Topology adaptive vessel network skeleton extraction with novel medialness measuring function. 
Vessel tree skeleton extraction is widely applied in vascular structure segmentation, however, conventional approaches often suffer from the adjacent interferences and poor topological adaptability.  To avoid these problems, a robust, topology adaptive tree-like structure skeleton extraction framework is proposed in this paper.  Specifically, to avoid the adjacent interferences, a local message passing procedure called Gaussian affinity voting (GAV) is proposed to realize adaptive scale-growing of vessel voxels.  Then the medialness measuring function (MMF) based on GAV, namely GAV-MMF, is constructed to extract medialness patterns robustly.  In order to improve topological adaptability, a level-set graph embedded with GAV-MMF is employed to build initial curve skeletons without any user interaction.  Furthermore, the GAV-MMF is embedded in stretching open active contours (SOAC) to drive the initial curves to the expected location, maintaining smoothness and continuity.  In addition, to provide an accurate and smooth final skeleton tree topology, topological checks and skeleton network reconfiguration is proposed.  The continuity and scalability of this method is validated experimentally on synthetic and clinical images for multi-scale vessels.  Experimental results show that the proposed method achieves acceptable topological adaptability for skeleton extraction of vessel trees.