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doi:10.22028/D291-26324
Titel: | Mathematical morphology on tensor data using the Loewner ordering |
VerfasserIn: | 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 |
Dokumenttyp: | Sonstiges |
Abstract: | 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 |
Datum des Eintrags: | 5-Mär-2012 |
Fakultät: | MI - Fakultät für Mathematik und Informatik |
Fachrichtung: | MI - Mathematik |
Sammlung: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Dateien zu diesem Datensatz:
Datei | Beschreibung | Größe | Format | |
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preprint_160_05.pdf | 1,71 MB | Adobe PDF | Öffnen/Anzeigen |
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