OBHMR: Robust Partial-to-full Generalized Point Set Registration with Overlap-guided Bidirectional Hybrid Mixture Model

In this paper, we introduce a novel overlap-based bidirectional point set registration approach, i.e., Overlap- guided Bidirectional Hybrid Mixture Registration (OBHMR), which incorporates geometric information (i.e., normal vectors) in both the correspondence and transformation stages and for- mulates the optimization objective of registration in a bidirec- tional manner. More importantly, to address the issue of partial- to-full registration, OBHMR utilises the predicted point-wise overlap score using networks to formulate the overlap-guided Hybrid Mixture Model consisting of the Gaussian Mixture Model (GMM) and Fisher Mixture Model (FMM). OBHMR contains four components: (1) the overlap-guided correspon- dence network that estimates the correspondence probabilities and calculates the point-wise overlap score; (2) the learning posterior module that estimates the overlap-guided HMM parameters; (3) the transformation module that computes the rigid transformation by formulating the optimisation objective in a bidirectional registration way, given correspondences and overlap-guided HMM parameters. Experiments using 1457 human femur and 1301 human hip models demonstrate signif- icant improvements in partial-to-full registration performance (p < 0.01) under different overlapping ratios, compared to state-of-the-art registration approaches. Furthermore, individ- ual contributions of three modules (i.e., additional normal vectors, overlap score estimation module and the bidirectional mechanism) in OBHMR have been validated in ablation studies. The results demonstrate OBHMR’s capability of tackling the challenging partial-to-full registration problems in computer- assisted orthopedic surgery. The codes are available at https: //github.com/Dxinz/DeepOBHMR.