Vessel tracking is an essential step for 3-D reconstruction and quantitative analysis of angiograms. We present a multiresolution vessel tracking method and its application to 2-D coronary angiographic images. The method consists of: 1. multiresolution wavelet decomposition; 2. wavelet denoising; 3. vessel valley map generation in a low-resolution image; 4. vascular tree construction; 5. valley course refinement using a "peg-quiver" algorithm; and 6. lumen diameter calculation using a derivative-free edge detection algorithm. A vessel valley map consisting of all vessel valley points can be generated using a star-scan scheme, followed by local minima detection along each scanline. The vessel paths and vascular trees are then constructed by using a recursive "depth-first" searching scheme on the valley map. A peg-quiver refinement algorithm produces optimal valley courses in high-resolution images by alternatively pegging and quivering the control points and the interpolated points. With high-resolution valley courses, vessel boundary is defined by exploiting vessel cross-section profiles. Compared to centerline-based vessel tracking, the vessel-tracking scheme using valley courses exhibits more simplicity, effectiveness, and stability.