Diffeomorphic nonlinear transformations: a local parametric approach for image registration

Many types of transformations are used to model deformations in medical image registration. While some focus on modeling local changes, some on continuity and invertibility, there is no closed-form nonlinear parametric approach that addresses all these properties. This paper presents a class of nonlinear transformations that are local, continuous and invertible under certain conditions. They are straightforward to implement, fast to compute and can be used particularly in cases where locally affine deformations need to be recovered. We use our new transformation model to demonstrate some results on synthetic images using a multi-scale approach to multi-modality mutual information based image registration. The original images were deformed using B-splines at three levels of scale. The results show that the proposed method can recover these deformations almost completely with very few iterations of a gradient based optimizer.