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. We guarantee some robustness of the latter estimate to
measurement errors. 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. Numerical experiments
demonstrate the competitive accuracy of this solution, its robustness to
corruption and its computational advantage for large puzzles
