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

Abstract

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. Note to Practitioners —This paper presents a novel rigid point set registration method that explicitly takes the anisotropic noise in both point sets into account. The proposed framework first formulates the probability density functions of generalised points in a bi-directional way, with which the bi-directional hybrid mixture model is built. The resulting objective function is minimised with the expectation maximisation technique. The algorithms are essential for real-world applications in that noise usually exists in both spaces to be registered and is generally anisotropic. The proposed method has demonstrated promising results on two human femur bone models, which indicates the great potential for it to be readily applied to related applications, especially medical scenarios, given that the two point sets are coarsely aligned. Future work will extend the presented method into scenarios of global registration.