A symmetric 4D registration algorithm for respiratory motion modeling.

We propose an effective 4D image registration algorithm for dynamic volumetric lung images. The registration will construct a deforming 3D model with continuous trajectory and smooth spatial deformation, and the model interpolates the interested region in the 4D (3D+T) CT images. The resultant non-rigid transformation is represented using two 4D B-spline functions, indicating a forward and an inverse 4D parameterization respectively. The registration process solves these two functions by minimizing an objective function that penalizes intensity matching error, feature alignment error, spatial and temporal non-smoothness, and inverse inconsistency. We test our algorithm for respiratory motion estimation on public benchmarks and on clinic lung CT data. The experimental results demonstrate the efficacy of our algorithm