Randomly Perturbed Free-Form Deformation for Nonrigid Image Registration

Abstract

B-spline based free-form deformation (FFD) is a widely used technique in nonrigid image registration. In general, a third-order B-spline function is used, because of its favorable trade-off between smoothness and computational cost. Compared with the third-order B-splines, a B-spline function with a lower order has shorter support length, which means it is computationally more attractive. However, a lower-order function is seldom used to construct the deformation field for registration since it is less smooth. In this work, we propose a randomly perturbed FFD strategy (RPFFD) which uses a lower-order B-spline FFD with a random perturbation around the original position to approximate a higher-order B-spline FFD in a stochastic fashion. For a given D-dimensional nth-order FFD, its corresponding (n − 1)th-order RPFFD has $(\frac{n}{n+1})^{D}$ times lower computational complexity. Experiments on 3D lung and brain data show that, with this lower computational complexity, the proposed RPFFD registration results in even slightly better accuracy and smoothness than the traditional higher-order FFD.