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In this paper, a level-set-based geometric regularization method is proposed which has the ability to estimate the local orientation of the evolving front and utilize it as shape induced information for anisotropic propagation. We show that preserving anisotropic fronts can improve elongations of the extracted structures, while minimizing the risk of leakage. To that end, for an evolving front using its shape-offset level-set representation, a novel energy functional is defined. It is shown that constrained optimization of this functional results in an anisotropic expansion flow which is useful for vessel segmentation. We have validated our method using synthetic data sets, 2-D retinal angiogram images and magnetic resonance angiography volumetric data sets. A comparison has been made with two state-of-the-art vessel segmentation methods. Quantitative results, as well as qualitative comparisons of segmentations, indicate that our regularization method is a promising tool to improve the efficiency of both techniques.