We describe a means to automatically and efficiently isolate the outer surface of the entire heart in Computer Tomography (CT) cardiac scans. Isolating the entire heart allows the coronary vessels on the surface of the heart to be easily visualized despite the proximity of surrounding organs such as the ribs and pulmonary blood vessels. Numerous techniques have been described for segmenting the left ventricle of the heart in images from various types of medical scanners but rarely has the entire heart been segmented. We make use of graph cuts to do the segmentation and introduce a novel means of initiating and constraining the graph-cut technique for heart isolation. The technique has been tested on 70 patient data sets. Results are compares with hand labeled results.