In order to facilitate the study of neuron migration, we propose a method for 3-D detection and tracking of centrosomes in time-lapse confocal image stacks of live neuron cells. We combine Laplacian-based blob detection, adaptive thresholding, and the extraction of scale and roundness features to find centrosome-like objects in each frame. We link these detections using the joint probabilistic data association filter (JPDAF) tracking algorithm with a Newtonian state-space model tailored to the motion characteristics of centrosomes in live neurons. We apply our algorithm to image sequences containing multiple cells, some of which had been treated with motion-inhibiting drugs. We provide qualitative results and quantitative comparisons to manual segmentation and tracking results showing that our motion estimates closely agree with those generated by neurobiology experts.