The segmentation of tubular tree structures like vessel systems in volumetric datasets is of vital interest for many medical applications. In this paper we present a novel, semi-automatic method for blood vessel segmentation and centerline extraction, by tracking the blood vessel tree from a user-initiated seed point to the ends of the blood vessel tree. The novelty of our method is in performing only two-dimensional cross-section analysis for segmentation of the connected blood vessels. The cross-section analysis is done by our novel single-scale or multi-scale circle enhancement filter, used at the blood vessel trunk or bifurcation, respectively. The method was validated for both synthetic and medical images. Our validation has shown that the cross-sectional centerline error for our method is below 0.8 pixels and the Dice coefficient for our segmentation is 80% ± 2.7%. On combining our method with an optional active contour post-processing, the Dice coefficient for the resulting segmentation is found to be 94% ± 2.4%. Furthermore, by restricting the image analysis to the regions of interest and converting most of the three-dimensional calculations to two-dimensional calculations, the processing was found to be more than 18 times faster than Frangi vesselness with thinning, 8 times faster than user-initiated active contour segmentation with thinning and 7 times faster than our previous method.