A new dynamical model for solving rotation averaging problem
This addresses a specific problem in computational geometry or robotics for applications like 3D reconstruction, but appears incremental as it builds on existing models like the Kuramoto model.
The paper tackles the rotation averaging problem by proposing a novel method based on a dynamical system generalization of the Kuramoto model on SO(3), and finds that it yields results approximately equal to the geometric average in simulations with real and random datasets.
The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group SO(3), which is known as the non-Abelian Kuramoto model. We have proposed a novel method for finding weighted and unweighted rotation average. In order to verify the correctness of our algorithms, we have compared the simulation results with geometric and projected average using real and random data sets. In particular, we have discovered that our method gives approximately the same results as geometric average.