Generalized 3-D Rigid Point Set Registration With Bidirectional Hybrid Mixture Models

In medical robotics and image-guided surgery (IGS), registration is needed in order to align together the coordinate frames of robots, medical imaging modalities, surgical tools, and patients. Existing registration algorithms often assume one point set to be a noise-free model while the other to contain noise and outliers. However, in real scenarios, noise and outliers can exist in both point sets to be registered. To eliminate the above-mentioned challenge, in this paper, we formally formulate the Bi-directional Generalised Rigid Point Set Registration (Bi-GRPSR) problem where normal vectors are adopted, bi-directional probability density function (PDFs) and Hybrid Mixture Models (HMMs) are constructed to derive the objective function. Bi-GRPSR considering anisotropic positional noise is thus cast as a maximum likelihood estimation (MLE) problem, which is solved by the proposed Bi-directional Generalised Anisotropic Coherent Point Drift (Bi-AGCPD) where spatially nearby points are considered to move coherently and iterative expectation maximization (EM) steps are involved. Experimental results on two human bone point sets, under different settings of noise, outliers, and overlapping ratios, validate the effectiveness and improvements of Bi-AGCPD over existing probabilistic and learning-based methods.