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

The reconstruction of 3 D bone shape from 2 D 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 3 D to 2 D registration recovering the posterior distribution of plausible reconstructions. This provides insight into the uncertainty of the inferred 3 D 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.