  Determining the trajectories of cells and their lineages or ancestries in
live-cell experiments are fundamental to the understanding of how cells behave
and divide. This paper proposes novel online algorithms for jointly tracking
and resolving lineages of an unknown and time-varying number of cells from
time-lapse video data. Our approach involves modeling the cell ensemble as a
labeled random finite set with labels representing cell identities and
lineages. A spawning model is developed to take into account cell lineages and
changes in cell appearance prior to division. We then derive analytic filters
to propagate multi-object distributions that contain information on the current
cell ensemble including their lineages. We also develop numerical
implementations of the resulting multi-object filters. Experiments using
simulation, synthetic cell migration video, and real time-lapse sequence, are
presented to demonstrate the capability of the solutions.
