Using Eigenvalue Derivatives for Edge Detection in DT-MRI Data

This paper introduces eigenvalue derivatives as a fundamental tool to discern the different types of edges present in matrix-valued images. It reviews basic results from perturbation theory, which allow one to compute such derivatives, and shows how they can be used to obtain novel edge detectors for matrix-valued images. It is demonstrated that previous methods for edge detection in matrix-valued images are simplified by considering them in terms of eigenvalue derivatives. Moreover, eigenvalue derivatives are used to analyze and refine the recently proposed Log-Euclidean edge detector. Application examples focus on data from diffusion tensor magnetic resonance imaging (DT-MRI).