Neurons have complex axonal and dendritic morphologies that are the structural building blocks of neural circuits. The traditional method to capture these morphological structures using manual reconstructions is time-consuming and partly subjective, so it appears important to develop automatic or semi-automatic methods to reconstruct neurons. Here we introduce a fast algorithm for tracking neural morphologies in 3D with simultaneous detection of branching processes. The method is based on existing tracking procedures, adding the machine vision technique of multi-scaling. Starting from a seed point, our algorithm tracks axonal or dendritic arbors within a sphere of a variable radius, then moves the sphere center to the point on its surface with the shortest Dijkstra path, detects branching points on the surface of the sphere, scales it until branches are well separated and then continues tracking each branch. We evaluate the performance of our algorithm on preprocessed data stacks obtained by manual reconstructions of neural cells, corrupted with different levels of artificial noise, and unprocessed data sets, achieving 90% precision and 81% recall in branch detection. We also discuss limitations of our method, such as reconstructing highly overlapping neural processes, and suggest possible improvements. Multi-scaling techniques, well suited to detect branching structures, appear a promising strategy for automatic neuronal reconstructions.