Procrustes alignment with the EM algorithm

Abstract

This paper casts the problem of point-set alignment via Procrustes analysis into a maximum likelihood framework using the EM algorithm. The aim is to improve the robustness of the Procrustes alignment to noise and clutter. By constructing a Gaussian mixture model over the missing correspondences between individual points, we show how alignment can be realised by applying singular value decomposition to a weighted point correlation matrix. Moreover, by gauging the relational consistency of the assigned correspondence matches, we can edit the point sets to remove clutter. We illustrate the effectiveness of the method matching stereogram. We also provide a sensitivity analysis to demonstrate the operational advantages of the method.