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