Experimental and Computational Study of Error and Uncertainty in Real-Time Camera-Based Tracking of a Two-Dimensional Marker for Orthopedic Surgical Navigation

Tracking of the position and orientation of a moving object by a camera can be accomplished by attaching a 2D marker with a specific pattern on the object. Recently, we have developed a projection-based surgical navigation system that can accurately guide in real-time the pre-operative plan of resection in orthopedic surgery, such as joint replacement or wide-resection of osteosarcoma (bone tumor). To this end, it is important to study the accuracy of registration and tracking due to various sources of errors, such as the printing resolution and quality of the 2D marker. In this study, we investigate and provide analysis of error and uncertainty for real-time tracking using a 2D marker with a camera. Experiments and computational simulations were conducted to quantify the estimation of errors in position and orientation due to the printing error of 2D markers using a 600-dpi laser printer. In addition, a theory of uncertainty propagation in a form of congruence transformation was derived for such systems and is illustrated with experimental results.