Weighted total least squares for rigid body transformation and comparative study on heteroscedastic points

Abstract

Aligning two point clouds is the iterated closest point algorithm which starts with two point clouds to estimate three translates and rotations. Traditional registration are searching the optimal solutions at the cost function of the minimum residual squares without consideration of points covariance. Closed-form or iterative least squares methods are performed to search the solutions, and total least squares (TLS) methods are introduced in recent years. The ordinary least squares (OLS) and OTLS methods can not work on the heteroscedastic cases. So element-wise weighted TLS (EWTLS) and row-wise weighted TLS (RWTLS) methods are introduced to solve the rigid body transformation problem after the initial values obtained by Procrustes analysis method. Comparative studies are made with the weighted and unweighted estimators of OLS, TLS, mixed OLS and TLS, EWTLS and RWTLS. The results indicate that the RWTLS method is the highest accuracy estimator, and be much more accurate than the unweighted OLS and TLS methods.