A comparative study on multivariate mathematical morphology

The successful application of univariate morphological operators on several domains, along with the increasing need for processing the plethora of available multivalued images, have been the main motives behind the efforts concentrated on extending the mathematical morphology framework to multivariate data. The few theoretical requirements of this extension, consisting primarily of a ranking scheme as well as extrema operators for vectorial data, have led to numerous suggestions with diverse properties. However, none of them has yet been widely accepted. Furthermore, the comparison research work in the current literature, evaluating the results obtained from these approaches, is either outdated or limited to a particular application domain. In this paper, a comprehensive review of the proposed multivariate morphological frameworks is provided. In particular, they are examined mainly with respect to their data ordering methodologies. Additionally, the results of a brief series of illustrative application oriented tests of selected vector orderings on colour and multispectral remote sensing data are also discussed.