Abstract Motivation The functionality of neurons and their role in neuronal networks is tightly connected to the cell morphology. A fundamental problem in many neurobiological studies aiming to unravel this connection is the digital reconstruction of neuronal cell morphology from microscopic image data. Many methods have been developed for this, but they are far from perfect, and better methods are needed. Results Here we present a new method for tracing neuron centerlines needed for full reconstruction. The method uses a fundamentally different approach than previous methods by considering neuron tracing as a Bayesian multi-object tracking problem. The problem is solved using probability hypothesis density filtering. Results of experiments on 2D and 3D fluorescence microscopy image datasets of real neurons indicate the proposed method performs comparably or even better than the state of the art. Availability and Implementation Software implementing the proposed neuron tracing method was written in the Java programming language as a plugin for the ImageJ platform. Source code is freely available for non-commercial use at https://bitbucket.org/miroslavradojevic/phd. Supplementary information Supplementary data are available at Bioinformatics online.