Multivariate models of inter-subject anatomical variability

This paper presents a very selective review of some of the approaches for multivariate modelling of inter-subject variability among brain images. It focusses on applying probabilistic kernel-based pattern recognition approaches to pre-processed anatomical MRI, with the aim of most accurately modelling the difference between populations of subjects. Some of the principles underlying the pattern recognition approaches of Gaussian process classification and regression are briefly described, although the reader is advised to look elsewhere for full implementational details. Kernel pattern recognition methods require matrices that encode the degree of similarity between the images of each pair of subjects. This review focusses on similarity measures derived from the relative shapes of the subjects' brains. Pre-processing is viewed as generative modelling of anatomical variability, and there is a special emphasis on the diffeomorphic image registration framework, which provides a very parsimonious representation of relative shapes. Although the review is largely methodological, excessive mathematical notation is avoided as far as possible, as the paper attempts to convey a more intuitive understanding of various concepts. The paper should be of interest to readers wishing to apply pattern recognition methods to MRI data, with the aim of clinical diagnosis or biomarker development. It also tries to explain that the best models are those that most accurately predict, so similar approaches should also be relevant to basic science. Knowledge of some basic linear algebra and probability theory should make the review easier to follow, although it may still have something to offer to those readers whose mathematics may be more limited.