In the past few years, sparse representation and compressive sensing have arisen as a very powerful and popular framework for signal and image processing. It has armed people with new mathematical principles and computational tools that can effectively and efficiently harness sparse, low-dimensional structures of high-dimensional data such as images and videos. In this talk, we contend that the same principles and tools are equally important for analyzing the meaning and semantics of images and help solve many outstanding problems in computer vision.
As an example, we will focus on the recent success of sparse representation in human face recognition. On one hand, tools from sparse representation such as L1-minimization have seen great empirical success in enhancing the robustness of face recognition with occlusion, illumination change, and registration error, leading to striking recognition performance far exceeding human expectation or capability. On the other hand, the peculiar structures of face images have led to new mathematical discovery of remarkable properties of L1 minimization that far exceed the existing sparse representation theory.
We will also illustrate with many other examples in computer vision the importance of sparsity as a guiding principle for extracting and harnessing the structures of high-dimensional visual data. In return, we will see that overwhelming empirical evidences from those examples suggest that an even richer set of new mathematical results can be developed if we systematically extend the theory of sparse representation to clustering or classification of high-dimensional visual data. The confluence of sparse representation and computer vision is leading us to a brand new mathematical foundation for high-dimensional pattern analysis and recognition.
This is joint work with my former PhD students John Wright, Allen Yang, and Shankar Rao.
Yi Ma is an associate professor at the Electrical & Computer Engineering Department of the University of Illinois at Urbana-Champaign. He is currently on leave as research manager of the Visual Computing group at Microsoft Research Asia in Beijing. His research interests include computer vision, image processing, and systems theory. Yi Ma received two Bachelors’ degree in Automation and Applied mathematics from Tsinghua University (Beijing, China) in 1995, a Master of Science degree in 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 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 CAREER Award from the National Science Foundation in 2004 and the Young Investigator Award from the Office of Naval Research in 2005. He is an associate editor of IEEE Transactions on Pattern Analysis and Machine Intelligence. He is a senior member of IEEE and a member of ACM, SIAM, and ASEE.