We present a fast and robust approach to tracking the evolving shape of whole fluorescent cells in time-lapse series. The proposed tracking scheme involves two steps. First, coherence-enhancing diffusion filtering is applied on each frame to reduce the amount of noise and enhance flow-like structures. Second, the cell boundaries are detected by minimizing the Chan-Vese model in the fast level set-like and graph cut frameworks. To allow simultaneous tracking of multiple cells over time, both frameworks have been integrated with a topological prior exploiting the object indication function. The potential of the proposed tracking scheme and the advantages and disadvantages of both frameworks are demonstrated on 2-D and 3-D time-lapse series of rat adipose-derived mesenchymal stem cells and human lung squamous cell carcinoma cells, respectively.