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

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