Generalized Coherent Point Drift With Multi-Variate Gaussian Distribution and Watson Distribution

Abstract

This paper introduces a novel rigid point set registration (PSR) approach that accurately aligns the pre-operative space and the intra-operative space together in the scenario of computer-assisted orthopedic surgery (CAOS).Motivated by considering anisotropic positional localization noise and utilizing undirected normal vectors in the point sets (PSs), the multivariate Gaussian distribution and the Watson distribution are utilized to model positional and normal vectors' error distributions respectively. In the proposed approach, with the above probability distributions, the PSR problem is then formulated as a maximum likelihood estimation (MLE) problem and solved under the expectation maximization (EM) framework. Our contributions are three folds. First, the rigid registration problem of aligning generalized points with undirected normal vectors is formally formulated in a probabilistic manner. Second, the MLE problem is solved under the EM framework. Third, the gradients of associated objective functions with respect to desired parameters are computed and provided. Experimental results on both the human pelvis and femur models demonstrate the potential clinical values and that the proposed approach owns significantly improved performances compared with existing methods.

A Novel Point Cloud Registration Method Based on ROPNet

“…Point cloud registration is the basis of 3D reconstruction [ 1 , 2 ], 3D localization [ 3 , 4 , 5 , 6 ], pose estimation [ 7 , 8 , 9 ], and other fields. With the development of deep learning, point cloud registration develops from traditional iterative closest point-based (ICP) [ 10 ] methods to approaches based on deep learning, such as PCRNet [ 11 ], D3feat [ 12 ], iterative distance-aware similarity matrix convolution network (IDAM) [ 13 ], point cloud registration with deep attention to the overlap region (PREDATOR) [ 14 ], robust point matching (RPMNet) [ 15 ], etc.…”

Geodesic-Based Bayesian Coherent Point Drift

“…The most common type of motion coherence is based on the proximity between points. The motion coherence of this type is typically introduced by imposing local rigidity on a shape surface [4], [5] and the penalty on a non-smooth deformation field [6], [7], [8], [9], [10], [11], [12]. Apart from the coherent moves based on proximity, nonrigid registration techniques impose the coherence based on prior knowledge to register shapes involving more specific deformations, such as human face [13], [14], human hand shape and pose [15], and human body pose [16], [17], [18], [19], [20].…”