Anisotropic 6-D Rigid Point Set Registration

Abstract

Registration of two point sets (PSs) is an essential problem in research areas of robotics, computer vision, measurements, computer-assisted interventions. Registration, however, is a challenging problem essentially because that point sets in real-world scenarios contain noise and outliers. Features such as normal vectors, which can be extracted from raw point sets, have potential to improve both registration accuracy and robustness. However, like positional vectors, the extracted normal vectors have localization errors as well. This paper explicitly considers the anisotropic error distributions with both positional and normal vectors in formulating and solving the point set registration problem. To achieve this aim, the multi-variate Gaussian distribution and the Kent distribution are utilised to model the positional and normal error vectors respectively. With the probabilistic models, the registration task is cast as a maximum likelihood estimation (MLE) problem where the latent variables are point correspondences between two point sets. Expectation maximisation technique is leveraged to solve the above formulated optimisation problem. Experimental results on human femur and pelvis point sets demonstrate that the proposed method has the best registration accuracy and robustness among all compared state-of-the-art methods. Results show that the proposed method can achieve sub-degree rotational error and sub-milimeter translational error values, under noise and a wide range of outliers.