Filtro riemanniano adaptativo baseado em centros de massas: uma aplicação à difusão tensorial de imagens por ressonância magnética - Alves, Charlan Dellon da Silva (2020)
This thesis presents an edge preserving and tensor filtering method for diffusion tensor image. The main idea consists in using the L α Riemannian centers of mass attached to the edge information estimated in the domain of the diffusion tensor so that the image edges not been smoothed in the filtering process. For α ∈ [1, 2], the method encompasses both the standard case of the Riemannian weighted mean filter (α = 2) and the Riemannian weighted median filter (α = 1) in only one filter. Aiming to establish the fundamentals for the well-posedness of the proposed filter, called adaptive Riemannian filter (ARF), we claimed a theoretical result previously stated in the literature on the continuity of the L α Riemannian centers of mass, with respect to the parameter α and the points in the neighborhood of the filtered tensor.