Errors-in-Variables Anisotropic Extended Orthogonal Procrustes Analysis

This letter presents a novel total least squares (TLS) solution of the anisotropic row-scaling Procrustes problem. The ordinary LS Procrustes approach finds the transformation parameters between origin and destination sets of observations minimizing errors affecting only the destination one. In this letter, we introduce the errors-in-variables model in the anisotropic Procrustes analysis problem and present a solution that can deal with the uncertainty affecting both sets of observations. The algorithm is applied to solve the image exterior orientation problem. Experiments show that the proposed TLS method leads to an accuracy in the parameters estimation that is higher than the one reached with the ordinary LS anisotropic Procrustes solution when the number of points, whose coordinates are known in both the image and the external systems, is small.