Robust NonRigid Point Set Registration Algorithm Considering Anisotropic Uncertainties Based on Coherent Point Drift Nonrigid point set registration (PSR) is an outstanding and fundamental problem in fields of robotics, computer vision, medical image analysis and imageguided surgery. The aim of a nonrigid registration problem is to align together two point sets that have been deformed. We have derived and presented a novel registration algorithm that nonrigidly registers two point sets together. The assumption of isotropic localization error is shared in the previous nonrigid registration algorithms. In this paper, the position localization error is generalized to the anisotropic cases, which means that the error distribution is not the same in different spatial directions. The motivation of considering the anisotropic characteristic is that the point localization error is actually different in three spatial directions in real applications. Mathematically, the difficulty in dealing with the anisotropic error case comes from the change from a standard deviation that is a scalar to a covariance matrix. The formulas for updating the parameters in both expectation and maximization steps are derived. In the expectation step, we compute the posterior probabilities that represent the correspondences between points in two PSs. In the maximization step, given the current posteriors, the covariance matrix of the position localization error and the nonrigid transformation are updated. To facilitate the proposed algorithm, the lowrank approximation variation of our method is also presented. We have demonstrated through experiments that the proposed algorithm outperforms the stateoftheart ones in terms of registration and accuracy and robustness to noise. More specifically, most of the experimental results have passed the statistical tests at the 5% significance level.

Joint Registration of Multiple Point Sets with Refinement The recent advances in fast and affordable 3D scanners, such as the Microsoft Kinect, have triggered new developments in 3D reconstruction. However, the geometric alignment of multiple point clouds is still a very challenging task. This paper addresses the problem of registering multiple point sets by building upon the stateoftheart Joint Registration of Multiple Point Clouds (JRMPC) algorithm. We advance over JRMPC by incorporating the surface normal orientation of each point in the Gaussian Mixture Models (GMM) employed by this method. We formally derive an expectationconditional maximization algorithm that iteratively estimates the refined model and transformation parameters. Experiments performed on both synthetic, real indoor and outdoor data prove that incorporating the orientation information substantially improves the parameter estimation, allowing for a 50% average reduction of the registration error compared to JRMPC. Our method is compared to other pairwise approaches, demonstrating the best performance on three different realistic datasets.