报告题目：Rate-Invariant Analysis of Trajectories on Riemannian Manifolds

报告人：苏敬勇 副教授

单位：美国德州理工大学

时间：2014年5月22日下午3:30-5:00

地点：校学术活动中心二楼小报告厅

报告人简历：苏敬勇，男，1983年出生，安徽巢湖人。本科于2006年本科毕业于哈尔滨工业大学自动化测试与控制系，2008年硕士毕业于哈尔滨工业大学深圳研究生院计算机科学与技术部，2013年博士毕业于美国佛罗里达州立大学统计系。2013年秋开始任职于德州理工大学数学与统计系，现为副教授。主要研究方向为统计形状分析，计算机视觉，医学图像处理等。在相关领域的顶级期刊，包括IEEE TPAMI, AOAS, JIVC, CVIU, CSDA等，和国际会议，包括CVPR，ICPR，ECCV等发表多篇论文。同时，担任诸多期刊和会议的审稿人，包括IEEE TPAMI，IEEE TIP，AOAS，ECCV，ICPR，CVIU等。最近的研究工作“Rate-Invariant Analysis of Trajectories on Riemannian Manifolds with Application in Visual Speech Recognition”被2014 IEEE CVPR选为Oral paper (5% rate).

报告摘要：

We consider the statistical analysis of trajectories on Riemannian manifolds that are observed under arbitrary temporal evolutions. Past methods rely on cross-sectional analysis, with the given temporal registration, and consequently may lose the mean structure and artificially inflate observed variances. We introduce a quantity that provides both a cost function for temporal registration and a proper distance for comparison of trajectories. This distance is used to define statistical summaries, such as sample means and covariances, of synchronized trajectories and “Gaussian-type” models to capture their variability at discrete times. It is invariant to identical time-warpings (or temporal reparameterizations) of trajectories. This is based on a novel mathematical representation of trajectories, termed transported square-root vector field (TSRVF), and the L2 norm on the space of TSRVFs. We illustrate this framework using several representative manifolds under different applications. In particular, we demonstrate: (1) improvements in mean structures and significant reductions in cross-sectional variances using real data sets, (2) statistical modeling for capturing variability in aligned trajectories, and (3) evaluating random trajectories under these models. Experimental results concern bird migration, hurricane tracking, human activity recognition, visual speech recognition and fiber analysis.