@TechReport{Banon:1995:ChTrEl,
               author = "Banon, Gerald J. F.",
                title = "Characterization of translation-invariant elementary morphological 
                         operators between gray-level images",
          institution = "Instituto Nacional de Pesquisas Espaciais - INPE",
                 year = "1995",
                 type = "research report",
               number = "INPE-5616-RPQ/671",
              address = "CP 515, 12201-970 S{\~a}o Jos{\'e} dos Campos, SP, Brazil",
                month = "November",
                 note = "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.",
             keywords = "mathematical morphology, dilation, erosion, anti-dilation, 
                         anti-erosion, translation invariance, window operator, neural 
                         network, hiejmans' operator, flat operator, characterization, 
                         image processing, measure.",
             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 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.",
           copyholder = "faria - tese",
        urlaccessdate = "18 maio 2024"
}