Vessel extraction is a critical task in clinical practice. In this paper, we propose a new approach for vessel extraction using an active contour model by defining a novel vesselness-based term, based on accurate analysis of the vessel structure in the image. To achieve the novel term, a simple and fast directional filter bank is proposed, which does not employ down sampling and resampling used in earlier versions of directional filter banks. The proposed model not only preserves the performance of the existing models on images with intensity inhomogeneity, but also overcomes their inability both to segment low contrast vessels and to omit non-vessel structures. Experimental results for synthetic images and coronary X-ray angiograms show desirable performance of our model.