Total Least Squares Registration of 3D Surfaces

Abstract

Co-registration of point clouds of partially scanned
 objects is the first step of the 3D modeling workflow. The aim of
 co-registration 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.