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.

Precise localization of moving targets is essential to increase local control of the cancer via dose escalation while reducing the severity of normal tissue complication. Localization of targets in real time with radio-opaque marker is less favorable considering the excess radiation dose to the patient and potential complications of implantation. Various external surrogates could provide indications of the targets' positions during the breathing process. However, there is a great deal of uncertainty in the correlation between external surrogates and internal target positions/trajectory during respiratory cycles. In order to address this problem, we have developed an algorithm that automatically establishes correspondences between the fluoroscopic sequence frames taken from the patient on the day of treatment and the various phases of a 4DCT planning data set. Image based mapping/synchronization procedure is performed using an underlying Markov model established for the breathing process. The mapping procedure is formulated as an optimization process and is solved efficiently using a dynamic programming technique. Results on the phantom, synthetic, and real patient data demonstrate the effectiveness of the proposed method in coping with respiratory correlation variations. The approach could primarily be used for automatic gating interval adaptation in the gated radiotherapy.