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Piecewise-diffeomorphic registration of 3D CT/MR pulmonary images with sliding conditions

In this paper, we present a new algorithm to register 3D multimodal images with sliding conditions in a diffeomorphic framework. Our driving motivation is to define one-to-one mappings between CT/MR pulmonary volumes acquired from patients with empyema. The main problem to overcome is that the pulmonary motion, which can be large, presents sliding conditions at the thoracic cage boundary. Our algorithm is therefore piecewise-diffeomorphic as it ensures the definition of one-to-one mappings with discontinuous deformations at the location of the sliding conditions. Its performance is demonstrated on 14 CT/MR image volumes of the chest. Results show that the estimated deformations are similar to those obtained using free-form deformations, with the additional property to ensure the invertibility of the deformations and to explicitly model the sliding motion at the thoracic cage boundary.