  We describe an automated analysis method to quantify the detailed growth
dynamics of a population of bacilliform bacteria. We propose an innovative
approach to frame-sequence tracking of deformable-cell motion by the automated
minimization of a new, specific cost functional. This minimization is
implemented by dedicated Boltzmann machines (stochastic recurrent neural
networks). Automated detection of cell divisions is handled similarly by
successive minimizations of two cost functions, alternating the identification
of children pairs and parent identification. We validate this automatic cell
tracking algorithm using recordings of simulated cell colonies that closely
mimic the growth dynamics of \emph{E. coli} in microfluidic traps. On a batch
of 1100 image frames, cell registration accuracies per frame ranged from 94.5\%
to 100\%, with a high average. Our initial tests using experimental image
sequences of \emph{E. coli} colonies also yield convincing results, with a
registration accuracy ranging from 90\% to 100\%.
