Automated, large-scale quantitative morphologic analysis of extended three-dimensional (3-D) branched structures such as neurons and vasculature is of broad interest to biomedicine, especially efforts such as the Human Brain Project, and angiogenesis. The present work has resulted in a key enabling technology for such studies - rapid, accurate fully-automatic 3-D tracing of such structures from confocal image stacks. The robustness and efficiency of the proposed method makes it attractive for large-scale applications such as high-throughput assays in the pharmaceutical industry, and initiatives such as the Human Brain Project. Also of interest are attempts to simulate computationally the electrochemical behavior of large collections of neurons for which actual, rather than simulated, neuro-anatomical data, would be valuable. Finally, of long-term interest are emerging studies of the development and growth of live neurons observed over time, for which the present method can provide a powerful morphometric tool.