Unifying framework for decomposition models of parametric and non-parametric image registration

Image registration aims to find spatial transformations such that the so-called given template image becomes similar in some sense to the reference image. Methods in image registration can be divided into two classes (parametric or non-parametric) based on the degree of freedom of the given method. In parametric image registration, the transformation is governed by a finite set of image features or by expanding the transformation in terms of basis functions. Meanwhile, in non-parametric image registration, the problem is modelled as a functional minimisation problem via the calculus of variations. In this paper, we provide a unifying framework for decomposition models for image registration which combine parametric and non-parametric models. Several variants of the models are presented with focus on the affine, diffusion and linear curvature models. An effective numerical solver is provided for the models as well as experimental results to show the effectiveness, robustness and accuracy of the models. The decomposition model of affine and linear curvature outperforms the competing models based on tested images.