Automated visual-tracking of cell populations in vitro using time-lapse phase contrast microscopy enables quantitative, systematic, and high-throughput measurements of cell behaviors. These measurements include the spatiotemporal quantification of cell migration, mitosis, apoptosis, and the reconstruction of cell lineages. The combination of low signal-to-noise ratio of phase contrast microscopy images, high and varying densities of the cell cultures, topological complexities of cell shapes, and wide range of cell behaviors poses many challenges to existing tracking techniques. This paper presents a fully automated multi-target tracking system that can efficiently cope with these challenges while simultaneously tracking and analyzing thousands of cells observed using time-lapse phase contrast microscopy. The system combines bottom-up and top-down image analysis by integrating multiple collaborative modules, which exploit a fast geometric active contour tracker in conjunction with adaptive interacting multiple models (IMM) motion filtering and spatiotemporal trajectory optimization. The system, which was tested using a variety of cell populations, achieved tracking accuracy in the range of 86.9-92.5%.