報(bào)告題目：Rate-Invariant Analysis of Trajectories on Riemannian Manifolds
報(bào)告人：蘇敬勇 副教授
單位：美國德州理工大學(xué)
時(shí)間：2014年5月22日下午3:30-5:00
地點(diǎn)：校學(xué)術(shù)活動(dòng)中心二樓小報(bào)告廳
報(bào)告人簡(jiǎn)歷：蘇敬勇，男，1983年出生，安徽巢湖人。本科于2006年本科畢業(yè)于哈爾濱工業(yè)大學(xué)自動(dòng)化測(cè)試與控制系，2008年碩士畢業(yè)于哈爾濱工業(yè)大學(xué)深圳研究生院計(jì)算機(jī)科學(xué)與技術(shù)部，2013年博士畢業(yè)于美國佛羅里達(dá)州立大學(xué)統(tǒng)計(jì)系。2013年秋開始任職于德州理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)系，現(xiàn)為副教授。主要研究方向?yàn)榻y(tǒng)計(jì)形狀分析，計(jì)算機(jī)視覺，醫(yī)學(xué)圖像處理等。在相關(guān)領(lǐng)域的頂級(jí)期刊，包括IEEE TPAMI, AOAS, JIVC, CVIU, CSDA等，和國際會(huì)議，包括CVPR，ICPR，ECCV等發(fā)表多篇論文。同時(shí)，擔(dān)任諸多期刊和會(huì)議的審稿人，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選為Oral paper (5% rate).
報(bào)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.
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