Learning High Dimensional Correspondences Based on Maximum Variance Unfolding

Correspondence is one of the crucial problems in robotic vision and automation. For matching two high dimensional data sets with a certain number of aligned training examples, a novel method is proposed in this paper. The maximum variance unfolding method is employed to exploit the similar underlying structures of two different data sets. Mappings between low embeddings of the two data sets are then established by least square regression on the training examples. Correspondences of unknown points can be assigned by searching the nearest neighbours of the mapping results. The validity of this algorithm is confirmed both in theory and practice. Three examples are performed to demonstrate the potential of our method.