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comparison research work in the current literature, evaluating the results obtained from these approaches, is either outdated or limited to a particular application domain.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.

In this paper, we present the results of applying global morphological texture descriptors to the problem of content-based remote sensing image retrieval. Specifically, we explore the potential of recently developed multiscale texture descriptors, namely, the circular covariance histogram and the rotation-invariant point triplets. Moreover, we introduce a couple of new descriptors, exploiting the Fourier power spectrum of the quasi-flat-zone-based scale space of their input. The descriptors are evaluated with the UC Merced Land Use-Land Cover data set, which has been only recently made public. The proposed approach is shown to outperform the best known retrieval scores, despite its shorter feature vector length, thus asserting the practical interest of global content descriptors as well as of mathematical morphology in this context. Index Terms-Content-based image retrieval (CBIR), mathematical morphology (MM), remote sensing, texture description.

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