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Titel: Highly accurate schemes for PDE-based morphology with general structuring elements
Verfasser: Breuß, Michael
Weickert, Joachim
Sprache: Englisch
Erscheinungsjahr: 2009
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-47709
hdl:20.500.11880/26573
http://dx.doi.org/10.22028/D291-26517
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 236
SciDok-Publikation: 6-Jun-2013
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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