Quantifying the behavior of cells individually, and in clusters as part of a population, under a range of experimental conditions, is a challenging computational task with many biological applications. We propose a versatile algorithm for segmentation and tracking of multiple motile epithelial cells during wound healing using time-lapse video. The segmentation part of the proposed method relies on a level set-based active contour algorithm that robustly handles a large number of cells. The tracking part relies on a detection-based multiple-object tracking method with delayed decision enabled by multi-hypothesis testing. The combined method is robust to complex cell behavior including division and apoptosis, and to imaging artifacts such as illumination changes.