Using Eigenvalue Derivatives for Edge Detection in DT-MRI Data

Schultz, Thomas; Seidel, Hans-Peter

doi:10.1007/978-3-540-69321-5_20

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Using Eigenvalue Derivatives for Edge Detection in DT-MRI Data

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Schultz, Thomas
Computer Graphics, MPI for Informatics, Max Planck Society;

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Seidel, Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

Schultz, T., & Seidel, H.-P. (2008). Using Eigenvalue Derivatives for Edge Detection in DT-MRI Data. In G. Rigoll (Ed.), Pattern Recognition (pp. 193-202). Berlin: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-1D51-F

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).