Statistics of Pose and Shape in Multi-object Complexes Using Principal Geodesic Analysis

Abstract

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.

Training models of anatomic shape variability

“…15, right, were taken from an autism shape study where the researcher used the SDSM based shape-to-shape metric to discriminate autism by shape characteristics. 11 We have also modeled hippocampi for a large statistical shape study. Temporal extensions to the method have enabled studies of heart motion, 49 which has obvious extensions to lung motion and 4D-ART.…”

“…Probabilistic segmentation can also provide a basis for image guided surgery ͑e.g., 9,10 ͒ and diagnosis. 11 Probabilistic segmentation is based on understanding the shape variability of the anatomic structures found in medical images. Robust probability density estimates of shape have been shown to be effective for object-based methods of probabilistic segmentation 9,12,13 for two reasons: ͑1͒ their relatively low dimensionality allows us efficiently to compute optimal solutions, and ͑2͒ the optimal solutions yield anatomically credible objects.…”

“…Using a SDSM, any particular shape in the space defined by the training set can be completely and uniquely identified by a few coefficients to within some small truncation error. Once trained, SDSMs can be used as the basis of numerical methods for shape discrimination, comparison, and interpolation, for longitudinal shape studies, 11 and for deformable image segmentation and registration. [22][23][24] ͑See Ref.…”

Volumetric segmentation of multiple basal ganglia structures using nonparametric coupled shape and inter-shape pose priors

“…Such dependencies are modeled and used, for example, in [9,10,11,12,13]. In this paper, we take a different approach, and introduce statistical joint prior models of multiple-structures into an active contour segmentation method in a nonparametric multivariate kernel density estimation framework.…”

Segmentation of Anatomical Structures by Connected Statistical Models

“…The coupling constraint dependent on all contours is introduced as an overlap penalty in energy functional (Zimmer and Olivo-Marin, 2005). The principal geodesic analysis (PGA) was applied to object pose and medial m-rep shape description (Styner et al, 2006). The problem of splitting image data into submodels for a given set of training images was addressed by Langs et al (2007), where minimum description length (MDL) principle was proposed as a criterion function.…”