Image registration using an extendable quadratic regulariser

Image registration algorithms are widely used in medical imaging to spatially align anatomical features. This work investigates the regularisation of the registration transformation by unification of the standard diffusion equation regulariser with the standard curvature regulariser. A variational nonrigid registration scheme is employed with periodic boundary conditions and tested over a range of regularisation parameters. A variable regularisation algorithm is also proposed that automatically adapts the regularisation as the registration progresses. Improved registration performance on two simulated biomechanical deformations of 3D breast MRI over four subjects is observed; correcting the simulated deformation residual by 69% and 73% respectively for diffusion regularisation, 36% and 45% for curvature regularisation and up to 73% and 75% for variable regularisation.