Uma Fundamentação Intervalar Aplicada à Morfologia Matemática

• Ano de defesa: 2008
• Autor(a) principal: Cruz, Marcia Maria de Castro
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Engenharia Elétrica; Automação e Sistemas; Engenharia de Computação; Telecomunicações
• Palavras-chave em Português: Imagens binárias; Imagens intervalares; Morfologia matemática; Matemática intervalar; Incerteza; Reticulados completo; Imagens em níveis de cinza; Dilatação; Erosão; CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA
• Link de acesso: https://repositorio.ufrn.br/jspui/handle/123456789/15127

This work present a interval approach to deal with images with that contain uncertainties, as well, as treating these uncertainties through morphologic operations. Had been presented two intervals models. For the first, is introduced an algebraic space with three values, that was constructed based in the tri-valorada logic of Lukasiewiecz. With this algebraic structure, the theory of the interval binary images, that extends the classic binary model with the inclusion of the uncertainty information, was introduced. The same one can be applied to represent certain binary images with uncertainty in pixels, that it was originated, for example, during the process of the acquisition of the image. The lattice structure of these images, allow the definition of the morphologic operators, where the uncertainties are treated locally. The second model, extend the classic model to the images in gray levels, where the functions that represent these images are mapping in a finite set of interval values. The algebraic structure belong the complete lattices class, what also it allow the definition of the elementary operators of the mathematical morphology, dilation and erosion for this images. Thus, it is established a interval theory applied to the mathematical morphology to deal with problems of uncertainties in images