Please use this identifier to cite or link to this item: doi:10.22028/D291-26503
Title: PDE-based morphology for matrix fields : numerical solution schemes
Author(s): Burgeth, Bernhard
Breuß, Michael
Didas, Stephan
Weickert, Joachim
Language: English
Year of Publication: 2007
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matrix-valued extension of the nonlinear morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images. Having these two basic operations at our disposal, more advanced morphological operators such as top hats or morphological derivatives for matrix fields with symmetric, positive semidefinite matrices can be constructed. The approach realises a proper coupling of the matrix channels rather than treating them independently. However, from the algorithmic side the usual scalar morphological PDEs are transport equations that require special upwind-schemes or novel high-accuracy predictor-corrector approaches for their adequate numerical treatment. In this chapter we propose the non-trivial extension of these schemes to the matrix-valued setting by exploiting the special algebraic structure available for symmetric matrices. Furthermore we compare the performance and juxtapose the results of these novel matrix-valued high-resolution-type (HRT) numerical schemes by considering top hats and morphological derivatives applied to artificial and real world data sets.
Link to this record: urn:nbn:de:bsz:291-scidok-47503
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 220
Date of registration: 5-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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