Skeletonization is an important procedure in morphological analysis of three-dimensional objects. A simplified object geometry allows easy semantic interpretation at the cost of high computational effort. This paper introduces a fast morphological thinning approach for skeletonization of tubular structures and objects of arbitrary shape. With minimized constraints for erosions at the surface, hit-ratio is increased allowing high performance thinning with large datasets. Time consuming neighbourhood checking is solved by use of fast indexing lookup tables. The novel algorithm homogenously erodes the object's surface, resulting in an accurate extraction of the centerline, even when the medial axis is placed between the actual voxel-grid. The thinning algorithm is applied for vessel tree analysis in the field of computer-based medical diagnostics and thus has to meet high robustness and performance requirements.