C-arm pose estimation using a set of coplanar ellipses in correspondence

C-arms are increasingly being used to assist in a large number of surgical procedures. Fairly accurate and fast pose estimates are needed for non-encoded c-arms that are commonly available in most operating rooms in order to attain quantitative feedback from the x-ray images. We propose the use of an image-based fiducial composed of a set of coplanar ellipses to track the c-arm. We adopt an existing method for planar homography and propose a variation consisting of three modifications: including a weighting scheme for the linear system used, orthonormalizing the vectors pertaining to the rotation component of the transformation, and fine tuning the estimates using a constrained optimization step. We show that these variations make the approach more robust to noise that typically arises in fluoroscopy imaging and guarantee the orthonormality of the estimated rotation. The performance of the modified algorithm is demonstrated using realistic x-ray simulations. We also run sensitivity analysis for segmentation and calibration errors that are likely to occur in a practical setting. Preliminary results show mean tracking accuracy within 0.5° and 0.9 mm for segmentation error variance up to 2 pixels squared. The algorithm also proves to be robust to calibration errors up to 1 cm.