Rapid DFT-based variational image registration with sliding boundary conditions

This paper builds on the tradition of developing computationally efficient nonrigid registration techniques that are easy to implement. All of the standard approaches for variational registration must either implicitly or explicitly assume boundary conditions for the deformation field being sought. Unfortunately, the most commonly used boundary conditions (homogeneous Dirichlet, homogeneous Neumann, and periodic) are either inflexible, not physically meaningful, or introduce problems with changing boundaries. In this paper, we argue that the choice of sliding boundary conditions can be more flexible, more physically meaningful, and less problematic than other boundary conditions. In order to enable the practical implementation of registration with sliding boundary conditions, we present DFT-based algorithms for variational registration with any of the standard quadratic regularizers. Finally, we illustrate the impact of registration with sliding boundary conditions on axially truncated CT chest volumes.