Vessel segmentation using 3D elastica regularization

Vascular diseases are among the most important health problems. Vessel segmentation is a very critical task for stenosis measurement and simulation, diagnosis and treatment planning. However, vessel segmentation is much more challenging than blob-like object segmentation due to the thin elongated anatomy of the blood vessels, which can easily appear disconnected in the acquired images due to noise and occlusion. In this paper, we present a generic vessel segmentation approach that extracts the vessels by globally minimizing the surface curvature. The low curvature model enforces surface continuity and prevents the formation of false positives (leakages) and false negatives (holes). We present two contributions: First, we introduce a generic 3D vessel segmentation model by penalizing the boundary surface curvature. Second, we introduce an attraction force as a generalization of the boundary length in the elastica model, which guarantees a complete global solution and avoids shrinkage bias of length regularization. Our results will illustrate that the approach works efficiently across different acquisition modalities and for different applications.