A unified framework for alignment and correspondence

This paper casts the problem of 2D point-set alignment and correspondence matching into a unified framework. Our aim in providing this unification is to constrain the recovery of pose parameters using relational constraints provided by the structural arrangement of the points. This structural information is provided by a neighbourhood graph for the points. We characterise the problem using distinct probability distributions for alignment errors and correspondence errors. The utility measure underpinning the work is the cross-entropy between probability distributions for alignment and assignment errors. This statistical framework interleaves the processes of finding point correspondences and estimating the alignment parameters. In the case of correspondence matching, the probability distribution models departures from edge consistency in the matching of the neighbourhood graphs. We investigate two different models for the alignment error process. In the first of these, we study Procrustes alignment. Here we show how the parameters of the similarity transform and the correspondence matches can be located using dual singular value decompositions. The second alignment process uses a point-distribution model. We show how this augmented point-distribution model can be matched to unlabelled point-sets which are subject to both additional clutter and point drop-out. Experimental results using both synthetic and real images are given.