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Volume: 4 | Article ID: art00089
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Quaternion colour representations and derived total orderings for morphological operators
Jesús Angulo
  DOI :  10.2352/CGIV.2008.4.1.art00089  Published Online :  January 2008
Abstract

The definition of morphological operators for colour images needs a total ordering between the colour points. A colour can be represented according to different algebraic structures, in particular in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied different alternatives to introduce the scalar part to obtain full colour quaternions. On the other hand, several total lexicographic orderings for quaternions according to their different decompositions have been defined. These quaternionic orderings have been characterised in order to identify the most useful to define morphological operators for colour images. The theoretical results are illustrated with examples of processed images.

Journal Title : Conference on Colour in Graphics, Imaging, and Vision
Publisher Name : Society of Imaging Science and Technology
Publisher Location : 7003 Kilworth Lane, Springfield, VA 22151, USA
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 DOI 10.2352/CGIV.2008.4.1.art00089
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Jesús Angulo, "Quaternion colour representations and derived total orderings for morphological operators"  in Proc. IS&T CGIV 2008/MCS'08 4th European Conf. on Colour in Graphics, Imaging, and Vision 10th Int'l Symp. on Multispectral Colour Science,  2008,  pp 417 - 422,  https://doi.org/10.2352/CGIV.2008.4.1.art00089

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Copyright © Society for Imaging Science and Technology 2008
72010351
Conference on Colour in Graphics, Imaging, and Vision
conf colour graph imag vis
2158-6330
Society of Imaging Science and Technology
7003 Kilworth Lane, Springfield, VA 22151, USA
2158-6330(20080101)2008:1L.417;1-
cgiv_v2008n1/splitsection89.xml
/ist/cgiv/2008/00002008/00000001/art00089
Articles
Quaternion colour representations and derived total orderings for morphological operators
AnguloJesús
01012008
2008
1
417
422
2008
The definition of morphological operators for colour images needs a total ordering between the colour points. A colour can be represented according to different algebraic structures, in particular in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied different alternatives to introduce the scalar part to obtain full colour quaternions. On the other hand, several total lexicographic orderings for quaternions according to their different decompositions have been defined. These quaternionic orderings have been characterised in order to identify the most useful to define morphological operators for colour images. The theoretical results are illustrated with examples of processed images.