No abstract

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. We explore the effectiveness of different choices of features as input to the discriminant analysis, using morphologic measures like volume, pose, shape and the combination of pose and shape. Our method is applied to a longitudinal pediatric autism study with object sets of 10 subcortical brain structures in a population of 70 samples. The results compare group discrimination by volume, pure shape or pose, and combinations thereof. 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.

Abstract.A main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper, we present work in progress 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 new methods of describing the statistics of object pose using a novel extension of PGA, which previously has been used for global shape statistics. These new pose statistics are then combined with shape statistics to form a more complete description of multi-object complexes. We demonstrate our methods in an application to a longitudinal pediatric autism study with object sets of 10 subcortical structures in a population of 20 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.

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.

Work in progress towards modeling shape statistics of multiobject complexes is presented. Constraints defined by the set of objects such as a compact representation of object shape relationships and correlation of shape changes might have advantages for automatic segmentation and group discrimination. We present a concept for statistical multi-object modeling and discuss the major challenges which are a reduction to a small set of descriptive features, calculation of mean and variability via curved statistics, the choice of aligning sets of multiple objects, and the problem of describing the statistics of object pose and object shape and their interrelationship. Shape modeling and analysis is demonstrated with an application to a longitudinal autism study, with shape modeling of sets of 10 subcortical structures in a population of 20 subjects.