Angiogenesis, the growth of new blood vessels from pre-existing vessels, is a critical step in cancer invasion. Better understanding of the angiogenic mechanisms is required to develop effective antiangiogenic therapies for cancer treatment. We culture angiogenic vessels in 3D microfluidic devices under different Sphingosin-1-phosphate (S1P) conditions and develop an automated vessel formation tracking system (AVFTS) to track the angiogenic vessel formation and extract quantitative vessel information from the experimental time-lapse phase contrast images. The proposed AVFTS first preprocesses the experimental images, then applies a distance transform and an augmented fast marching method in skeletonization, and finally implements the Hungarian method in branch tracking. When applying the AVFTS to our experimental data, we achieve 97.3% precision and 93.9% recall by comparing with the ground truth obtained from manual tracking by visual inspection. This system enables biologists to quantitatively compare the influence of different growth factors. Specifically, we conclude that the positive S1P gradient increases cell migration and vessel elongation, leading to a higher probability for branching to occur. The AVFTS is also applicable to distinguish tip and stalk cells by considering the relative cell locations in a branch. Moreover, we generate a novel type of cell lineage plot, which not only provides cell migration and proliferation histories but also demonstrates cell phenotypic changes and branch information.