GHMM: Learning Generative Hybrid Mixture Models for Generalized Point Set Registration in Computer-Assisted Orthopedic Surgery

In computer-assisted orthopedic surgery (CAOS), the overlay of pre-operative information onto the surgical scene is achieved through the registration of pre-operative 3D models with the intra-operative surface. The accuracy and robustness of this registration are crucial for effective interventional guidance. To enhance these qualities in CAOS, we explore the use of normal vectors and the concept of joint registration of two point sets, to simultaneously utilize more useful geometrical information and consider noise and outliers in both pre-operative and intra-operative spaces. We present a novel end-to-end hybrid learning-based registration method for CAOS by utilizing generalized point sets that consist of positional and normal vectors, which are considered to be generated from an unknown Generative Hybrid Mixture Model (GHMM) composed of Gaussian Mixture Models (GMMs) and Fisher Mixture Models (FMMs). The joint registration is cast as a maximum likelihood estimation (MLE) problem that aims to minimize the distances between the generalized points and the hybrid distributions. Our proposed approach, termed GHMM, has been extensively validated on various medical data sets (i.e., 291 human femur and 260 hip models) and the public dataset ModelNet40, outperforming state-of-the-art registration methods significantly (p-value<0.01). This suggests the potential of GHMM for applications in orthopedic surgical navigation and object localization. Furthermore, even under different noises and lower overlap ratio conditions, all evaluation metrics of GHMM are superior to other probabilistic methods, demonstrating GHMM's great capability to handle the partial-to-full registration problem and robustness to disturbances.