Background: Patient motions are a repeatedly reported phenomenon in oral and maxillofacial cone beam CT scans, leading to reconstructions of limited usability. In certain cases, independent movements of the mandible induce unpredictable motion patterns. Previous motion correction methods are not able to handle such complex cases of patient movements. Purpose: Our goal was to design a combined motion estimation and motion correction approach for separate cranial and mandibular motions, solely based on the 2D projection images from a single scan. Methods: Our iterative three-step motion correction algorithm models the two articulated motions as independent rigid motions. First of all, we segment cranium and mandible in the projection images using a deep neural network. Next, we compute a 3D reconstruction with the poses of the object's trajectories fixed. Third, we improve all poses by minimizing the projection error while keeping the reconstruction fixed.Step two and three are repeated alternately. Results: We find that our marker-free approach delivers reconstructions of up to 85% higher quality, with respect to the projection error, and can improve on already existing techniques, which model only a single rigid motion. We show results of both synthetic and real data created in different scenarios. The reconstruction of motion parameters in a real environment was evaluated on acquisitions of a skull mounted on a hexapod, creating a realistic, easily reproducible motion profile. Conclusions: The proposed algorithm consistently enhances the visual quality of motion impaired cone beam computed tomography scans, thus eliminating the need for a re-scan in certain cases, considerably lowering radiation dosage for the patient. It can flexibly be used with differently sized regions of interest and is even applicable to local tomography.