We present a fully automatic method to track and quantify the morphodynamics of differentiating neurons in fluorescence time-lapse microscopy datasets. While previous efforts have successfully quantified the dynamics of organelles such as the cell body, nucleus, or chromosomes of cultured cells, neurons have proved to be uniquely challenging due to their highly deformable neurites which expand, branch, and collapse. Our approach is capable of robustly detecting, tracking, and segmenting all the components of each neuron present in the sequence including the nucleus, soma, neurites, and filopodia. To meet the demands required for high-throughput processing, our framework is designed to be extremely efficient, capable of processing a single image in approximately two seconds on a conventional notebook computer. For validation of our approach, we analyzed neuronal differentiation datasets in which a set of genes was perturbed using RNA interference. Our analysis confirms previous quantitative findings measured from static images, as well as previous qualitative observations of morphodynamic phenotypes that could not be measured on a large scale. Finally, we present new observations about the behavior of neurons made possible by our quantitative analysis, which are not immediately obvious to a human observer.