Quaternion colour representations and derived total orderings for morphological operators

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. © 2008 Society for Imaging Science and Technology.