The paper presents numerical algorithms, post processing and validation steps for an automated cell tracking and cell lineage tree reconstruction from large-scale 3D+time two-photon laser scanning microscopy images of early stages of Zebrafish (Danio rerio) embryo development. The cell trajectories are extracted as centered paths inside segmented spatio-temporal tree structures representing cell movements and divisions. Such paths are found by using a suitably designed and computed constrained distance functions and by a backtracking in the steepest descent direction of a potential field based on a combination of these distance functions combination. Since the calculations are performed on big data, parallelization is required to speed up the processing. By careful choice and tuning of algorithm parameters we can adapt the calculations to the microscope images of vertebrae species. Then we can compare the results with ground truth data obtained by manual checking of cell links by biologists and measure the accuracy of our algorithm. Using an automatic validation process and visualization tool that can display ground truth data and our result simultaneously, along with the original 3D data, we can easily verify the correctness of the tracking.