A polyline tree representation of a coronary artery tree imaged in a volume data set is obtained, and its topology is extracted to give a topological representation indicating the relative positions of vessels in the tree. The topological representation is compared with a set of topological rules to find possible anatomical classifications for each vessel, and a set of candidate labeled polyline trees is generated by labeling the polyline tree with labels showing each combination of possible anatomical classifications. Each candidate labeled tree is filtered according to a set of geometric rules pertaining to spatial characteristics of vessels in arterial trees, and any labeled tree not satisfying the geometric rules is rejected A figure of merit is calculated for each remaining candidate by comparing features of the vessels measured from the polyline tree and from the volume data set with features of correctly classified vessels in other data sets to determine the probable correctness of the labeling of each candidate, and the candidate with the best figure of merit is selected as showing the proper classification of the vessels.