A high-order solution for the distribution of target registration error in rigid-body point-based registration.

Rigid registration of pre-operative surgical plans to intraoperative coordinates of a patient is an important step in computer-assisted orthopaedic surgery. A good measure for registration accuracy is the target registration error (TRE) which is the distance after registration between a pair of corresponding points not used in the registration process. However, TRE is not a deterministic value, since there is always error in the localized features (points) utilized in the registration. In this situation, the distribution of TRE carries more information than TRE by itself. Previously, the distribution of TRE has been estimated with the accuracy of the first-order approximation. In this paper, we analytically approximate the TRE distribution up to at least the second-order accuracy based on the Unscented Kalman Filter algorithm.