报告题目：Bayesian models of variability and regression for manifold data: applications to understanding brain shape
报告人：Tom Fletcher 副教授 (University of Utah, USA)
Riemannian manifolds have proven to be effective representations of nonlinear data from images, including image transformations and shape. In this talk I will present a probabilistic formulation for two closely related statistical models for Riemannian manifold data: geodesic regression and principal geodesic analysis. These models generalize linear regression and principal component analysis to the manifold setting. The foundation of the approach is the particular choice of a Riemannian normal distribution law as the likelihood model. Under this distributional assumption, least-squares fitting of geodesic models is equivalent to maximum-likelihood estimation when the manifold is a homogeneous space. I will also show a method for maximum-likelihood estimation of the dispersion of the noise, as well as a novel method for Monte Carlo sampling from the Riemannian normal distribution. Finally, I'll show several examples of these methods applied to study the variability and age-related shape changes in the brain from MRI data.
Fletcher现任美国Utah大学School of Computing的Scientific Computing and Imaging Institute的副教授。其主要研究领域为运用统计和微分几何处理计算机视觉和医学图像处理中的相关问题。Fletcher教授在Journal of Neuroimaging, International Journal of Computer Vision，Computer Vision and Pattern Recognition 等顶级期刊和会议上发表了几十篇论文，是MICCAI等多个重要会议的Program Committee 成员。