Toward an End-to-End Calibration for Mobile C-Arm in Combination with a Depth Sensor for Surgical Augmented Reality Applications

C-arm X-ray imaging is commonly applied in operating rooms for guiding orthopedic surgeries. Augmented Reality (AR) with C-arm X-ray images during surgery is an efficient way to facilitate procedures for surgeons. However, the accurate calibration process for surgical AR based on C-arm is essential and still challenging due to the limitations of C-arm imaging systems, such as instability of C-arm calibration parameters and the narrow field of view. We extend existing methods using a depth camera and propose a new calibration procedure consisting of calibration of the C-arm imaging system, and 3D/2D calibration of an RGB-D camera and C-arm system with a new method to achieve reliable data and promising accuracy and, at the same time, consistent with standard surgical protocols. For the calibration procedure, we apply bundle adjustment equations with a 3D designed Lego multi-modal phantom, in contrast to the previous methods in which planar calibration phantoms were applied. By using our method, the visualization of the X-ray image upon the 3D data was done, and the achieved mean overlay error was 1.03 mm. The evaluations showed that the proposed calibration procedure provided promising accuracy for AR surgeries and it improved the flexibility and robustness of existing C-arm calibration methods for surgical augmented reality (using C-arm and RGB-D sensor). Moreover, the results showed the efficiency of our method to compensate for the effects of the C-arm movement on calibration parameters. It was shown that the obtained overlay error was improved for the non-zero rotation movement of C-arm by using a virtual detector.