Efficient Algorithms for Rotation Averaging Problems
This work addresses a fundamental but difficult problem in computer vision, offering incremental improvements in algorithm efficiency and convergence for rotation averaging tasks.
The paper tackles the rotation averaging problem in computer vision by proposing two efficient algorithms, a block coordinate descent-based method and a successive upper-bound minimization-based method, which demonstrate superior convergence performance and achieve globally optimal solutions in numerical experiments.
The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of \yhedit{a} fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.