DeepBHMR: Learning Bidirectional Hybrid Mixture Models for Generalized Rigid Point Set Registration

In this paper, we introduce a novel normal- assisted learning-based rigid registration approach, i.e., Deep Bi-directional Hybrid Mixture Registration (DeepBHMR). Our approach utilises helpful normal vectors explicitly in both correspondence and transformation stages and formulates the optimization objective of registration in a bi-directional way that considers noise in both point sets. DeepBHMR consists of three modules: (1) the correspondence network that esti- mates the correspondence probability relating points within one generalized point set (i.e., positional and normal vectors) with components of Hybrid Mixture Models (HMMs) rep- resenting the other generalized point set; (2) the posterior module that computes HMMs parameters; (3) the transfor- mation module that computes the rotation matrix and the translation vector given the estimated generalized-point to hybrid-distribution correspondences and HMMs parameters. DeepBHMR has been validated on 291 human femur and 260 hip models, and extensive experimental results demonstrate that DeepBHMR outperforms the state-of-the-art registration methods (p-value < 0.01). In the circumstance of femur bones, the mean rotation and translation error values are around 1◦ (i.e., 1.01◦) and less than 1 mm (i.e., 0.36mm), respectively. Furthermore, even under the large transformation (i.e., in the range of [0, 180]◦and [0, 100] mm), the mean RMSE values being 3.05 mm is still satisfactory. Additionally, the results demonstrate the DeepBHMR’s favorable generalizability from femur shapes to hip shapes. We have carefully validated the significant benefits of incorporating normal vectors and the bidirectional mechanism. DeepBHMR can successfully handle the challenging scenario of large transformation and partial registration. The codes are available at https://github. com/zzyrobot/DeepBHMR.git.