Globally Optimal Estimates for Rotation Averaging Problems

This paper investigates the difficulty of obtaining the global optimum in rotation averaging problems and presents different representations of rotation matrix. One of the drawbacks is that there is a 2-to-1 mapping when using the angle-axis and quaternion representation of rotation matrix. By using the chordal metric and a hierarchy of convex relaxations to the non-convex rotation averaging problems, the global optimum is obtained most of the time and the ambiguity caused by the other two representations of rotation matrix can be avoided. The experiments show that the polynomial optimization method works efficiently and reliably and the results are certified to be the global minimizer most of the time.