For many problems in computer vision, image processing, and pattern recognition, we need to process and analyze tremendous amount of high-dimensional mixed data such as images, videos, and biomedical data. By “mixed data,” we mean that the data consist of multiple inhomogeneous subsets (in terms of their geometric, statistical, or dynamical characteristics) and each subset can be more easily modeled or represented than the whole data set. Thus, in this talk, we address two fundamental questions: “Why and how to segment multivariate mixed data?”

In this talk, we will introduce a new compression-based approach to segment mixed data. In this way, segmentation becomes part of the optimal solution to data compression. Based on a proper measure of the coding length of the mixed data, we will provide a remarkably effective algorithm for segmenting data that are drawn from an arbitrary mixture of non-degenerate or almost-degenerate Gaussians. The algorithm shows superior performance over conventional clustering techniques such as expectation maximization (EM), K-means, or other classical agglomerative methods.

Our work makes it possible for “segmentation” to take its rightful place as a fundamental mathematical concept that is deeply related to other concepts in data compression, coding, channel capacity, and even phase transition in statistical physics. We will demonstrate many successful applications of our methods in image processing, computer vision, and biomedical engineering.

Brief Bio:

Yi Ma is an associate professor at the Electrical & Computer Engineering Department of the University of Illinois at Urbana-Champaign. His main research interests include computer vision and systems theory. He received two Bachelors’ degree in Automation and Applied Mathematics from Tsinghua University (Beijing, China) in 1995, a Master of Science degree in Electrical Engineering and Computer Science (EECS) in 1997, a Master of Arts degree in Mathematics in 2000, and a PhD degree in EECS in 2000, all from the University of California at Berkeley. Yi Ma is the recipient of the Regents’ Fellowship from UC Berkeley from 1995 to 1996. He received the David Marr Best Paper Prize at the International Conference on Computer Vision 1999 and the Longuet-Higgins Best Paper Prize at the European Conference on Computer Vision 2004. He also received the young faculty CAREER Award from the National Science Foundation in 2004 and the Young Investigator Award from the Office of Naval Research in 2005. He is the first author of a textbook on the geometry of computer vision, entitled: “An Invitation to 3-D Vision: From Images to Geometric Models,” published in 2003 by Springer; and he is currently writing a second book on “Generalized Principal Component Analysis: Modeling and Segmentation of Multivariate Mixed Data,” to be published early next year.