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). © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Schultz, T., & Seidel, H. P. (2008). Using eigenvalue derivatives for edge detection in DT-MRI data. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5096 LNCS, pp. 193–202). https://doi.org/10.1007/978-3-540-69321-5_20
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