SIAM Journal on Imaging Sciences, Volume 13, Issue 4, Page 1717-1753, January 2020.
We propose a novel mathematical framework to address the problem of automatically solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal square pieces that are arbitrarily rotated and shuffled, and asks to recover the original image given the transformed pieces. The main contribution of this work is a method for recovering the rotations of the pieces when both shuffles and rotations are unknown. A major challenge of this procedure is estimating the graph connection Laplacian without the knowledge of shuffles. A careful combination of our proposed method for estimating rotations with any existing method for estimating shuffles results in a practical solution for the jigsaw puzzle problem. Our theory guarantees, in a clean setting, that our basic idea of recovering rotations is robust to some corruption of the connection graph. Numerical experiments demonstrate the competitive accuracy of this solution, its robustness to corruption, and its computational advantage for large puzzles.

中文翻译：

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通过图连接拉普拉斯算术解决拼图游戏

SIAM影像科学杂志，第13卷，第4期，第1717-1753页，2020年1月。
我们提出了一种新颖的数学框架来解决自动解决大型拼图难题的问题。此问题假设有一个大图像，该图像被切成任意旋转和混洗的等角正方形小块，并要求根据变换后的块恢复原始图像。这项工作的主要贡献是一种在混洗和旋转均未知的情况下恢复碎片旋转的方法。此过程的主要挑战是在不了解混洗的情况下估计图连接拉普拉斯算子。将我们提出的估计旋转的方法与任何现有的估计随机播放的方法进行仔细的结合，可以为拼图游戏问题提供切实可行的解决方案。我们的理论保证在干净的环境中，我们恢复旋转的基本思想对于连接图的某些损坏是有力的。数值实验证明了该解决方案的竞争性准确性，对腐败的鲁棒性以及对大型拼图的计算优势。