Discrimination analysis using multi-object statistics of shape and pose

A main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper, we present work towards modeling the shape and pose variability of sets of multiple objects. Principal geodesic analysis (PGA) is the extension of the standard technique of principal component analysis (PCA) into the nonlinear Riemannian symmetric space of pose and our medial m-rep shape description, a space in which use of PCA would be incorrect. In this paper, we discuss the decoupling of pose and shape in multi-object sets using different normalization settings. Further, we introduce methods of describing the statistics of object pose and object shape, both separately and simultaneously using a novel extension of PGA. We demonstrate our methods in an application to a longitudinal pediatric autism study with object sets of 10 subcortical structures in a population of 47 subjects. The results show that global scale accounts for most of the major mode of variation across time. Furthermore, the PGA components and the corresponding distribution of different subject groups vary significantly depending on the choice of normalization, which illustrates the importance of global and local pose alignment in multi-object shape analysis. Finally, we present results of using distance weighted discrimination analysis (DWD) in an attempt to use pose and shape features to separate subjects according to diagnosis, as well as visualize discriminating differences.