Segmentation of hepatic arteries in multi-phase computed tomography (CT) images is indispensable in liver surgery planning. During image acquisition, the hepatic artery is enhanced by the injection of contrast agent. The enhanced signals are often not stably acquired due to non-optimal contrast timing. Other vascular structure, such as hepatic vein or portal vein, can be enhanced as well in the arterial phase, which can adversely affect the segmentation results. Furthermore, the arteries might suffer from partial volume effects due to their small diameter. To overcome these difficulties, we propose a framework for robust hepatic artery segmentation requiring a minimal amount of user interaction. First, an efficient multi-scale Hessian-based vesselness filter is applied on the artery phase CT image, aiming to enhance vessel structures with specified diameter range. Second, the vesselness response is processed using a Bayesian classifier to identify the most probable vessel structures. Considering the vesselness filter normally performs not ideally on the vessel bifurcations or the segments corrupted by noise, two vessel-reconnection techniques are proposed. The first technique uses a directional morphological operator to dilate vessel segments along their centerline directions, attempting to fill the gap between broken vascular segments. The second technique analyzes the connectivity of vessel segments and reconnects disconnected segments and branches. Finally, a 3D vessel tree is reconstructed. The algorithm has been evaluated using 18 CT images of the liver. To quantitatively measure the similarities between segmented and reference vessel trees, the skeleton coverage and mean symmetric distance are calculated to quantify the agreement between reference and segmented vessel skeletons, resulting in an average of 0:55±0:27 and 12:7±7:9 mm (mean standard deviation), respectively.