Synchronization Problems in Computer Vision with Closed-Form Solutions

In this paper we survey and put in a common framework several works that have been developed in different contexts, all dealing with the same abstract problem, called synchronization by some authors, or averaging, or graph optimization by others. The problem consists in recovering some variables from a set of pairwise relation measurements. In particular, we concentrate on instances where the variables and the measures belong to a (semi-)group and the measures are their mutual differences (or ratios, depending on how the group operation is called). The groups we deal with have a matrix representation, which leads to an elegant theory and closed-form solutions.