We have developed methods for segmentation and tracking of cells in time-lapse phase-contrast microscopy images. Our multi-object Bayesian algorithm detects and tracks large numbers of cells in presence of clutter and identifies cell division. To solve the data association problem, the assignment of current measurements to cell tracks, we tested various cost functions with both an optimal and a fast, suboptimal assignment algorithm. We also propose metrics to quantify cell migration properties, such as motility and directional persistence, and compared our findings of cell migration with the standard random walk model. We measured how cell populations respond to the physical stimuli presented in the environment, for example, the stiffness property of the substrate. Our analysis of hundreds of spatio-temporal cell trajectories revealed significant differences in the behavioral response of fibroblast cells to changes in hydrogel conditions.