Please use this identifier to cite or link to this item: doi:10.22028/D291-26517
Title: Highly accurate schemes for PDE-based morphology with general structuring elements
Author(s): Breuß, Michael
Weickert, Joachim
Language: English
Year of Publication: 2009
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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 to this record: urn:nbn:de:bsz:291-scidok-47709
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 236
Date of registration: 6-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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