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Decomposition of optical flow on the sphere

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Abstract

We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the \(2\)-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are motivated by recent trends in image analysis. In particular we treat \(u+v\) decomposition as well as hierarchical decomposition. Helmholtz decomposition of motion fields is obtained as a natural by-product of the chosen numerical method based on vector spherical harmonics. All models are tested on time-lapse microscopy data depicting fluorescently labelled endodermal cells of a zebrafish embryo.

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Acknowledgments

We thank Pia Aanstad from the University of Innsbruck for sharing her biological insight and for kindly providing the microscopy data. This work has been supported by the Vienna Graduate School in Computational Science (IK I059-N) funded by the University of Vienna. In addition, we acknowledge the support by the Austrian Science Fund (FWF) within the national research networks “Photoacoustic Imaging in Biology and Medicine” (project S10505-N20, Reconstruction Algorithms for PAI) and “Geometry + Simulation” (project S11704, Variational Methods for Imaging on Manifolds).

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Authors and Affiliations

  1. Computational Science Center, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 , Vienna, Austria

    Clemens Kirisits, Lukas F. Lang & Otmar Scherzer

  2. Radon Institute of Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Str. 69, 4040 , Linz, Austria

    Otmar Scherzer

Authors
  1. Clemens Kirisits
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  2. Lukas F. Lang
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  3. Otmar Scherzer
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Correspondence to Lukas F. Lang.

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Kirisits, C., Lang, L.F. & Scherzer, O. Decomposition of optical flow on the sphere. Int J Geomath 5, 117–141 (2014). https://doi.org/10.1007/s13137-013-0055-8

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