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		<reportnumber>INPE-5616-RPQ/671</reportnumber>
		<citationkey>Banon:1995:ChTrEl</citationkey>
		<title>Characterization of translation-invariant elementary morphological operators between gray-level images</title>
		<year>1995</year>
		<type>RPQ</type>
		<numberofpages>65</numberofpages>
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		<author>Banon, Gerald Jean Francis,</author>
		<resumeid>8JMKD3MGP5W/3C9EMTE</resumeid>
		<orcid>0000-0001-6942-4440</orcid>
		<group>DPI-INPE-MCT-BR</group>
		<affiliation>Instituto Nacional de Pesquisas Espaciais (INPE)</affiliation>
		<e-mailaddress>sergio@sid.inpe.br</e-mailaddress>
		<institution>INPE</institution>
		<city>São José dos Campos</city>
		<edition>x</edition>
		<transferableflag>1</transferableflag>
		<keywords>mathematical morphology, dilation, erosion, anti-dilation, anti-erosion, translation invariance, window operator, neural network, Hiejmans' operator, flat operator, characterization, image processing, measure, Morfologia matemática, dilatação, erosão, anti-dilatação, anti-erosão, invariância de tradução, operador de janela, rede neural, operador de Hiejmans, operador plano, caracterização, processamento de imagem, medida.</keywords>
		<abstract>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 the 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. The characterization by confrontation is the natural one within the theory of operator decomposition. The characterization by selection and the one by decomposition correspond, respectively, to efficient serial and parallel computational implementations.</abstract>
		<area>SRE</area>
		<language>en</language>
		<textlanguage>en</textlanguage>
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		<notes>A 12 page abstract has appeared in the SPIE's vol. 2568.</notes>
		<notes>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.</notes>
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