Edge Detection from MRI and DTI Images with an Anisotropic Vector Field Flow Using a Divergence Map

Abstract: The aim of this work is the extraction of edges from Magnetic Resonance Imaging (MRI) and Diffusion Tensor Imaging (DTI) images by a deformable contour procedure, using an external force field derived from an anisotropic flow. Moreover, we introduce a divergence map in order to check the convergence of the process. As we know from vector calculus, divergence is a measure of the magnitude of a vector field convergence at a given point. Thus by means level curves of the divergence map, we have automatically selected an initial contour for the deformation process. If the initial curve includes the areas from which the vector field diverges, it will be able to push the curve towards the edges. Furthermore the divergence map highlights the presence of curves pointing to the most significant geometric parts of boundaries corresponding to high curvature values. In this way, the skeleton of the extracted object will be rather well defined and may subsequently be employed in shape analysis and morphological studies.