Modelos variacionais aplicados a computação visual

• Autor(a) principal: Santos, Ítalo Messias Félix
• Data de Publicação: 2020
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/316
• topic: Processamento de imagem - Técnicas digitais; Computação gráfica; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::METODOLOGIA E TECNICAS DA COMPUTACAO

In this master’s thesis, we explore analytical and numerical approaches that allow us to bring together variational techniques applied to visual computing (image processing and computer graphics). In this way, we study a version of the functional proposed by Mumford and Shah that is simply rewritten as an energy functional defined by two arguments, these being the piecewise continuous version of an input data and its respective discontinuity points. Then, we explore schems of numerical solutions based on finite elements and finite differences, in addition, we seek possible simplifications for the functional in order to expand the Bourdin’s model applications. In the area of computer graphics we focus on fluid animation. We examined the model named Gradient Vector Flow (GVF), which is defined by a diffusion-reaction vector equation. In this line, we dedicate the studies and analyzes to the preservation of a singular point, in the original field. In this line, we dedicate the studies and analyzes to the preservation of a singular point in the original field, with respect to boundary conditions of the GVF solution, assuming a compact domain, with rectangular geometry. In this respect, we use approximations based on well-collocation method using Haar wavelet functions compared to methods based on explicit finite differences and, a new method, based on implicit finite differences, developed in this dissertation. The focus was to find the method that best preserve the topology of the initial vector field. In these models, the parameters chosen are important for the quality of the results. In this sense, we carried out a study with respect to the sensitivity of the methods to the variation of the parameters and we presented a parameterization model based on inverse problems, directing the research towards the calibration of the methods presented in this dissertation.