Abstract
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).
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Schultz, T., Seidel, HP. (2008). Using Eigenvalue Derivatives for Edge Detection in DT-MRI Data. In: Rigoll, G. (eds) Pattern Recognition. DAGM 2008. Lecture Notes in Computer Science, vol 5096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69321-5_20
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DOI: https://doi.org/10.1007/978-3-540-69321-5_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69320-8
Online ISBN: 978-3-540-69321-5
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