Perspective pinhole model with planar source for augmented reality surgical navigation based on C-arm imaging

For augmented reality surgical navigation based on C-arm imaging, accuracy of the overlaid augmented reality onto the X-ray image is imperative. However, overlay displacement is generated when a conventional pinhole model describing a geometric relationship of a normal camera is adopted for C-arm calibration. Thus, a modified model for C-arm calibration is proposed to reduce this displacement, which is essential for accurate surgical navigation. Based on the analysis of displacement pattern generated for three-dimensional objects, we assumed that displacement originated by moving the X-ray source position according to the depth. In the proposed method, X-ray source movement was modeled as variable intrinsic parameters and represented in the pinhole model by replacing the point source with a planar source. The improvement which represents a reduced displacement was verified by comparing overlay accuracy for augmented reality surgical navigation between the conventional and proposed methods. The proposed method achieved more accurate overlay on the X-ray image in spatial position as well as depth of the object volume. We validated that intrinsic parameters that describe the source position were dependent on depth for a three-dimensional object and showed that displacement can be reduced and become independent of depth by using the proposed planar source model.