The segmentation and analysis of blood vessels has received much attention in the research community. The results aid numerous applications for diagnosis and treatment of vascular diseases. Here we use level set propagation with local phase information to capture the boundaries of vessels. The basic notion is that local phase, extracted using quadrature filters, allows us to distinguish between lines and edges in an image. Noting that vessels appear either as lines or edge pairs, we integrate multiple scales and capture information about vessels of varying width. The outcome is a "global" phase which can be used to drive a contour robustly towards the vessel edges. We show promising results in 2D and 3D. Comparison with a related method gives similar or even better results and at a computational cost several orders of magnitude less. Even with very sparse initializations, our method captures a large portion of the vessel tree.