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An approach to color-morphology based on Einstein addition and Loewner order

  • In this article, a new method to process color images via mathematical morphology is presented. Precisely, each pixel of an image contained in the rgb-space is converted into a 2 x 2-matrix representing a point in a color bi-cone. The supremum and infimum needed for dilation and erosion, respectively, are calculated with respect to the Loewner order. Since the result can be outside the bi-cone, a map is proposed to ensure the algebraic closure in the bi-cone. A new addition and subtraction based on Einstein’s Relativity Theory is used to define morphological operation such as top-hats, gradients, and morphological Laplacian. Since the addition and subtraction is defined in the unit ball, a suitable mapping between those two spaces is constructed. A comparison with the component-wise approach and the full ordering using lexicographical cascades approach demonstrate the feasibility and capabilities of the proposed approach.

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Metadaten
Author: Andreas Kleefeld, Bernhard Burgeth
URL:http://www.sciencedirect.com/science/journal/01678655/47
DOI:https://doi.org/10.1016/j.patrec.2014.01.018
ISSN:0167-8655
Title of the source (English):Pattern Recognition Letters
Document Type:Scientific journal article not peer-reviewed
Language:English
Year of publication:2014
Tag:Color space; Einstein addition; Loewner order; Mathematical morphology
Volume/Year:47
First Page:29
Last Page:39
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Numerische Mathematik und Wissenschaftliches Rechnen
Institution name at the time of publication:Fakultät für Mathematik, Naturwissenschaften und Informatik (eBTU) / LS Mathematik, insbesondere Numerische Mathematik und Wissenschaftliches Rechnen
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