input data.
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001046459 7001_ $$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
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