A network can often be represented as a graph. Max-flow/min-cuts over a given graph can be used to find optimal solutions for many complicated network problems. It is known that these kind of problems are often NP-hard and they pose some very challenging minimization problems for simulations. In this talk, we will show how to use graph and cuts methods for some image processing and computer vision problems. Especially, we shall present our recent work extending the concept of max-flow/min-cuts to "networks" that are infinite dimension, i.e. we will talk about continuous max-flow/min-cuts problems. When we discrete these continuous max-flow problems, we come back to the ordinary finite dimension max-flow problems. The continuous max-flow models can be solved through the solution of some partial differential equations. One advantage of the continuous max-flow problem is that we can use many convex optimization methods to solve it. We are released from some restricted searching algorithms for network problems.

Prof. Xue-Cheng Tai is a member of the Department of Mathematics at the University of Bergen of Norway.  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 100 top quality international conference and journal papers. He is the winner of the 8th Feng Kang Prize for scientific computing in 2009. 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.