Nonlinear Operations for Colour Images Based on Pairwise Vector Ordering

A new vector ordering is proposed and its application to colour image processing demonstrated. Partial ordering is first used rank the vectors in groups of two and then a simple reduced ordering is applied to each pair to give a full ordering. As the initial ordering is based on pairs of vectors, the technique is termed pairwise vector ordering. The new ordering is used to develop a median filter and colour morphological operations. A quantitative evaluation shows the pairwise vector median to be less effective for noise reduction than the well known vector median filter, albeit with reduced complexity. Colour morphological erosions and dilations based on the pairwise ordering are shown to produce well behaved results that conform with expectations, without any of the problems associated with applying the operations to the individual channels. Their application to multiscale image analysis is also investigated.