Optical Flow on Evolving Sphere-Like Surfaces

TL;DR

This paper introduces a method for estimating optical flow on evolving sphere-like surfaces, specifically applied to tracking cell motion in live zebrafish embryo microscopy data, using spherical harmonics.

Contribution

It develops a variational approach using vector spherical harmonics for optical flow on evolving surfaces parametrized from the sphere, tailored for biological imaging applications.

Findings

Successful estimation of cell motion on embryo surfaces

Effective use of Galerkin method with spherical harmonics

Numerical results demonstrate applicability to microscopy data

Abstract

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.