001047562 001__ 1047562
001047562 005__ 20251128084740.0
001047562 020__ $$a978-3-032-09543-5 (print)
001047562 020__ $$a978-3-032-09544-2 (electronic)
001047562 0247_ $$2doi$$a10.1007/978-3-032-09544-2_29
001047562 0247_ $$2ISSN$$a0302-9743
001047562 0247_ $$2ISSN$$a1611-3349
001047562 037__ $$aFZJ-2025-04388
001047562 041__ $$aEnglish
001047562 1001_ $$00000-0002-6268-7050$$aWelk, Martin$$b0$$eCorresponding author
001047562 1112_ $$aDiscrete Geometry and Mathematical Morphology$$cGroningen$$d2025-11-03 - 2025-11-06$$gDGMM 2025$$wNetherlands
001047562 245__ $$aMorphological PDEs with Rotationally Invariant Space-Fractional Derivatives
001047562 260__ $$aCham$$bSpringer Nature Switzerland$$c2025
001047562 29510 $$aDiscrete Geometry and Mathematical Morphology
001047562 300__ $$a401 - 414
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001047562 4900_ $$aLecture Notes in Computer Science$$v16296
001047562 520__ $$aThe spatial derivatives in Hamilton-Jacobi partial differential equations for the definition of morphological operations such as dilation and erosion for grey-value images are replaced by fractional derivatives of arbitrary positive order. Focus is laid on geometric invariance with respect to reflections and rotations so that directional bias towards the coordinate directions is avoided. Discretisation of directional fractional derivatives via truncated general power series ultimately leads to an optimisation problem for the advection direction. We numerically compare the proposed fractional morphological operations with conventional counterparts and a simpler fractional-order alternative on grey-value images to show interesting phenomena and gain insights into the effects of the non-local nature of the fractional derivatives which merit further investigation.
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001047562 588__ $$aDataset connected to CrossRef Book Series, Journals: juser.fz-juelich.de
001047562 7001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b1$$ufzj
001047562 7001_ $$0P:(DE-HGF)0$$aBreuß, Michael$$b2
001047562 7001_ $$0P:(DE-HGF)0$$aBurgeth, Bernhard$$b3
001047562 773__ $$a10.1007/978-3-032-09544-2_29$$p401–414$$v16296
001047562 8564_ $$uhttps://link.springer.com/chapter/10.1007/978-3-032-09544-2_29
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001047562 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a Saarland University$$b3
001047562 9131_ $$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
001047562 9141_ $$y2025
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