Modelos variacionais em processamento de imagens - formulação primal e dual

• Autor(a) principal: Freitas, Karla Barbosa de
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/16789
• topic: 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

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.