Decomposition of Optical Flow on the Sphere
This work addresses motion analysis in spherical domains for biological imaging, but appears incremental as it adapts existing methods to a specific geometry.
The authors tackled the problem of estimating and decomposing motion fields on the 2-sphere using variational regularization methods, with results tested on time-lapse microscopy data of zebrafish embryo cells.
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.