Um estudo comparativo sobre a influência dos k-centróides no processo de segmentação de imagens em DTI-RM

Abstract

Diffusion tensor magnetic resonance imaging (DT-MRI) is a non-invasive and effective technique for detecting tumors or anomalies in living tissues. In DT-RMI, machine learning algorithms such as K -Means can be used in processes like image segmentation. The K -Means algorithm originally uses centers of mass defined under a Euclidean setting. The objective is to identify similar elements to group them in classes belonging to the same region of the image. On the other hand, the existence and uniqueness of minimizing geodesic segments, as well as closed expressions for computing distances between two arbitrary points in some Riemannian spaces, as it happens in the manifold of symmetric positive definite matrices, enable the well-posedness of centers of mass under a non-Euclidean setting. Therefore, images in DT-RMI, whose pixels, in the two-dimensional case, or voxels, in the three-dimensional one, are respectively represented by symmetric positive definite matrices of order 2 and 3, can be treated as well from a non-Euclidean setting, which uses the natural geometry of this manifold. In this work, we developed a comparative study on the influence of some centers of mass, defined both from a Euclidean and Riemannian setting, in the image segmentation process using the K -Means algorithm..