Morphological operators on complex signals

This paper presents a novel approach to the generalization of mathematical morphology to complex signals and images. This generalization is strongly dependent upon the issue of multivariate order relationships. Although there is no natural way to order multivariate data such as complex numbers, it is possible to design an order relationship such that it meets criteria that are appropriate to complex signal processing. We first outline the criteria that the order relationship should meet. We then propose a new order relationship that meets these criteria. Based on this order relationship, we construct the basic operators in mathematical morphology: dilations and erosions. (C) 2003 Elsevier B.V. All rights reserved.