Reproject and correct optimization in determining C-arm extrinsic parameters based on geometry constraints

The precision of C-arm extrinsic parameters is critical to computer assisted surgery systems to implement the registration of X-ray image and surgery physical space intraoperatively. Feature point extraction errors may cause deviation of extrinsic parameters using current calibration methods. A projection method was adopted to literally analyze the influence of point error to the precision of extrinsic parameters and among the parameters the translation along the optical axis was found to be less convergent and prone to fall in false optimum state. A statistical projection ratio applying geometry constraints was presented as a restriction to rectify the initial parameter estimated using linear method along the optical axis, so that a coarse transformation between the world coordinate and the camera coordinate can be determined. A 'reproject and correct' approach was proposed to correct the estimated extrinsic parameters based on the reprojection of the physical space to images with intrinsic parameters preoperatively determined and calculate the extrinsic parameters directly without iteration. Simulation results show that this method is more robust and precise compared to the current linear calibration method.