State of the art cardiac CT enables the acquisition of imaging data of the heart over the entire cardiac cycle at concurrent high spatial and temporal resolution. However, in clinical practice, acquisition is increasingly limited to 3D images. Estimating the shape of the cardiac structures throughout the entire cardiac cycle from a 3D image is therefore useful in applications such as the alignment of preoperative CTA to intra-operative X-ray images for improved guidance in coronary interventions. We hypothesize that the motion of the heart is partially explained by its shape and therefore investigate the use of three regression methods for motion estimation from single-phase shape information. Quantitative evaluation on 150 4D computed tomography angiography (CTA) images showed a small, but statistically significant, increase in the accuracy of the predicted shape sequences when using any of the regression methods, compared to shape-independent motion prediction by application of the mean motion. The best results were achieved using principal component regression resulting in point-to-point errors of 2.3 ± 0.5 mm, compared to values of 2.7 ± 0.6 mm for shape-independent motion estimation. Finally, we showed that this significant difference withstands small variations in important parameter settings of the landmarking procedure.