Constructing Data-Driven Optimal Representations for Iterative Pairwise Non-rigid Registration

A hamiltonian particle method for diffeomorphic image registration

Diffeomorphic image registration, where images are aligned using diffeomorphic warps, is a popular subject for research in medical image analysis. We introduce a novel algorithm for computing diffeomorphic warps that solves the Euler equations on the diffeomorphism group explicitly, based on a discretisation of the Hamiltonian, rather than using an optimiser. The result is an algorithm that is many times faster than those considered previously.

An adaptive irregular grid approach for 3D deformable image registration

Deformable registration is an important application in medical image analysis and processing. We propose a physics-based parametric approach for deformable image registration, where non-rigid transformations are computed using an irregular grid of control points distributed within the image domain. The image is modelled as a three-dimensional (3D) homogeneous infinite elastic medium. It is assumed that a Gaussian-shaped force is applied at every control point, where the strengths, directions and influence areas of the forces as well as the positions of the control points are considered as free parameters whose optimization leads to maximization of the similarity measure between the images to be registered. For optimization, a computationally efficient Levenberg-Marquardt method is used. The proposed approach has certain advantages over traditional landmark-based methods or the registration methods based on regular grids, for example B-splines, since comparable results can be achieved by using less control points. Experimental results with 3D clinical images demonstrate that our method is capable of successfully coping with complex registration tasks.

A unified information-theoretic approach to groupwise non-rigid registration and model building

The non-rigid registration of a group of images shares a common feature with building a model of a group of images: a dense, consistent correspondence across the group. Image registration aims to find the correspondence, while modelling requires it. This paper presents the theoretical framework required to unify these two areas, providing a groupwise registration algorithm, where the inherently groupwise model of the image data becomes an integral part of the registration process. The performance of this algorithm is evaluated by extending the concepts of generalisability and specificity from shape models to image models. This provides an independent metric for comparing registration algorithms of groups of images. Experimental results on MR data of brains for various pairwise and groupwise registration algorithms is presented, and demonstrates the feasibility of the combined registration/modelling framework, as well as providing quantitative evidence for the superiority of groupwise approaches to registration.

Constructing diffeomorphic representations for the groupwise analysis of nonrigid registrations of medical images

Groupwise nonrigid registrations of medical images define dense correspondences across a set of images, defined by a continuous deformation field that relates each target image in the group to some reference image. These registrations can be automatic, or based on the interpolation of a set of user-defined landmarks, but in both cases, quantifying the normal and abnormal structural variation across the group of imaged structures implies analysis of the set of deformation fields. We contend that the choice of representation of the deformation fields is an integral part of this analysis. This paper presents methods for constructing a general class of multi-dimensional diffeomorphic representations of deformations. We demonstrate, for the particular case of the polyharmonic clamped-plate splines, that these representations are suitable for the description of deformations of medical images in both two and three dimensions, using a set of two-dimensional annotated MRI brain slices and a set of three-dimensional segmented hippocampi with optimized correspondences. The class of diffeomorphic representations also defines a non-Euclidean metric on the space of patterns, and, for the case of compactly supported deformations, on the corresponding diffeomorphism group. In an experimental study, we show that this non-Euclidean metric is superior to the usual ad hoc Euclidean metrics in that it enables more accurate classification of legal and illegal variations.