An improved discontinuity-preserving image registration model and its fast algorithm

Recently, Chumchob-Chen(2010) proposed a discontinuity-preserving image registration model which was more flexible than those common techniques such as the diffusion and total variation based regularization techniques. However, each component of displacement field is regularized separately in this model and then the nonlinear diffusion processes resulting from the first variation of the discontinuity-preserving regularization do not enforce coupling between the primary components of the displacement field. Thus the discontinuity-preserving model may prevent to obtain a good registration in some situations, for example non-smooth registration problems with non-axis-aligned discontinuities. To utilize interdependence between the primary components of the deformation field for smooth and non-smooth registration problems, we propose an improved discontinuity-preserving image registration model in this paper, second we propose an idea of relaxed fixed point combining with Gauss-Newton scheme with Armijo's line search for solving the new model and further to combine with a multilevel method to achieve fast convergence. Numerical experiments not only confirm that our proposed method is efficient and stable, but also it can give more satisfying registration results according to image quality.