4D numerical schemes for cell image segmentation and tracking. Finite Volumes for

Abstract The paper introduces techniques for space-time segmentation and tracking in time sequences of 3D images of zebrafish embryogenesis. Instead of treating each 3D image individually, we consider the whole time sequence as a single 4D image and perform the extraction of objects and cell tracking in four dimensions. The segmentation of the spatiotemporal objects corresponding to the time evolution of the individual cells is realized by using the generalized subjective surface model that is discretized by a 4D finite volume scheme. Afterwards, we use the distance functions to the borders of the segmented spatiotemporal objects and to the initial cell center positions in order to backtrack the cell trajectories that can be understood as 4D parametrized curves. The distance functions are obtained by numerical solution of the time relaxed eikonal equation