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

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

Black Hole Motion as Catalyst of Orbital Resonances

The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f(E). We show that this effect is operative out to a radius of approx 3 to 4 times the hole's influence radius, R_bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a `warm' and `hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ~18% the local root mean-square velocity dispersion sigma.Comment: revised version, typos fixed, added references, 20 pages MN styl

Integrated Segmentation and Interpolation of Sparse Data

This paper addresses the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data by integrating integrate these stages in a level set framework. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We introduce 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