title: Principal geodesic analysis for the study of nonlinear statistics of shape.
abstract: A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space. While this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points, it does not handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or m-rep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are not elements of a Euclidean vector space. They are in fact elements of a nonlinear Riemannian symmetric space. In this paper, we develop the method of principal geodesic analysis, a generalization of principal component analysis to the manifold setting. We demonstrate its use in describing the variability of medially-defined anatomical objects. Results of applying this framework on a population of hippocampi in a schizophrenia study are presented.
authors.affiliation: Medical Image Display and Analysis Group, University of North Carolina at Chapel Hill, Chapel Hill, NC 27514, USA. fletcher@cs.unc.edu
authors.forename: P Thomas
authors.initials: PT
authors.lastname: Fletcher
authors.forename: Conglin
authors.initials: C
authors.lastname: Lu
authors.forename: Stephen M
authors.initials: SM
authors.lastname: Pizer
authors.forename: Sarang
authors.initials: S
authors.lastname: Joshi
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003196:Computer Graphics; D003198:Computer Simulation; D006624:Hippocampus / Q000473:pathology; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012559:Schizophrenia / Q000473:pathology; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique