We present a novel computational framework for the analysis of high-throughput microscopy videos of living cells. The proposed framework is generally useful and can be applied to different datasets acquired in a variety of laboratory settings. This is accomplished by tying together two fundamental aspects of cell lineage construction, namely cell segmentation and tracking, via a Bayesian inference of dynamic models. In contrast to most existing approaches, which aim to be general, no assumption of cell shape is made. Spatial, temporal, and cross-sectional variation of the analysed data are accommodated by two key contributions. First, time series analysis is exploited to estimate the temporal cell shape uncertainty in addition to cell trajectory. Second, a fast marching (FM) algorithm is used to integrate the inferred cell properties with the observed image measurements in order to obtain image likelihood for cell segmentation, and association. The proposed approach has been tested on eight different time-lapse microscopy data sets, some of which are high-throughput, demonstrating promising results for the detection, segmentation and association of planar cells. Our results surpass the state of the art for the Fluo-C2DL-MSC data set of the Cell Tracking Challenge (Maška et al., 2014).