Automatic self-gated 4D-MRI construction from free-breathing 2D acquisitions applied on liver images Abstract Purpose MRI slice reordering is a necessary step when three-dimensional (3D) motion of an anatomical region of interest has to be extracted from multiple two-dimensional (2D) dynamic acquisition planes, e.g., for the construction of motion models used for image-guided radiotherapy. Existing reordering methods focus on obtaining a spatially coherent reconstructed volume for each time. However, little attention has been paid to the temporal coherence of the reconstructed volumes, which is of primary importance for accurate 3D motion extraction. This paper proposes a fully automatic self-sorting four-dimensional MR volume construction method that ensures the temporal coherence of the results. Methods First, a pseudo-navigator signal is extracted for each 2D dynamic slice acquisition series. Then, a weighted graph is created using both spatial and motion information provided by the pseudo-navigator. The volume at a given time point is reconstructed following the shortest paths in the graph starting that time point of a reference slice chosen based on its pseudo-navigator signal. Results The proposed method is evaluated against two state-of-the-art slice reordering algorithms on a prospective dataset of 12 volunteers using both spatial and temporal quality metrics. The automated end-exhale extraction showed results closed to the median value of the manual operators. Furthermore, the results of the validation metrics show that the proposed method outperforms state-of-the-art methods in terms of both spatial and temporal quality. Conclusion Our approach is able to automatically detect the end-exhale phases within one given anatomical position and cope with irregular breathing.