In this paper, a novel active contour model is proposed for vessel tree segmentation. First, we introduce a region competition-based active contour model exploiting the gaussian mixture model, which mainly segments thick vessels. Second, we define a vascular vector field to evolve the active contour along its center line into the thin and weak vessels. The vector field is derived from the eigenanalysis of the Hessian matrix of the image intensity in a multiscale framework. Finally, a dual curvature strategy, which uses a vesselness measure-dependent function selecting between a minimal principal curvature and a mean curvature criterion, is added to smoothen the surface of the vessel without changing its shape. The developed model is used to extract the liver and lung vessel tree as well as the coronary artery from high-resolution volumetric computed tomography images. Comparisons are made with several classical active contour models and manual extraction. The experiments show that our model is more accurate and robust than these classical models and is, therefore, more suited for automatic vessel tree extraction.