  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.
