数学大讲堂

Graph Cut, Convex Relaxation and Continuous Max-flow methods for image processing and computer vision

嘉宾简介Xue-Cheng Tai received the licentiate degree and the Ph.D. degree in applied mathematics from Jyvaskalya University, Jyvaskalya, Finland in 1989 and 1991, respectively. After holding several research positions in Europe, he became an Associate Professor in 1994 at the University of Bergen, Bergen, Norway, and a Professor in 1997. He was also a faculty member of Nanyang Technological University of Singapore from 2007 to 2010. He has been a Member of the "Center for Mathematics for Applications" in Oslo and a Member of the "Center of Integrated Petroleum Research" in Bergen. He is now a Professor at Hong Kong Baptist University.

His research interests include Numerical PDEs, optimization techniques, inverse problems, and image processing. He has done significant research work his research areas and published over 150 top quality international conference and journal papers. He is the winner of the 8th Feng Kang Prize for scientific computing and also the winner of the Nanyang Award for Research Excellence of NTU at Singapore in 2011. He served as organizing and program committee members for a number of international conferences and has been often invited for international conferences. He has served as referee and reviewers for many premier conferences and journals. Dr. Tai serves as member of the editor board for a number of international journals.

 

讲座简介:Minimization methods and variational models are becoming fundamental for image processing/computer vision/machine learning. Graph cut methods, which originated from combinatorial mathematics, have been widely used due to their fast speed and robustness with minimizations. Variational methods are also widely used and they often lead to some complex nonlinear partial differential equations. Fast numerical solvers and robust (global) minimization methods are needed and crucial. Recent research has revealed that graph cut methods (in the discrete setting) and some variational models (in the continuous setting) are solving the same numerical problems. The observation of these connections leads to interesting techniques to convexify some complicated variational models and also to produce fast numerical schemes thanks to some advanced techniques from convex programming.

This talk will start with graph cut method for image processing and computer vision, then continues with some important variational models. Especially, we will present some recent continuous cut and continuous max-flow models and show their applications to image processing and computer vision. Connection between the discrete graph cut and continuous max-flow models will be revealed. Duality relationship between the different models will be discussed. Convex relaxation of more general variational models will be proposed following these discussions. Fast numerical algorithms becoming natural after convex relaxation and using convex programing techniques. In the end, we will present applications to image segmentation, image restoration, surface construction, machine learning, computer vision and graph theory.