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We address the problem of object modelling from 3D and 4D sparse data acquired as different sequences which are misaligned with respect to each other. Such data may result from various imaging modalities and can therefore present very diverse spatial configurations and appearances. We focus on medical tomographic data, made up of sets of 2D slices having arbitrary positions and orientations, and which may have different gains and contrasts even within the same dataset. The analysis of such tomographic data is essential for establishing a diagnosis or planning surgery.Modelling from sparse and misaligned data requires solving the three inherently related problems of registration, segmentation, and interpolation. We propose a new method to integrate these stages in a level set framework. Registration is particularly challenging by the limited number of intersections present in a sparse dataset, and interpolation has to handle images that may have very different appearances. Hence, registration and interpolation exploit segmentation information, rather than pixel intensities, for increased robustness and accuracy. We achieve this by first introducing a new level set scheme based on the interpolation of the level set function by radial basis functions. This new scheme can inherently handle sparse data, and is more numerically stable and robust to noise than the classical level set. We also present a new registration algorithm based on the level set method, which is robust to local minima and can handle sparse data that have only a limited number of intersections. Then, we integrate these two methods into the same level set framework.The proposed method is validated quantitatively and subjectively on artificial data and MRI and CT scans. It is compared against a state-of-the-art, sequential method comprising traditional mutual information based registration, image interpolation, and 3D or 4D segmentation of the registered and interpolated volume. In our experiments, the proposed framework yields similar segmentation results to the sequential approach, but provides a more robust and accurate registration and interpolation. In particular, the registration is more robust to limited intersections in the data and to local minima. The interpolation is more satisfactory in cases of large gaps, due to the method taking into account the global shape of the object, and it recovers better topologies at the extremities of the shapes where the objects disappear from the image slices. As a result, the complete integrated framework provides more satisfactory shape reconstructions than the sequential approach

Integrated Registration, Segmentation, and Interpolation for 3D/4D Sparse Data