@TechReport{Banon:1995:ChTrEl,
               author = "Banon, Gerald Jean Francis",
                title = "Characterization of translation-invariant elementary morphological 
                         operators between gray-level images",
          institution = "INPE",
                 year = "1995",
                 type = "RPQ",
               number = "INPE-5616-RPQ/671",
              address = "S{\~a}o Jos{\'e} dos Campos",
                 note = "{A 12 page abstract has appeared in the SPIE's vol. 2568.} and 
                         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.",
             keywords = "mathematical morphology, dilation, erosion, anti-dilation, 
                         anti-erosion, translation invariance, window operator, neural 
                         network, Hiejmans' operator, flat operator, characterization, 
                         image processing, measure, Morfologia matem{\'a}tica, 
                         dilata{\c{c}}{\~a}o, eros{\~a}o, anti-dilata{\c{c}}{\~a}o, 
                         anti-eros{\~a}o, invari{\^a}ncia de tradu{\c{c}}{\~a}o, 
                         operador de janela, rede neural, operador de Hiejmans, operador 
                         plano, caracteriza{\c{c}}{\~a}o, processamento de imagem, 
                         medida.",
             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.",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)}",
             language = "en",
                pages = "65",
                  ibi = "83LX3pFwXQZeBBx/PNoH",
                  url = "http://urlib.net/ibi/83LX3pFwXQZeBBx/PNoH",
           targetfile = "target.pdf",
        urlaccessdate = "05 maio 2024"
}