Mathematical morphology for vector images using statistical depth

Authors:
Santiago Velasco-Forero;Jesus Angulo
Affiliations:
CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES ParisTech, Fontainebleau Cedex - France;CMM-Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES ParisTech, Fontainebleau Cedex - France
Venue:
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Year:
2011

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Abstract

The open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the "deepest" point a "center-outward ordering" of a multidimensional data distribution and they can be therefore used to construct morphological operators. The fundamental assumption of this data-driven approach is the existence of "background/foreground" image representation. Examples in real color and hyperspectral images illustrate the results.