Joint Map and Symmetry Synchronization

Most existing techniques in map computation (e.g., in the form of feature or dense correspondences) assume that the underlying map between an object pair is unique. This assumption, however, easily breaks when visual objects possess self-symmetries. In this paper, we study the problem of jointly optimizing self-symmetries and pair-wise maps among a collection of similar objects. We introduce a lifting map representation for encoding both symmetry groups and maps between symmetry groups. Based on this representation, we introduce a reweighted non-linear least square framework for joint symmetry and map synchronization. Experimental results show that this approach outperforms state-of-the-art methods for self-symmetry group extraction from a single object as well as joint map optimization among a object collection.