Total variation and mean curvature PDEs on the space of positions and orientations

Remco Duits, Etienne St-Onge, Jim Portegies, Bart Smets

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Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space (Formula Presented) of positions and orientations as a Lie group quotient in SE(d). For (Formula Presented) this is called ‘total roto-translation variation’ by Chambolle & Pock. We extend this to (Formula Presented), by a PDE-approach with a limiting procedure for which we prove convergence. We also include a Mean Curvature Flow (MCF) in our PDE model on (Formula Presented). This was first proposed for (Formula Presented) by Citti et al. and we extend this to d=3. Furthermore, for d=2 we take advantage of locally optimal differential frames in invertible orientation scores (OS). We apply our TVF and MCF in the denoising/enhancement of crossing fiber bundles in DW-MRI. In comparison to data-driven diffusions, we see a better preservation of bundle boundaries and angular sharpness in fiber orientation densities at crossings. We support this by error comparisons on a noisy DW-MRI phantom. We also apply our TVF and MCF in enhancement of crossing elongated structures in 2D images via OS, and compare the results to nonlinear diffusions (CED-OS) via OS.

Originele taal-2Engels
TitelScale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings
RedacteurenJan Lellmann, Jan Modersitzki, Martin Burger
Plaats van productieBerlin
UitgeverijSpringer
Pagina's211-223
Aantal pagina's13
ISBN van elektronische versie978-3-030-22368-7
ISBN van geprinte versie978-3-030-22367-0
DOI's
StatusGepubliceerd - 5 jun 2019
Evenement7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019 - Hofgeismar, Duitsland
Duur: 30 jun 20194 jul 2019

Publicatie series

NaamLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11603 LNCS
ISSN van geprinte versie0302-9743
ISSN van elektronische versie1611-3349

Congres

Congres7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019
LandDuitsland
StadHofgeismar
Periode30/06/194/07/19

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  • Citeer dit

    Duits, R., St-Onge, E., Portegies, J., & Smets, B. (2019). Total variation and mean curvature PDEs on the space of positions and orientations. In J. Lellmann, J. Modersitzki, & M. Burger (editors), Scale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings (blz. 211-223). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11603 LNCS). Springer. https://doi.org/10.1007/978-3-030-22368-7_17