  In this work we consider optical flow on evolving Riemannian 2-manifolds
which can be parametrised from the 2-sphere. Our main motivation is to estimate
cell motion in time-lapse volumetric microscopy images depicting fluorescently
labelled cells of a live zebrafish embryo. We exploit the fact that the
recorded cells float on the surface of the embryo and allow for the extraction
of an image sequence together with a sphere-like surface. We solve the
resulting variational problem by means of a Galerkin method based on vector
spherical harmonics and present numerical results computed from the
aforementioned microscopy data.
