A non-rigid image registration method based on multi-level B-spline and L2-regularization

To solve the problem that the cost function of the classic free-form deformation (FFD) cannot simulate transformation field of images with large elastic deformation or local distortion in image registration better, and to increase the registration accuracy and robustness, a new non-rigid image registration method based on the classic hierarchical FFD is proposed. Since the smooth term has a significant influence on registration accuracy, and its coefficient is not easy to be controlled in the classic hierarchical B-spline based FFD, a L2-regularization term with faster and more stable optimization is introduced in the cost function of the proposed model. By coordinating the coefficients of this regularization term and the smooth term, this novel L2-regularized FFD model is able to solve the problem of low registration accuracy caused by strong smooth constraint while maintaining the images topologies. The introduced L2-regularization term can impose a spatial constraint on the control lattices transformation field, and the over-registration problem can be suppressed to a certain extent, so it can register the images with local large distortion. A series of registration experiments of natural images and medical images show that the new method has an obvious advantage over the classic model in registration accuracy measured by mean square error.