Efficient Algorithms for Rotation Averaging Problems

• URL: http://arxiv.org/abs/2103.10024v1
• Date: Thu, 18 Mar 2021 05:22:45 GMT
• Title: Efficient Algorithms for Rotation Averaging Problems
• Authors: Yihong Dong, Lunchen Xie and Qingjiang Shi
• Abstract summary: The averaging problem is a fundamental task in computer applications. We propose a block-based averaging algorithm with guaranteed convergence to stationary points. We also propose an alternative averaging algorithm by applying upper-bound minimization.
• Score: 17.101725065752486
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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