We address rotation averaging and its application to real-world 3D reconstruction. Local optimisation based approaches are the defacto choice, though they only guarantee a local optimum. Global optimizers ensure global optimality in low noise conditions, but they are inefficient and may easily deviate under the influence of outliers or elevated noise levels. We push the envelope of global rotation averaging by formulating it as a semi-definite program that can be solved efficiently by applying the Burer-Monteiro method. Both memory and time requirements are thereby largely reduced through a low-rank factorisation. Combined with a fast view graph filtering as preprocessing, and a local optimiser as post-processing, the proposed hybrid approach is robust to outliers. Compared against state-of-the-art globally optimal methods, our approach is 1 ~ 2 orders of magnitude faster while maintaining the same or better accuracy. We apply the proposed hybrid rotation averaging approach to incremental Structure from Motion (SfM) by adding the resulting global rotations as regularizers to bundle adjustment. Overall, we demonstrate high practicality of the proposed method as bad camera poses are effectively corrected and drift is reduced.
翻译:我们处理的是平均轮换及其应用于现实世界的3D重建。 以地方优化为基础的方法是自成一体的选择,尽管它们只能保证当地的最佳做法。 全球优化者在低噪音条件下确保全球最佳性,但它们效率低下,而且很容易在外部噪音水平或高噪音水平的影响下偏离。 我们把全球轮换的范围推向平均半确定程序,将之作为半确定性程序,采用布勒-蒙泰罗方法可以有效解决。 记忆和时间要求因此通过低等级因素化而大大降低。 结合作为预处理的快速图形过滤器和作为后处理的本地优化器,拟议的混合方法对离线者是强有力的。 与最先进的全球最佳方法相比,我们的方法速度更快1~2级,同时保持相同或更准确性。 我们采用拟议的混合平均轮换方法从运动(SfM)到递增结构,将由此产生的全球轮换方法作为正规化的组合调整方法。 总体而言,我们证明拟议的方法作为坏相机的配置非常实用性,并且减少了漂移。