Revisiting Distribution-Based Registration Methods

Normal Distribution Transformation (NDT) registration is a fast, learning-free point cloud registration algorithm that works well in diverse environments. It uses the compact NDT representation to represent point clouds or maps as a spatial probability function that models the occupancy likelihood in an environment. However, because of the grid discretization in NDT maps, the global minima of the registration cost function do not always correlate to ground truth, particularly for rotational alignment. In this study, we examined the NDT registration cost function in-depth. We evaluated three modifications (Student-t likelihood function, inflated covariance/heavily broadened likelihood curve, and overlapping grid cells) that aim to reduce the negative impact of discretization in classical NDT registration. The first NDT modification improves likelihood estimates for matching the distributions of small population sizes; the second modification reduces discretization artifacts by broadening the likelihood tails through covariance inflation; and the third modification achieves continuity by creating the NDT representations with overlapping grid cells (without increasing the total number of cells). We used the Pomerleau Dataset evaluation protocol for our experiments and found significant improvements compared to the classic NDT D2D registration approach (27.7% success rate) using the registration cost functions 'heavily broadened likelihood NDT' (HBL- NDT) (34.7% success rate) and 'over-lapping grid cells NDT' (OGC-NDT) (33.5% success rate). However, we could not observe a consistent improvement using the Student-t likelihood-based registration cost function (22.2% success rate) over the NDT P2D registration cost function (23.7% success rate). A comparative analysis with other state-of-art registration algorithms is also presented in this work. We found that HBL-NDT worked best for easy initial pose difficulties scenarios making it suitable for consecutive point cloud registration in SLAM application.