An Effective Diffeomorphic Model and Its Fast Multigrid Algorithm for Registration of Lung CT Images

Abstract

Abstract Image registration is the process of aligning sets of similar, but different, intensity image functions to track changes between the images. In medical image problems involving lung images, variational registration models are a very powerful tool which can aid in effective treatment of various lung conditions and diseases. However, a common drawback of many variational models, such as the diffusion model and even optic flow models, is the lack of control of folding in the deformations leading to physically inaccurate transformations. For this reason, such models are generally not suitable for real life lung imaging problems where folding cannot occur. There are two approaches offering reliable solutions (though not necessarily accurate). The first approach is a parametric model such as the affine registration model, still widely used in many applications, but is unable to track local changes or yield accurate results. The second approach is to impose an extra constraint on the transformation of registration at the cost of increased non-linearity. An alternative to the second approach, achieving diffeomorphic transforms without adding any constraints, is an inverse consistent model such as by Christensen and Johnson (2001) from computing explicitly both the forward and inverse transforms. However, one must deal with the strong non-linearity in the formulation. In this paper we first propose a simplified inverse consistent model to avoid the inclusion of strong non-linearities and then a fast non-linear multigrid (NMG) technique to overcome the extra computational work required by the inverse consistent model. Experiments, performed on real medical CT images, show that our proposed inverse consistent model is robust to both parameter choice and non-folding in the transformations when compared with diffusion type models.