We present a fully automatic segmentation algorithm for the whole heart (four chambers, left ventricular myocardium and trunks of the aorta, the pulmonary artery and the pulmonary veins) in cardiac MR image volumes with nearly isotropic voxel resolution, based on shape-constrained deformable models. After automatic model initialization and reorientation to the cardiac axes, we apply a multi-stage adaptation scheme with progressively increasing degrees of freedom. Particular attention is paid to the calibration of the MR image intensities. Detailed evaluation results for the various anatomical heart regions are presented on a database of 42 patients. On calibrated images, we obtain an average segmentation error of 0.76mm.