Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor
This work addresses camera pose estimation for computer vision applications, offering a novel approach that exploits higher-order interactions beyond pairwise methods.
The paper tackled the problem of recovering camera poses from the block trifocal tensor in three-view geometry, establishing a low multilinear rank of (6,4,4) and developing an algorithm that significantly improves location estimation accuracy in experiments.
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.