We propose a new segmentation algorithm based on competing fuzzy connectedness theory, which is then used for visualizing coronary arteries in 3D CT angiography (CTA) images. The major difference compared to other fuzzy connectedness algorithms is that an additional data structure, the connectedness tree, is constructed at the same time as the seeds propagate. In preliminary evaluations, accurate result have been achieved with very limited user interaction. In addition to improving computational speed and segmentation results, the fuzzy connectedness tree algorithm also includes automated extraction of the vessel centerlines, which is a promising approach for creating curved plane reformat (CPR) images along arteries' long axes.