Total Least Squares Registration of 3D Surfaces

Abstract

ABSTRACT:Co-registration of point clouds of partially scanned objects is the first step of the 3D modeling workflow. The aim of coregistration is to merge the overlapping point clouds by estimating the spatial transformation parameters. In computer vision and photogrammetry domain one of the most popular methods is the ICP (Iterative Closest Point) algorithm and its variants. There exist the 3D Least Squares (LS) matching methods as well (Gruen and Akca, 2005). The co-registration methods commonly use the least squares (LS) estimation method in which the unknown transformation parameters of the (floating) search surface is functionally related to the observation of the (fixed) template surface. Here, the stochastic properties of the search surfaces are usually omitted. This omission is expected to be minor and does not disturb the solution vector significantly. However, the a posteriori covariance matrix will be affected by the neglected uncertainty of the function values of the search surface. . This causes deterioration in the realistic precision estimates. In order to overcome this limitation, we propose a method where the stochastic properties of both the observations and the parameters are considered under an errors-in-variables (EIV) model. The experiments have been carried out using diverse laser scanning data sets and the results of EIV with the ICP and the conventional LS matching methods have been compared.

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“…Compared with traditional constrained least squares (CLS) methods, it could well solve the impact of random errors. Aydar et al [36] considered stochastic properties of both observations and parameters and proposed a total least square (TLS) registration of 3D surfaces, where an EIV model was utilized and its parameters were estimated by a TLS method. Ge and Wunderlich [37] proposed a surface-based-matching of 3D point clouds with a nonlinear Gauss-Helmert model to solve the weighted total least-squares problem.…”