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Segmentation of blood vessels and extraction of their centerlines in 3D angiography are essential to diagnosis and prognosis of vascular diseases, and advanced image processing and analysis. In this paper, we propose a semi-automatic method to perform those two tasks simultaneously. A user supplies two end points to the algorithm and a vessel centerline between the two given points is extracted automatically. Local vessel widths are estimated as byproducts. Additional anchor points can be added in between to handle difficult situation. Our method is based upon a polygonal line algorithm. This algorithm is used to find principal curves, nonlinear generalization of principal components, from point clouds. We discuss an application of principal curve to vessel extraction from a theoretical view point. A novel algorithm is then proposed for the application. No data interpolation is needed in the algorithm and centerlines extracted are adaptive to the vasculature complexity on account of their nonparametric representation. We have tested the method on two synthetic data sets and two clinical data sets. Results show that it has high robustness to variation in image resolution, voxel anisotropy and noise. Moreover, centerlines obtained are in subvoxel precision and local widths estimated are accurate under limit of image resolution.