Abstract

Variational models offer high resolution solutions of many common image processing tasks by treating images as functions rather than matrices. In this talk, I first discuss the simple models based on mean curvature by Lysaker-Osher-Tai (2004) and Zhu-Chan (2008,2012) as well as total variation (TV) regularisation by Rudin-Osher-Fatemi (1992). Recent results on choosing the best coupling parameter in a TV model and on fast algorithms for curvature models are also shown.

Then I discuss the modeling problem of image registration which is another important task in image processing, where regularization is a major issue in designing new models. The prevously well-known regularisers such as the TV and optical flow based ones turn out to be much less effective than a mean curvature regulariser. Finally I show how to use the mean curvature to design a registration model suitable for multi-modality registration.