QuadSync: 通过Tucker分解进行四焦点张量同步
QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition
AI总结：
本文提出通过Tucker分解实现四焦点张量同步的新框架，展示了其在多相机恢复中的有效性，并建立了四焦点、三焦点和二焦点张量之间的关系。
摘要：
在结构从运动中，四焦点张量比成对的对应物（本质矩阵）包含更多信息，但通常被认为不实用且仅具有理论价值。本文挑战这种观点，提出了一种新的框架来从对应的四焦点张量集合中恢复n个相机。我们形成了块四焦点张量，并证明其允许一个Tucker分解，其因子矩阵是堆叠的相机矩阵，因此具有(4, 4, 4, 4)的多线性秩，与n无关。我们开发了第一个四焦点张量同步算法，使用Tucker分解、交替方向乘子法和迭代加权最小二乘法。我们进一步建立了块四焦点、三焦点和二焦点张量之间的关系，并引入了一种联合同步这三个实体的算法。数值实验表明我们的方法在现代数据集上的有效性，表明在同步中使用高阶信息的潜力和重要性。
英文摘要：
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover $n$ cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,~4,~4,~4) independent of $n$. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.
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