Fast free-form deformable registration via calculus of variations

In this paper, we present a fully automatic, fast and accurate deformable registration technique. This technique deals with free-form deformation. It minimizes an energy functional that combines both similarity and smoothness measures. By using calculus of variations, the minimization problem was represented as a set of nonlinear elliptic partial differential equations (PDEs). A Gauss-Seidel finite difference scheme is used to iteratively solve the PDE. The registration is refined by a multi-resolution approach. The whole process is fully automatic. It takes less than 3 min to register two three-dimensional (3D) image sets of size 256 × 256 × 61 using a single 933 MHz personal computer. Extensive experiments are presented. These experiments include simulations, phantom studies and clinical image studies. Experimental results show that our model and algorithm are suited for registration of temporal images of a deformable body. The registration of inspiration and expiration phases of the lung images shows that the method is able to deal with large deformations. When applied to the daily CT images of a prostate patient, the results show that registration based on iterative refinement of displacement field is appropriate to describe the local deformations in the prostate and the rectum. Similarity measures improved significantly after the registration. The target application of this paper is for radiotherapy treatment planning and evaluation that incorporates internal organ deformation throughout the course of radiation therapy. The registration method could also be equally applied in diagnostic radiology.