Uncertainty Reduction in Contour-Based 3D/2D Registration of Bone Surfaces

The reconstruction of 3D bone shape from 2D X-ray contours is an ill-posed problem. For medical applications, it is important to estimate the uncertainty of the reconstructions. While traditional optimisation methods produce a single point-estimate, we frame the problem as Bayesian inference. We apply a Monte Carlo sampling based non-rigid 3D to 2D registration recovering the posterior distribution of plausible reconstructions. This provides insight into the uncertainty of the inferred 3D reconstruction. As an application, we demonstrate the use of the method in selecting X-ray viewing conditions in order to maximise accuracy while minimising reconstruction uncertainty. We evaluated reconstruction accuracy and variance for the femur bone from bi-planar views.