Globally optimal curvature-regularized fast marching for vessel segmentation

Abstract

We introduce a novel fast marching approach with curvature regularization for vessel segmentation. Since most vessels have a smooth path, curvature can be used to distinguish desired vessels from short cuts, which usually contain parts with high curvature. However, in previous fast marching approaches, curvature information is not available, so it cannot be used for regularization directly. Instead, usually length regularization is used under the assumption that shorter paths should also have a lower curvature. However, for vessel segmentation, this assumption often does not hold and leads to short cuts. We propose an approach, which integrates curvature regularization directly into the fast marching framework, independent of length regularization. Our approach is globally optimal, and numerical experiments on synthetic and real retina images show that our approach yields more accurate results than two previous approaches. © 2013 Springer-Verlag.