Modelos variacionais em processamento de imagens - formulação primal e dual

• Ano de defesa: 2011
• Autor(a) principal: Freitas, Karla Barbosa de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Restauração de imagens; Espaços BV; Equação de Euler-Lagrange; Variação total; Formulação Primal e Dual; Processamento de imagens; Image restoration; BV spaces; Euler-lagrange equation; Total variation; Primal and dual formulation; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16789

This work presents some problems of image processing whose formulations are variational. To illustrate these formulations, we consider the model proposed by Rudin, Osher and Fatemi (ROF), in which deals with image denoising. For a better understanding, we explore some variational calculus concepts, as Euler-Lagrange equations, Total Variation (TV) regularizing terms and image processing methods based on TV . We discuss primal and dual formulations of a variational model, the equivalence between them and its resolution methods. Furthermore, we study a Primal-Dual formulation and its numerical algorithm. Applications related to denoising and image segmentation are presented to illustrate the effectiveness of the methodology.