The vessel extraction is very important for the vascular disease diagnosis and grading of the stenoses and aneurysms in vessels. This aids in brain surgery and making angioplasty. The presence of noise in the MRA image, etc., turns the vessel extraction into a difficult problem. In this paper, we derive a vessel extraction algorithm based on TFA and EMS algorithms. We prove the convergence of the proposed method within a few iterations. Results of applying the presented method on real 2D MRA images demonstrate that our method is very efficient.