We address the problem of object modeling from 3D and 3D+T data made up of images, which contain different parts of an object of interest, are separated by large spaces, and are misaligned with respect to each other. These images have only a limited number of intersections, hence making their registration particularly challenging. Furthermore, such data may result from various medical imaging modalities and can, therefore, present very diverse spatial configurations. Previous methods perform registration and object modeling (segmentation and interpolation) sequentially. However, sequential registration is ill-suited for the case of images with few intersections. We propose a new methodology, which, regardless of the spatial configuration of the data, performs the three stages of registration, segmentation, and shape interpolation from spaced and misaligned images simultaneously. We integrate these three processes in a level set framework, in order to benefit from their synergistic interactions. We also propose a new registration method that exploits segmentation information rather than pixel intensities, and that accounts for the global shape of the object of interest, for increased robustness and accuracy. The accuracy of registration is compared against traditional mutual information based methods, and the total modeling framework is assessed against traditional sequential processing and validated on artificial, CT, and MRI data.

We address the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data and propose a new method to integrate these stages in a level set framework. The interpolation process uses segmentation information rather than pixel intensities for increased robustness and accuracy. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We achieve this by introducing a new level set scheme based on the interpolation of the level set function by radial basis functions. The proposed method is validated quantitatively and/or subjectively on artificial data and MRI and CT scans and is compared against the traditional sequential approach, which interpolates the images first, using a state-of-the-art image interpolation method, and then segments the interpolated volume in 3D or 4D. In our experiments, the proposed framework yielded similar segmentation results to the sequential approach but provided a more robust and accurate interpolation. In particular, the interpolation was more satisfactory in cases of large gaps, due to the method taking into account the global shape of the object, and it recovered better topologies at the extremities of the shapes where the objects disappear from the image slices. As a result, the complete integrated framework provided more satisfactory shape reconstructions than the sequential approach.