Novel 4-D Open-Curve Active Contour and curve completion approach for automated tree structure extraction

We present novel approaches for fully automated extraction of tree-like tubular structures from 3-D image stacks. A 4-D Open-Curve Active Contour (Snake) model is proposed for simultaneous 3-D centerline tracing and local radius estimation. An image energy term, stretching term, and a novel region-based radial energy term constitute the energy to be minimized. This combination of energy terms allows the 4-D open-curve snake model, starting from an automatically detected seed point, to stretch along and fit the tubular structures like neurites and blood vessels. A graph-based curve completion approach is proposed to merge possible fragments caused by discontinuities in the tree structures. After tree structure extraction, the centerlines serve as the starting points for a Fast Marching segmentation for which the stopping time is automatically chosen. We illustrate the performance of our method with various datasets.