Image registration is anther important task in image processing, where regularization is a major issue in designing new models. The total variation (TV) semi-norm based regularization is much well-known for image denoising and also useful in registration modelling, with recent work generalised with the help of Bregman distance. However mean curvature regularization serves as a strong competitor to the TV. In this talk, I shall first review the mean curvature model by Lysaker-Osher-Tai (2004) and the related Zhu-Chan (2008,2012) models for image denoising. Then I briefly discuss 2 ways of speeding up the computational convergence. Finally I show how to use the mean curvature to minimize the deformation fields in a registration model and highlight the advantages of the resulting new model.