The accurate assessment of variations in coronary arterial dimensions plays an important role in the evaluation of ischemic heart disease and the effectiveness of treatment. Although there exist a variety of edge detection algorithms in the literature, most of them are human interactive and may provide a poor estimate on coronary lesion. In this paper, we present a new method for automatic identification of arterial borders. The proposed algorithm makes use of mathematical morphology to segment blood vessels which follow a tree structure, based on a priori knowledge of coronary anatomy. Finally, an adaptive tracking strategy is applied to automatically identify 2-D arterial borders along both sides of the vessels. This is accomplished by using an edge detection model at a branching point, matched filters, and the tree structure of the coronary artery. Experimental results show that our approach not only is insensitive to the intensity variations of background and noise, but also can extract the boundary of the coronary artery accurately.