Multi-Object Analysis of Volume, Pose, and Shape Using Statistical Discrimination

One goal of statistical shape analysis is the discrimination between two populations of objects. Whereas traditional shape analysis was mostly concerned with single objects, analysis of multi-object complexes presents new challenges related to alignment and pose. In this paper, we present a methodology for discriminant analysis of multiple objects represented by sampled medial manifolds. Non-Euclidean metrics that describe geodesic distances between sets of sampled representations are used for alignment and discrimination. Our choice of discriminant method is the distance-weighted discriminant because of its generalization ability in high-dimensional, low sample size settings. Using an unbiased, soft discrimination score, we associate a statistical hypothesis test with the discrimination results. We explore the effectiveness of different choices of features as input to the discriminant analysis, using measures like volume, pose, shape, and the combination of pose and shape. Our method is applied to a longitudinal pediatric autism study with 10 subcortical brain structures in a population of 70 subjects. It is shown that the choices of type of global alignment and of intrinsic versus extrinsic shape features, the latter being sensitive to relative pose, are crucial factors for group discrimination and also for explaining the nature of shape change in terms of the application domain.