A unified and efficient approach for free-form deformable registration

We propose a novel numerical approach for solving the free-form deformable registration problem. The central idea is to utilize the well understood techniques from variational deformable registration problems. We demonstrate that it is possible to formulate the free-form deformable registration problem as the optimization of an energy functional as in the dense deformation case. This energy functional possesses image distance and regularization terms, which are both functions of the free-form deformation control points. We then setup a semi-backward (implicit) partial differential equation that optimizes the established energy functional. In addition to being mathematically justified, this approach provides both accuracy and speed. Our evaluation on synthetic, real, two dimensional, and three dimensional data demonstrates accuracy and computational effectiveness.