Abstract. 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 symmetry groups and pair-wise maps among a collection of symmetric objects. We introduce a lifting map representation for encoding both symmetry groups and maps between symmetry groups. Based on this representation, we introduce a computational framework for joint symmetry and map synchronization. Experimental results show that this approach outperforms state-of-theart approaches for symmetry detection from a single object as well as joint map optimization among an object collection.