A nonparametric defocus-based approach to reconstructing thin 3D structures in optical sectioning microscopy

Modeling the electrical properties of neurons (e.g. with a distributed transmission line) requires extensive knowledge of 3D morphological structure, such as dendritic trajectories from the soma. Confocal microscopy provides sharp contrast for acquiring such 3D information, but these microscopes are expensive and not widely accessible, which prompts many researchers to resort to the more accessible optical sectioning microscopy (OSM) techniques using camera lucida to recover 3D structure. Unfortunately, this method is slower and subjective because it requires extensive human intervention. We present and validate a new elegantly simple nonparametric method for semi-automated 3D spatial reconstruction of dendritic trajectories within an OSM slice. We exploit the thin structure of the dendrites and apply depth from defocus techniques for automatic range-finding in the microscope slide without specific knowledge of the optical transfer function of the microscope. Specifically, we interpolate the depth of focus which maximizes the radial high frequency energy in an image patch. In this way, we accurately and efficiently estimate the 3D structure of the dendritic arborization