Survey of Point Cloud Registration Methods and New Statistical Approach

The use of a 3D range scanning device for autonomous object description or unknown environment mapping leads to the necessity of improving computer methods based on identical point pairs from different point clouds (so-called registration problem). The registration problem and three-dimensional transformation of coordinates still require further research. The paper attempts to guide the reader through the vast field of existing registration methods so that he can choose the appropriate approach for his particular problem. Furthermore, the article contains a regression method that enables the estimation of the covariance matrix of the transformation parameters and the calculation of the uncertainty of the estimated points. This makes it possible to extend existing registration methods with uncertainty estimates and to improve knowledge about the performed registration. The paper's primary purpose is to present a survey of known methods and basic estimation theory concepts for the point cloud registration problem. The focus will be on the guiding principles of the estimation theory: ICP algorithm; Normal Distribution Transform; Feature-based registration; Iterative dual correspondences; Probabilistic iterative correspondence method; Point-based registration; Quadratic patches; Likelihood-field matching; Conditional random fields; Branch-and-bound registration; PointReg. The secondary purpose of this article is to show an innovative statistical model for this transformation problem. The new theory needs known covariance matrices of identical point coordinates. An unknown rotation matrix and shift vector have been estimated using a nonlinear regression model with nonlinear constraints. The paper ends with a relevant numerical example.