Characterization of translation-invariant elementary operators for gray-level morphology
Gerald Jean Francis Banon · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
The four classes of mathematical morphology elementary operators: dilations, erosions, anti- dilations, and anti-erosions have proved to be of fundamental importance of the decomposition/representation of any mapping between complete lattices. In this paper, we are concerned with the characterization of translation invariant window elementary operators (with window W) that transform a gray-level image with finite range K1 into a gray-level image with possibly different finite range K2. Three types of characterization are presented. In the first characterization, called 'characterization by confrontation' each elementary operator depends on a family of mappings from W to K1, called structuring element. In the second characterization, called 'characterization by selection' each elementary operator depends on a family of mappings from W to K2, called impulse response. Finally, in the third characterization, called 'characterization by decomposition' each elementary operator depends on a family of mappings for K1 to K2, called elementary look up tables.