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.

中文翻译：

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演化的类球体表面上的光流

在这项工作中，我们考虑了可以从 2 球体参数化的演化黎曼 2 流形上的光流。我们的主要动机是在描绘活斑马鱼胚胎荧光标记细胞的延时体积显微镜图像中估计细胞运动。我们利用记录的细胞漂浮在胚胎表面的事实，并允许提取图像序列和球状表面。我们通过基于矢量球谐函数的伽辽金方法解决了由此产生的变分问题，并提供了从上述显微镜数据计算的数值结果。