Statistical Analysis of Anatomical Shape and Function

We present a computational framework for image-based statistical analysis of anatomical image data in different populations. Applications of such analysis include understanding developmental and anatomical aspects of disorders when comparing patients vs. normal controls, studying morphological changes caused by aging, or even differences in normal anatomy, for example, differences between genders. Once a quantitative description of anatomy is extracted from input images, the problem of identifying differences between the two groups can be reduced to one of the classical questions in machine learning, namely constructing a classifier function for assigning new examples to one of the two groups while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data that are captured by the discriminative model. In contrast, interpretation of the statistical model in the original input domain is an important component of image-based analysis. We introduce a novel approach to such interpretation that yields detailed descriptions of the detected differences in anatomically meaningful terms of organ development and deformation. Estimating statistical significance of the detected differences between the two groups of images is a challenging problem due to high dimensionality of data and a relatively small number of training examples. We demonstrate a non-parametric technique, based on permutation testing, for estimation of statistical significance in the context of discriminative analysis. This approach provides a weaker statistical guarantee than the classical convergence bounds, but is nevertheless useful in applications of machine learning that involve a large number of highly correlated features and a limited number of training examples. Example domains that give rise to such problems include view-based object recognition, text classification, gene expression analysis. We demonstrate the proposed analysis framework on several examples of studies of changes in the brain anatomy due to healthy aging and disorders, as well as of brain activation in response to visual stimuli.