Decomposition of optical flow on the sphere

Original Paper

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.

Keywords

Optical flow Vector spherical harmonics Biomedical imaging Computer vision Variational methods  Vector field decomposition 

Mathematics Subject Classification

92C55 92C37 92C17 35A15 68U10 33C55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Clemens Kirisits
    • 1
  • Lukas F. Lang
    • 1
  • Otmar Scherzer
    • 1
    • 2
  1. 1.Computational Science CenterUniversity of ViennaViennaAustria
  2. 2.Radon Institute of Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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