We present a computational framework for image-based analysis and interpretation of statistical differences in anatomical shape between populations. Applications of such analysis include understanding developmental and anatomical aspects of disorders when comparing patients versus normal controls, studying morphological changes caused by aging, or even differences in normal anatomy, for example, differences between genders. Once a quantitative description of organ shape 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 of constructing a classifier function for assigning new examples to one of the two groups while making as few misclassifications as possible. The resulting classifier must be interpreted in terms of shape differences between the two groups back in the image domain. We demonstrate a novel approach to such interpretation that allows us to argue about the identified shape differences in anatomically meaningful terms of organ deformation. Given a classifier function in the feature space, we derive a deformation that corresponds to the differences between the two classes while ignoring shape variability within each class. Based on this approach, we present a system for statistical shape analysis using distance transforms for shape representation and the support vector machines learning algorithm for the optimal classifier estimation and demonstrate it on artificially generated data sets, as well as real medical studies.
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