揭示三视图张量的低秩结构，提升相机位姿同步精度。
Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor
- 基于张量分解发现三视图张量具低多线性秩(6,4,4)
- 噪声无情况下该秩约束足以恢复相机位姿
- 相比传统成对方法，可显著提高定位精度
三视图张量的块张量提供了场景三视角几何的关键信息。其背后的同步问题旨在从块三视图张量中恢复相机位姿（位置与朝向，至全局变换等价）。本文建立了该张量的显式Tucker分解，揭示在适当缩放条件下其多线性秩恒为(6,4,4)，与相机数量无关。证明该秩约束在无噪声情况下足以实现相机位姿恢复。该约束启发了一种基于块三视图张量高阶奇异值分解的同步算法。在真实数据集上的实验表明，该算法相比当前最优全局同步方法，在定位估计精度上具有显著提升潜力。整体表明，同步问题中的高阶交互关系可被利用以超越传统的成对方法。
原文摘要 · Abstract (English)
The block tensor of trifocal tensors provides crucial geometric information on the three-view geometry of a scene. The underlying synchronization problem seeks to recover camera poses (locations and orientations up to a global transformation) from the block trifocal tensor. We establish an explicit Tucker factorization of this tensor, revealing a low multilinear rank of $(6,4,4)$ independent of the number of cameras under appropriate scaling conditions. We prove that this rank constraint provides sufficient information for camera recovery in the noiseless case. The constraint motivates a synchronization algorithm based on the higher-order singular value decomposition of the block trifocal tensor. Experimental comparisons with state-of-the-art global synchronization methods on real datasets demonstrate the potential of this algorithm for significantly improving location estimation accuracy. Overall this work suggests that higher-order interactions in synchronization problems can be exploited to improve performance, beyond the usual pairwise-based approaches.
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