Robust Non-Rigid Point Set Registration Algorithm Considering Anisotropic Uncertainties Based on Coherent Point Drift

Non-rigid 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 non-rigid registration problem is to align together two point sets that have been deformed. We have derived and presented a novel registration algorithm that non-rigidly registers two point sets together. The assumption of isotropic localization error is shared in the previous non-rigid 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 non-rigid transformation are updated. To facilitate the proposed algorithm, the low-rank approximation variation of our method is also presented. We have demonstrated through experiments that the proposed algorithm outperforms the state-of-the-art 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.