3DMNDT: 3D Multi-View Registration Method Based on the Normal Distributions Transform

Abstract

The normal distributions transform (NDT) is an effective paradigm for point set registration. This method was initially designed for pair-wise registration and suffers from the accumulated error problem when directly applied to multi-view registration. Under the framework of point-to-cluster correspondence, this paper proposes a novel multi-view registration method named 3D multi-view registration based on the normal distributions transform (3DMNDT), which integrates the k-means clustering and Lie algebra optimizer to achieve multi-view registration. More specifically, the multi-view registration is cast into the maximum likelihood estimation problem. Firstly, k-means clustering is utilized to divide all data points into different clusters, where one normal distribution is computed to locally model the probability of measuring a data point in each cluster. Subsequently, the multi-view registration problem is formulated by the NDT-based likelihood function. To maximize this likelihood function, the Lie algebra optimizer is introduced and developed to optimize each rigid transformation sequentially. 3DMNDT implements data point clustering, NDT computing, and rigid transformation optimization alternately until the desired registration results are obtained. Experimental results tested on benchmark data sets illustrate that 3DMNDT can achieve state-of-the-art performance for multi-view registration. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by solving the problem of registering multiple point sets. The normal distributions transform (NDT) is a well-known pair-wise registration method widely applied in the robotic domain. This paper extends the original NDT and proposes a novel registration method to simultaneously align more than two point sets. The multi-view registration is cast into the maximum likelihood estimation problem. Subsequently, the k-means clustering and Lie algebra optimizer are integrated to estimate registration parameters. Experimental results demonstrate its superior performance on the accuracy, efficiency, and robustness for multi-view registration of point sets.