Complete ordering and multivariate mathematical morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Total ordering based on space filling curves for multivalued morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Granulometries and pattern spectra for radar signals
Signal Processing
A comparative study on multivariate mathematical morphology
Pattern Recognition
On lexicographical ordering in multivariate mathematical morphology
Pattern Recognition Letters
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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.