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Lattice auto-associative memories induced supervised ordering defining a multivariate morphology on hyperspectral data

Mathematical morphology is the non-linear Lattice Theory based construction of image filters. It has been very successful for binary and grayscale images, where the intensity values come from complete lattices. However, for multivariate images, such as hyperspectral images, the definition of a total order is needed. In this paper we follow the line of research producing such orderings from the construction of supervised classifiers. We use Lattice Associative Memories to model the classes and the Chebyschev distance between recalled and original input as the discriminant function. Besides lexicographic order is applied to resolve classification ties. The resulting system provides a complete ordering on the hyperspectral image pixels allowing the definition of morphological operators and filters. We demonstrate some results on the well known Pavia image.