Multi-Phase Relaxation Labeling for Square Jigsaw Puzzle Solving

We present a novel method for solving square jigsaw puzzles based on global optimization. The method is fully automatic, assumes no prior information, and can handle puzzles with known or unknown piece orientation. At the core of the optimization process is nonlinear relaxation labeling, a well-founded approach for deducing global solutions from local constraints, but unlike the classical scheme here we propose a multi-phase approach that guarantees convergence to feasible puzzle solutions. Next to the algorithmic novelty, we also present a new compatibility function for the quantification of the affinity between adjacent puzzle pieces. Competitive results and the advantage of the multi-phase approach are demonstrated on standard datasets.

Relaxation Labeling Meets GANs: Solving Jigsaw Puzzles with Missing Borders

This paper proposes JiGAN, a GAN-based method for solving Jigsaw puzzles with eroded or missing borders. Missing borders is a common real-world situation, for example, when dealing with the reconstruction of broken artifacts or ruined frescoes. In this particular condition, the puzzle's pieces do not align perfectly due to the borders' gaps; in this situation, the patches' direct match is unfeasible due to the lack of color and line continuations. JiGAN, is a two-steps procedure that tackles this issue: first, we repair the eroded borders with a GAN-based image extension model and measure the alignment affinity between pieces; then, we solve the puzzle with the relaxation labeling algorithm to enforce consistency in pieces positioning, hence, reconstructing the puzzle. We test the method on a large dataset of small puzzles and on three commonly used benchmark datasets to demonstrate the feasibility of the proposed approach.