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Pairwise compatibility measure (CM) is a key component in solving the jigsawpuzzle problem (JPP) and many of its recently proposed variants. With the rapidrise of deep neural networks (DNNs), a trade-off between performance (i.e.,accuracy) and computational efficiency has become a very significant issue.Whereas an end-to-end DNN-based CM model exhibits high performance, it becomesvirtually infeasible on very large puzzles, due to its highly intensivecomputation. On the other hand, exploiting the concept of embeddings toalleviate significantly the computational efficiency, has resulted in degradedperformance, according to recent studies. This paper derives an advanced CMmodel (based on modified embeddings and a new loss function, called hard batchtriplet loss) for closing the above gap between speed and accuracy; namely a CMmodel that achieves SOTA results in terms of performance and efficiencycombined. We evaluated our newly derived CM on three commonly used datasets,and obtained a reconstruction improvement of 5.8% and 19.5% for so-calledType-1 and Type-2 problem variants, respectively, compared to best knownresults due to previous CMs.

Edge2Vec: A High Quality Embedding for the Jigsaw Puzzle Problem