Vertebrae segmentation, identification and localization using a graph optimization and a synergistic cycle

This paper considers the segmentation, identification and localization of vertebrae in CT images. Although these three tasks are related, they face specific problems that add up when they are addressed together. For example neighboring vertebrae with similar shapes perturb the identification and vertebrae with complex or even pathological morphologies impact the segmentation. Consequently, the three tasks tend to be approached independently, e.g. labelling (localization and identification) or segmenting only, or, when treated globally, a sequential strategy is used. Sequential methods however are prone to accumulate errors as they are not able to recover from mistakes of the previous module. In this work, we propose to combine all three tasks and leverage their interdependence: locations ease the segmentation, the segmentations in turn improve the locations and they all contribute and benefit from the identification task. To this purpose we propose a virtuous cycle to enforce coherence between the three tasks. Within such a cycle, the tasks interoperate and are iterated until a global consistency criterion is satisfied. Our experiments validate this strategy with anatomically coherent results that outperform the state of the art on the VerSe20 challenge benchmark. Our code and model are openly available for research purposes at https://gitlab.inria.fr/spine/vertebrae_segmentation.