title: Geodesic regression on orientation distribution functions with its application to an aging study.
abstract: In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above.
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore.
authors.forename: Jia
authors.initials: J
authors.lastname: Du
authors.affiliation: Department of Mathematics, National University of Singapore, Singapore.
authors.forename: Alvina
authors.initials: A
authors.lastname: Goh
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore.
authors.forename: Sergey
authors.initials: S
authors.lastname: Kushnarev
authors.affiliation: Department of Biomedical Engineering, National University of Singapore, Singapore; Singapore Institute for Clinical Sciences, Agency for Science, Technology and Research, Singapore; Clinical Imaging Research Centre, National University of Singapore, Singapore. Electronic address: bieqa@nus.edu.sg.
authors.forename: Anqi
authors.initials: A
authors.lastname: Qiu
mesh_terms: D000328:Adult; D000368:Aged; D000375:Aging / Q000473:pathology*; D000465:Algorithms; D001921:Brain / Q000473:pathology*; D038524:Diffusion Magnetic Resonance Imaging; D005260:Female; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008297:Male; D008875:Middle Aged; D010363:Pattern Recognition, Automated / Q000379:methods; D055815:Young Adult
keywords: Orientation distribution function; Regression analysis; Riemannian manifold