Please use this identifier to cite or link to this item:
doi:10.22028/D291-26324
Title: | Mathematical morphology on tensor data using the Loewner ordering |
Author(s): | Burgeth, Bernhard Feddern, Christian Welk, Martin Weickert, Joachim |
Language: | English |
Year of Publication: | 2005 |
Free key words: | dilation erosion matrix-valued images positive definite matrix |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
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 to this record: | urn:nbn:de:bsz:291-scidok-46281 hdl:20.500.11880/26380 http://dx.doi.org/10.22028/D291-26324 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 160 |
Date of registration: | 5-Mar-2012 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Files for this record:
File | Description | Size | Format | |
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preprint_160_05.pdf | 1,71 MB | Adobe PDF | View/Open |
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