Principal curves as skeletons of tubular objects: locally characterizing the structures of axons

Developments in image acquisition technology make high volumes of neuron images available to neuroscientists for analysis. However, manual processing of these images is not practical and is infeasible for larger and larger scale studies. Reliable interpretation and analysis of high volume data requires accurate quantitative measures. This requires analysis algorithms to use mathematical models that inherit the underlying geometry of biological structures in order to extract topological information. In this paper, we first introduce principal curves as a model for the underlying skeleton of axons and branches, then describe a recursive principal curve tracing (RPCT) method to extract this topology information from 3D microscopy imagery. RPCT first finds samples on the one dimensional principal set of the intensity function in space. Then, given an initial direction and location, the algorithm iteratively traces the principal curve in space using our principal curve tracing (PCT) method. Recursive implementation of PCT provides a compact solution for extracting complex tubular structures that exhibit bifurcations.