Please use this identifier to cite or link to this item: doi:10.22028/D291-26316
Title: A shock-capturing algorithm for the differential equations of dilation and erosion
Author(s): Breuß, Michael
Weickert, Joachim
Language: English
Year of Publication: 2005
Free key words: morphological dilation
morphological erosion
finite difference methods
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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.
Link to this record: urn:nbn:de:bsz:291-scidok-46213
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 153
Date of registration: 24-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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