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Decomposition of optical flow on the sphere. (English) Zbl 1327.92023

Summary: 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.

MSC:

92C55 Biomedical imaging and signal processing
35A15 Variational methods applied to PDEs
68U10 Computing methodologies for image processing
35R01 PDEs on manifolds
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