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Titel: Mathematical morphology on tensor data using the Loewner ordering
Verfasser: Burgeth, Bernhard
Feddern, Christian
Welk, Martin
Weickert, Joachim
Sprache: Englisch
Erscheinungsjahr: 2005
Freie Schlagwörter: dilation
erosion
matrix-valued images
positive definite matrix
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: The notions of maximum and minimum are the key to the powerful tools of greyscale morphology. Unfortunately these notions do not carry over directly to tensor-valued data. Based upon the Loewner ordering for symmetric matrices this paper extends the maximum and minimum operation to the tensor-valued setting. This provides the ground to establish matrix-valued analogues of the basic morphological operations ranging from erosion/dilation to top hats. In contrast to former attempts to develop a morphological machinery for matrices, the novel definitions of maximal/minimal matrices depend continuously on the input data, a property crucial for the construction of morphological derivatives such as the Beucher gradient or a morphological Laplacian. These definitions are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. The morphological operations resulting from a component-wise maximum/minimum of the matrix channels disregarding their strong correlation fail to be rotational invariant. Experiments on DT-MRI images as well as on indefinite matrix data illustrate the properties and performance of our morphological operators.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-46281
hdl:20.500.11880/26380
http://dx.doi.org/10.22028/D291-26324
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 160
SciDok-Publikation: 5-Mär-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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