Robust and Accurate 3D Curve to Surface Registration with Tangent and Normal Vectors

Abstract

This paper presents a robust and accurate approach for the rigid registration of pre-operative and intraoperative point sets in image-guided surgery (IGS). Three challenges are identified in the pre-to-intraoperative registration: the intra-operative 3D data (usually forms a 3D curve in space) (1) is often contaminated with noise and outliers; (2) usually only covers a partial region of the whole pre-operative model; (3) is usually sparse. To tackle those challenges, we utilize the tangent vectors extracted from the sparse intraoperative data points and the normal vectors extracted from the pre-operative model points. Our first contribution is to formulate a novel probabilistic distribution of the error between a pair of corresponding tangent and normal vectors. The second contribution is, based on the novel distribution, we formulate the registration of two multi-dimensional (6D) point sets as a maximum likelihood (ML) problem and solve it under the expectation maximization (EM) framework. Our last contribution is, in order to facilitate the computation process, the derivatives of the objective function with respect to desired parameters are presented. We conduct extensive experiments to demonstrate that our approach outperforms the state-of-the-art methods. Importantly, in the context of anteriro cruciate ligament (ACL) reconstruction, our method can achieve as low as 0.6795 mm mean target registration error (TRE) value with considerable noises and very limited overlapping ratios.