Free-form deformation using lower-order B-spline for nonrigid image registration.

In traditional free-form deformation (FFD) based registration, a B-spline basis function is commonly utilized to build the transformation model. As the B-spline order increases, the corresponding B-spline function becomes smoother. However, the higher-order B-spline has a larger support region, which means higher computational cost. For a given D-dimensional nth-order B-spline, an mth-order B-spline where (m < or = n) has (m +1/n + 1)D times lower computational complexity. Generally, the third-order B-spline is regarded as keeping a good balance between smoothness and computation time. A lower-order function is seldom used to construct the deformation field for registration since it is less smooth. In this research, we investigated whether lower-order B-spline functions can be utilized for efficient registration, by using a novel stochastic perturbation technique in combination with a postponed smoothing technique to higher B-spline order. Experiments were performed with 3D lung and brain scans, demonstrating that the lower-order B-spline FFD in combination with the proposed perturbation and postponed smoothing techniques even results in better accuracy and smoothness than the traditional third-order B-spline registration, while substantially reducing computational costs.