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URN: urn:nbn:de:bsz:291-scidok-46213
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4621/


A shock-capturing algorithm for the di fferential equations of dilation and erosion

Breuß, Michael ; Weickert, Joachim

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Freie Schlagwörter (Englisch): morphological dilation , morphological erosion , finite difference methods
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer: 153
Sprache: Englisch
Erstellungsjahr: 2005
Publikationsdatum: 24.02.2012
Kurzfassung auf Englisch: Dilation and erosion are the fundamental operations in morphological image processing. Algorithms that exploit the formulation of these processes in terms of partial differential equations offer advantages for non-digitally scalable structuring elements and allow sub-pixel accuracy. However, the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel, flux corrected transport (FCT) type algorithm for morphological dilation / erosion with a flat disc. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. In a subsequent corrector step we compensate for these artifacts by means of a stabilised inverse diffusion process that requires a specific nonlinear multidimensional formulation. We prove a discrete maximum-minimum principle in this multidimensional framework. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance very well.
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