Solving Jigsaw Puzzles with Linear Programming

We propose a novel Linear Program (LP) based formulation for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the standard NP-hard formulation, that can describe both jigsaws with pieces of unknown position and puzzles of unknown position and orientation. The main contribution and strength of our approach comes from the LP assembly strategy. In contrast to existing greedy methods, our LP solver exploits all the pairwise matches simultaneously, and computes the position of each piece/component globally. The main advantages of our LP approach include: (i) a reduced sensitivity to local minima compared to greedy approaches, since our successive approximations are global and convex and (ii) an increased robustness to the presence of mismatches in the pairwise matches due to the use of a weighted L1 penalty. To demonstrate the effectiveness of our approach, we test our algorithm on public jigsaw datasets and show that it outperforms state-of-the-art methods.