%0 Report
%@ INPE-5616-RPQ/671
%T Characterization of translation-invariant elementary morphological operators between gray-level images
%D 1995
%8 November
%9 research report
%A Banon, Gerald J. F.,
%I Instituto Nacional de Pesquisas Espaciais - INPE
%C CP 515, 12201-970 São José dos Campos, SP, Brazil
%K mathematical morphology, dilation, erosion, anti-dilation, anti-erosion, translation invariance, window operator, neural network, hiejmans' operator, flat operator, characterization, image processing, measure.
%X The four classes of Mathematical Morphology elementary operators: dilations, erosions, anti-dilations and anti-erosions have proved to be of fundamental importance to 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 from K1 to K2, called Elementary Look Up Tables.
%O A 12 page abstract has appeared in the SPIE's vol. 2568; this work has been supported by ProTeM-CC/CNPq through the AnIMoMat project, contract 680067/94-9, and by CNPq under contract 300966/90-3.