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We describe an efficient and accurate method for segmenting sets of subcortical structures in 3D MR images of the brain. We first find the approximate position of all the structures using a global Active Appearance Model (AAM). We then refine the shape and position of each structure using a set of individual AAMs trained for each. Finally we produce a detailed segmentation by computing the probability that each voxel belongs to the structure, using regression functions trained for each individual voxel. The models are trained using a large set of labelled images, using a novel variant of 'groupwise' registration to obtain the necessary image correspondences. We evaluate the method on a large dataset, and demonstrate that it achieves results comparable with some of the best published.

Determining groupwise correspondence across a set of unlabelled examples of either shapes or images, by the use of an optimisation procedure, is a well-established technique that has been shown to produce quantitatively better models than other approaches. However, the computational cost of the optimisation is high, leading to long convergence times. In this paper, we show how topologically non-trivial shapes can be mapped to regular grids (called shape images). This leads to an initial reduction in computational complexity. By also considering the question of regularisation, we show that a non-parametric fluid regulariser can be applied in a principled manner, the fluid flowing on the shape surface itself, whilst not loosing the computational gain made by the use of shape images. We show that this non-parametric regularisation leads to a further considerable gain, when compared to previous parametric regularisation methods. Quantitative evaluation is performed on biological datasets, and shown to yield a substantial decrease in convergence time, with no loss of model quality.

The analysis of deformation fields, such as those generated by non-rigid registration algorithms, is central to the quantification of normal and abnormal variation of structures in the registered images. The correct choice of representation 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 that these representations are suitable for the description of deformations of medical images in 2 and 3 dimensions. Furthermore, we show that the non-Euclidean metric inherent in this representation is superior to the usual ad hoc Euclidean metrics in that it enables more accurate classification of legal and illegal variations.