I will survey developments in the application of invariants of various types, including differential invariant signatures and joint invariant histograms, for object recognition and symmetry detection in digital images. Recent applications, including automated jigsaw puzzle assembly and cancer detection, will be presented.
Peter J. Olver received his Ph.D. from Harvard University in 1976 under the guidance of Prof. Garrett Birkhoff. After being a Dickson Instructor at the University of Chicago and a postdoc at the University of Oxford, he has been on the faculty of the School of Mathematics at the University of Minnesota since 1980, and a full professor since 1985. As of July, 2008, he has been serving as the Head of the Department. He has supervised 20 Ph.D. students to date, with 3 more currently supervised, as well as mentoring 23 postdocs and visiting students from around the world. He has also supervised 17 undergraduate research projects, many of which have led to publications. His research interests revolve around the applications of symmetry and Lie groups to differential equations. Over the years, he has done research in fluid mechanics, elasticity, quantum mechanics, mathematical physics, Hamiltonian mechanics, the calculus of variations, differential geometry, classical invariant theory, computer vision, and geometric numerical methods. He is the author of over 130 papers in refereed journals, and an additional 46 that appeared in conference proceedings. He was named a "Highly Cited Researcher'' by Thomson-ISI in 2003. His research has received continuous NSF funding since 1981. He is the author of 5 books, including the definitive text on applications of Lie groups to differential equations, which was published in 1986, translated into Russian, and also republished in China. His most recent book is an undergraduate text on partial differential equations, published by Springer in 2014.