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Quaternion colour representations and derived total orderings for morphological operators

Summary: Quaternion colour representations and derived total orderings
for morphological operators
Jes´us Angulo; Centre de Morphologie Math´ematique - Ecole des Mines de Paris; 35, rue Saint-Honor´e, 77305 Fontainebleau
cedex - France
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 par-
ticular in this paper we focus on real quaternions. The paper
presents two main contributions. On the one hand, we have stud-
ied different alternatives to introduce the scalar part to obtain
full colour quaternions. On the other hand, several total lexi-
cographic 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 de-
fine morphological operators for colour images. The theoretical
results are illustrated with examples of processed images.
Let ci = (ri,gi,bi) be the triplet of the red, green and blue
intensities for the pixel i of a digital colour image. The defini-


Source: Angulo,Jesús - Centre de Morphologie Mathématique, Ecole des Mines de Paris


Collections: Computer Technologies and Information Sciences