Centerline Computation and Geometric Analysis of Branching Tubular Surfaces with Application to Blood Vessel Modeling

In this work we present a robust and accurate method for the computation of centerlines inside branching tubular objects starting from a piecewise linear representation of their boundary. The algorithm is based on solving the Eikonal equation on the Voronoi diagram embedded into the object, with wavefront speed inversely proportional to Voronoi ball radius values. As a result, provably accurate centerlines and maximal inscribed ball radius values along them are provided. In the same framework, a method for local surface characterization is also developed, allowing robust computation of the distance of surface points to centerlines and disclosing the relationship of surface points with centerlines. A new surface-based quantity is finally proposed, the normalized tangency deviation, which provides a scale-invariant criterion for surface characterization. The developed methods are applied to 3D models of vascular segments in the context of patient-specific anatomical characterization.