Solving Jigsaw Puzzles By the Graph Connection Laplacian

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 shifted and asks to recover the original image given the transformed pieces. The main contribution of this work is a theoretically-guaranteed method for recovering the unknown orientations of the puzzle pieces by using the graph connection Laplacian associated with the puzzle. Iterative application of this method and other methods for recovering the unknown shifts result in a solution for the large jigsaw puzzle problem. This solution is not greedy, unlike many other solutions. Numerical experiments demonstrate the competitive performance of the proposed method.