Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor
<|reference_start|>Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor: 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.<|reference_end|>
@article{miao2024tensor-based,
    title={Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal
  Tensor},
    author={Daniel Miao, Gilad Lerman and Joe Kileel},
    journal={arXiv preprint arXiv:2409.09313},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.09313},
    primaryClass={cs.CV cs.NA math.NA math.OC}
}