Lopata Hall, Room 101
Efficient Algorithms for Statistical Analysis of Manifold-valued Data with
Applications to Neuro-imaging and Computer Vision
With the advent of new sensing technologies and high powered computing resources, manifold-valued data sets have become ubiquitous in Science and Engineering. The most commonly encountered examples are for e.g., diffusion tensor, structure tensor, probability density fields, directional fields and others. Since these data do not reside in a vector space, standard vector-space operations to process them are inappropriate and mathematical tools borrowed from the field of Differential Geometry are required. As in conventional image analysis, it will be useful to compute statistics from these data sets in order characterize the data quantitatively. Once again, it is important to respect the geometry of the space in which these data lie and thus motivating the development of manifold-valued statistics. In this talk, I will present recursive/online algorithms for efficiently computing the Fr´echet (intrinsic) mean of the manifold-valued data as well as the Principal Geodesic Analysis (PGA). Several applications of these algorithms to data drawn from the domains of Computer Vision and Neuro-imaging will be presented interspersed during the talk.
Baba Vemuri received his PhD in Electrical and Computer Engineering from the University of Texas at Austin and is currently the Wilson and Marie Collins professor of Engineering at the Department of CISE, University of Florida, Gainesville. His research interests include Medical Image computing, Computer Vision, Machine Learning and Information Geometry. He has published over two hundred refereed journal and conference articles in the aforementioned areas and received several best paper awards. He has served as a program chair and area chair of several area conferences. He was an associate editor for several area journals and is currently an associate editor for the Journal of Medical Image Analysis (MedIa) and the International Journal of Computer Vision (IJCV). Professor Vemuri is a fellow of the IEEE and ACM and a recipient of the IEEE Computer Society's Technical Achievement Award (2017) for, "pioneering and sustaining contributions to Computer Vision and Medical Image Analysis."