中央研究院 資訊科學研究所

Information Geometry is an amalgam of Information theory and the theory of smooth manifolds. It allows one to ask questions about statistics of data that live on manifolds. As data acquisition mechanisms become more advanced over time, there is a need for more sophisticated analysis tools. Specifically, matrix-valued data analysis has gained popularity over the past decade in the fields of Computer Vision and Medical Image Analysis. In Computer Vision, features such as covariance matrices are common to many application domains such as tracking, texture analysis etc. In Medical Image Analysis, diffusion tensor imaging has gained a lot of traction in the recent past. The common thread between these two disparate applications is that the data (derived or acquired) are matrix-valued, specifically involving symmetric positive definite (SPD) matrices. In this talk, I will present novel methods to process these data sets. In the first part of this talk, I will present a novel probabilistic dynamic model on the space of SPD matrices (Pn) -- based on Riemannian geometry and probability theory -- in conjunction with an intrinsic recursive filter for tracking a time sequence of SPD matrix measurements in a Bayesian framework. This newly developed filtering method is used for the covariance descriptor updating problem in covariance tracking, leading to a new and efficient video tracking algorithm. I will present synthetic and real data examples of video tracking along with comparisons to state-of-the-art techniques.

In the second part of the talk, I will present a novel Bregman divergence called total Bregman divergence (tBD) that is statistically robust and yields a closed form solution to the problem of computing the L1 norm center of a population of SPD matrices. As an application of its use, I will present a technique for the piece-wise smooth segmentation of diffusion weighted MRI (DW-MRI) data sets approximated by fields of SPD matrices. DW-MRI is a non-invasive imaging technique that allows the measurement of directionally dependent water molecular diffusion through tissue in vivo. The directional dependence of water diffusion allows one to infer the axonal connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications.

Baba C. Vemuri received the PhD degree in electrical and computer engineering from the University of Texas at Austin in 1987. After his PhD, he joined the Department of Computer and Information Sciences at the University of Florida, Gainesville, and is currently a university research foundation professor of computer and information sciences and engineering. He was a coprogram chair of the 11th IEEE International Conference on Computer Vision (ICCV 2007). He has been an area chair and a program committee member of several IEEE conferences. He was an associate editor for several journals, including the IEEE Transactions on Pattern Analysis and Machine Intelligence (from 1992 to 1996), the IEEE Transactions on Medical Imaging (from 1997 to 2003) and the journal of Computer Vision and Image Understanding (from 2000-2010). He is currently an associate editor for the Journal of Medical Image Analysis. His research interests include medical image analysis, computational vision, modeling for vision and graphics, and applied mathematics. For the last several years, his research work has primarily focused on information geometric methods. Along this theme, he has been developing algorithms for the analysis of diffusion weighted MRI and diffusion tensor MRI, 3D image segmentation, unimodal and multimodal image (rigid+nonrigid) registration, nonrigid registration of 3D point sets, metric learning, and large margin classifiers. He has published more than 150 refereed journal articles and conference proceedings on medical image analysis, computer vision, graphics, and applied mathematics. He received the US National Science Foundation Research Initiation Award (NSF RIA) in 1988 and the Whitaker Foundation Award in 1994. He was a recipient of the Best Peer Reviews at the Third European Conference on Computer Vision (ECCV 1994), the Best Poster Award at the 17th International Conference on Information Processing in Medical Imaging (IPMI 2001), as well as at IPMI 2005. He is a fellow of the IEEE and ACM.