A Novel Hybrid Scheme Using Genetic Algorithms and Deep Learning for the Reconstruction of Portuguese Tile Panels

This paper presents a novel scheme, based on a unique combination of genetic algorithms (GAs) and deep learning (DL), for the automatic reconstruction of Portuguese tile panels, a challenging real-world variant of the jigsaw puzzle problem (JPP) with important national heritage implications. Specifically, we introduce an enhanced GA-based puzzle solver, whose integration with a novel DL-based compatibility measure (DLCM) yields state-of-the-art performance, regarding the above application. Current compatibility measures consider typically (the chromatic information of) edge pixels (between adjacent tiles), and help achieve high accuracy for the synthetic JPP variant. However, such measures exhibit rather poor performance when applied to the Portuguese tile panels, which are susceptible to various real-world effects, e.g., monochromatic panels, non-squared tiles, edge degradation, etc. To overcome such difficulties, we have developed a novel DLCM to extract high-level texture/color statistics from the entire tile information. Integrating this measure with our enhanced GA-based puzzle solver, we have demonstrated, for the first time, how to deal most effectively with large-scale real-world problems, such as the Portuguese tile problem. Specifically, we have achieved 82% accuracy for the reconstruction of Portuguese tile panels with unknown piece rotation and puzzle dimension (compared to merely 3.5% average accuracy achieved by the best method known for solving this problem variant). The proposed method outperforms even human experts in several cases, correcting their mistakes in the manual tile assembly

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 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