A Geometrical Calibration Method for C-Arm CT Based on a Nonlinear Registration Model

The image quality of C-arm computed tomography (CT) degrades due to the nonideal projection geometry due to mechanical vibrations of the gantry during the CT scan; therefore, geometrical calibration methods need to be applied to derive the view-specific projection matrices, which are incorporated in the reconstruction processes. Previous geometrical calibration methods either require specific calibration phantoms or long computational time due to the 3-D-2-D registration process. This work begins with a theoretical derivation on how the perturbed geometrical parameters impact the projection images. It was found that with small perturbations of the view angle and the altitude angle, the relationship between the projection images under the ideal geometry and those under the perturbed geometry can be related based on a model-based 2-D deformation dependent on the perturbed geometrical parameters. Guided by the theoretical derivations, a new geometrical correction method was proposed, which generates the geometrical parameters based on 2-D-2-D registrations between the ideal projection images and the perturbed projection images. The proposed method was applied to offline and online calibration and was validated by both numerical experiments and physical experiments.