Principal Curves for Lumen Center Extraction and Flow Channel Width Estimation in 3-D Arterial Networks: Theory, Algorithm, and Validation

We present an energy-minimization-based framework for locating the centerline and estimating the width of tubelike objects from their structural network with a nonparametric model. The nonparametric representation promotes simple modeling of nested branches and n -way furcations, i.e., structures that abound in an arterial network, e.g., a cerebrovascular circulation. Our method is capable of extracting the entire vascular tree from an angiogram in a single execution with a proper initialization. A succinct initial model from the user with arterial network inlets, outlets, and branching points is sufficient for complex vasculature. The novel method is based upon the theory of principal curves. In this paper, theoretical extension to grayscale angiography is discussed, and an algorithm to find an arterial network as principal curves is also described. Quantitative validation on a number of simulated data sets, synthetic volumes of 19 BrainWeb vascular models, and 32 Rotterdam Coronary Artery volumes was conducted. We compared the algorithm to a state-of-the-art method and further tested it on two clinical data sets. Our algorithmic outputs-lumen centers and flow channel widths-are important to various medical and clinical applications, e.g., vasculature segmentation, registration and visualization, virtual angioscopy, and vascular atlas formation and population study.