Generalized Non-rigid Point Set Registration with Hybrid Mixture Models Considering Anisotropic Positional Uncertainties

Abstract

Image-to-patient or pre-operative to intra-operative registration is an essential problem in computer-assisted surgery (CAS). Non-rigid or deformable registration is still a challenging problem with partial overlapping between point sets due to limited camera view, missing data due to tumor resection and the surface reconstruction error intra-operatively. In this paper, we propose and validate a normal-vector assisted non-rigid registration framework for accurately registering soft tissues in CAS. Two stages including rigid and non-rigid registrations are involved in the framework. In the stage of the rigid registration that does the initial alignment, the normal vectors extracted from the point sets are used while the position uncertainty is assumed to be anisotropic. With the normal vectors incorporated, the algorithm can better recover the point correspondences and is more robust to intra-operative partial data which is often the case in a typical laparoscopic surgery. In the stage of the non-rigid registration, the anisotropic coherent point drift (CPD) method is formulated, where the isotropic error assumption is generalized to anisotropic cases. Extensive experiments on the human liver data demonstrate our proposed algorithm’s several great advantages over the existing state-of-the-art ones. First, the rigid transformation matrix is recovered more accurately. Second, the proposed registration framework is much more robust to partial scan. Besides, the anisotropic CPD outperforms the original CPD significantly in terms of robustness to noise.