Solving Jigsaw Puzzles By the Graph Connection Laplacian
This work addresses a specific problem in computer vision for automated puzzle-solving, presenting an incremental improvement by combining rotation recovery with existing shuffle methods.
The authors tackled the problem of automatically solving large jigsaw puzzles with unknown rotations and shuffles of pieces, proposing a method to recover rotations using the graph connection Laplacian, which demonstrated competitive accuracy and computational efficiency in numerical experiments.
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.