title: Bayesian principal geodesic analysis for estimating intrinsic diffeomorphic image variability.
abstract: In this paper, we present a generative Bayesian approach for estimating the low-dimensional latent space of diffeomorphic shape variability in a population of images. We develop a latent variable model for principal geodesic analysis (PGA) that provides a probabilistic framework for factor analysis in the space of diffeomorphisms. A sparsity prior in the model results in automatic selection of the number of relevant dimensions by driving unnecessary principal geodesics to zero. To infer model parameters, including the image atlas, principal geodesic deformations, and the effective dimensionality, we introduce an expectation maximization (EM) algorithm. We evaluate our proposed model on 2D synthetic data and the 3D OASIS brain database of magnetic resonance images, and show that the automatically selected latent dimensions from our model are able to reconstruct unobserved testing images with lower error than both linear principal component analysis (LPCA) in the image space and tangent space principal component analysis (TPCA) in the diffeomorphism space.
authors.affiliation: Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah 84102 United States. Electronic address: miaomiao@sci.utah.edu.
authors.forename: Miaomiao
authors.initials: M
authors.lastname: Zhang
authors.affiliation: Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah 84102 United States.
authors.forename: P Thomas
authors.initials: PT
authors.lastname: Fletcher
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D059906:Neuroimaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods; D025341:Principal Component Analysis
keywords: Bayesian estimation; Diffeomorphic image registration; Dimensionality reduction; Principal geodesic analysis