Non-Commutative Harmonic Analysis in Object Recognition and Tracking

Drexel University, Philadelphia PA

Investigators

Abstract

The principal investigator, a professor of mathematics, will visit the Department of Computer and Information Science in the School of Engineering and Applied Science at the University of Pennsylvania to initate a collaborative research program in computer vision emphasizing omnidirectional sensors, which are visual sensors with unusually large fields of view. These new sensors have numerous applications in surveillance, navigation, and communications, yet they have raised a host of complex new mathematical questions because they are not accurately modelled with the conventional methods of computer vision and image processing. Remarkably, the relevant mathematics is the representation theory of non-compact Lie groups, non-commutative harmonic analysis, and the associated algorithms. To make a contribution to this field, it is essential for the principal investigator to be immersed in a laboratory active in vision research where inevitable technological advances in performance and equipment cause continuous change in the requirements and complexity of the models. The PI will investigate applications of noncommutative harmonic analysis on Lie groups and their homogeneous spaces to two of the major problems in computer vision: object recognition and tracking. The noncommutative Fourier transform will be especially helpful for these problems as well as in discovering analytical invariants for images needed for template matching. After the PI's leave at Penn, he intends to establish an image science group at Drexel that includessa colleagues who are experts in mirror design and differential geometry. This group will develop courses and seminars fostering cross-fertilization among students and faculty from computer science and electrical and computer engineering departments in the College of Engineering. With the close physical proximity of Penn with Drexel, the PI expects the collaborations initiated during his leave will continue with joint seminars, joint research students, and research projects. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).