High-Order Oriented Cylindrical Flux for Curvilinear Structure Detection and Vessel Segmentation

Jierong Wang, Albert C. S. Chung

Abstract: In this paper, we present a novel blood vessel structure detector, namely Oriented Cylinder Flux (OCF). Our method formulates blood vessels as curvilinear cylinders with circular cross-sections, incorporating two-step computations. First, OCF computes cross-section responses based on the normal spaces generated by two eigenvectors in the Optimally Oriented Flux (OOF). Second, OCF accumulates the cross-section responses along the curvilinear structures. We then modify OCF to fit into a high-order tensor framework on a unit sphere \(\mathbf {S}^3\), which is able to encode multi-orientation information within a single voxel. A random walker based graphical framework is employed to measure the angular coherence among the decomposed rank-1 tensors. In the synthetic and clinical image experiments, the proposed method achieves high segmentation performance under various radii of the curvilinear structures and different levels of random noise, demonstrating that it has a strong noise-resistant ability and can be used to deal with the shrinking problem, which is one of the main problems in blood vessel segmentation.