PURPOSE: Four-dimensional computed tomography (4D CT) can provide patient-specific motion information for radiotherapy planning and delivery. Motion estimation in 4D CT is challenging due to the reduced image quality and the presence of artifacts. We aim to improve the robustness of deformable registration applied to respiratory-correlated imaging of the lungs, by using a global problem formulation and pursuing a restrictive parametrization for the spatiotemporal deformation model. METHODS: A spatial transformation based on free-form deformations was extended to the temporal domain, by explicitly modeling the trajectory using a cyclic temporal model based on B-splines. A global registration criterion allowed to consider the entire image sequence simultaneously and enforce the temporal coherence of the deformation throughout the respiratory cycle. To ensure a parametrization capable of capturing the dynamics of respiratory motion, a prestudy was performed on the temporal dimension separately. The temporal parameters were tuned by fitting them to diaphragm motion data acquired for a large patient group. Suitable properties were retained and applied to spatiotemporal registration of 4D CT data. Registration results were validated using large sets of landmarks and compared to consecutive spatial registrations. To illustrate the benefit of the spatiotemporal approach, we also assessed the performance in the presence of motion-induced artifacts. RESULTS: Cubic B-splines gave better or similar fitting results as lower orders and were selected because of their inherently stronger regularization. The fitting and registration errors increased gradually with the temporal control point spacing, representing a trade-off between achievable accuracy and sensitivity to noise and artifacts. A piecewise smooth trajectory model, allowing for a discontinuous change of speed at end-inhale, was found most suitable to account for the sudden changes of motion at this breathing phase. The spatiotemporal modeling allowed a reduction of the number of parameters of 45%, while maintaining registration accuracy within 0.1 mm. The approach reduced the sensitivity to artifacts. CONCLUSIONS: Spatiotemporal registration can provide accurate motion estimation for 4D CT and improves the robustness to artifacts.