Stochastic Framework for Symmetric Affine Matching between Point Sets

This paper presents a new approach to obtain symmetry in point matching problem. Here, symmetric matching means the essential property that the choices of source and target should not determine the eventual matching results. Most earlier approaches to achieve symmetric matching have been in deterministic fashions, where symmetry constraints are added into the matching cost functions to impose source-target symmetric property during the matching process. Nevertheless, these modified cost functions cannot generally converge to real ground truth, and further, the perfect source-target symmetry cannot be achieved. Given initial forward and backward matching matrices pair, computed from any reasonable matching strategies, our approach yields perfectly symmetric mapping matrices from a stochastic framework that simultaneously considers the errors underneath the initial matching matrices and the imperfectness of the symmetry constraint. An iterative generalized total least square (GTLS) strategy has been developed such that perfect source-target symmetry is imposed