One goal of statistical shape analysis is the discrimination between two populations of objects. Whereas traditional shape analysis was mostly concerned with studying single objects, analysis of multi-object complexes presents new challenges related to alignment and relative object pose. In this paper, we present a methodology for discriminant analysis of sets multiple shapes. Shapes are represented by sampled medial manifolds including normals to the boundary. Non-Euclidean metrics that describe geodesic distance between sets of sampled representations are used for shape alignment and discrimination. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Using an unbiased, soft discrimination score we can associate a statistical hypothesis test with the discrimination results. Furthermore, localization and nature significant differences between populations can be visualized via the average best discriminating axis
