M?todo de ponto proximal para c?mputo de filtro de m?dia riemanniano em DTI-RM

• Ano de defesa: 2014
• Autor(a) principal: Alves, Charlan Dellon da Silva
• Orientador(a): Greg?rio, Ronaldo Malheiros
• Banca de defesa: Farias, Ricardo, Cavalcante, Jos? Airton Chaves
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal Rural do Rio de Janeiro
• Programa de Pós-Graduação: Programa de P?s-Gradua??o em Modelagem Matem?tica e Computacional
• Departamento: Instituto de Ci?ncias Exatas
• País: Brasil
• Palavras-chave em Português: filtro de m?dia riemanniana; difus?o tensorial de imagens; m?todo de ponto proximal
• Palavras-chave em Inglês: Riemannian average filter; diffusion tensor images; method of proximal point
• Área do conhecimento CNPq: Matem?tica
• Link de acesso: https://tede.ufrrj.br/jspui/handle/jspui/3045

This paper aims to apply the proximal point method with Schur decomposition to the computation of the Riemannian average as image filter in diffusion tensor magnetic resonance imaging (DT-MRI). In DT-MRI, the image is subdivided into volumetric units called voxels. Analytically, each voxel is the three-dimensional representation of mathematical information relating to a symmetric positive definite matrix of order 3. Geometrically, the voxel takes the form of an ellipsoid whose axes are given by the eigenvectors of the matrix corresponding to it, and the repective lengths of the axes, the eigenvalues. One of the main stages of the processing images in DT-MRI is filtering. At this stage, smoothing techniques and cleaning noises coming from the apparatus used for acquisition are commonly employed. First, in our study, the tensors are generated from a given sequence of real images captured by an resonance magnetic machine, subsequently, a function plotting tensor data from Matlab is used to display the image of the tensor field. In the next step, we implemented the filter of Riemannian average in Matlab that was applied in each image generated previously with the objective of soften it. To accomplish this task is necessary solving an optimization problem for each voxel traversed, defined by information about their neighbors tensor. In geral, noise are characterized by voxels whose representations matrices contain negatives eigenvalues e their geometric representations are given by ellipsoids whose orientation is contrary to the observed anisotropic diffusion region. To filter out noise, usually is replaced defective voxel by an average calculated from its nearest neighbors. In this research we propose a methodology of proximal point in Hadamard manifold as a tool for determining the Riemannian average. From the theoretical point of view, this methodology is which has of most sophisticated in optimization suffering only performance analysis when applied to real situations