Edge2Vec: A High Quality Embedding for the Jigsaw Puzzle Problem

Pairwise compatibility measure (CM) is a key component in solving the jigsaw puzzle problem (JPP) and many of its recently proposed variants. With the rapid rise 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 becomes virtually infeasible on very large puzzles, due to its highly intensive computation. On the other hand, exploiting the concept of embeddings to alleviate significantly the computational efficiency, has resulted in degraded performance, according to recent studies. This paper derives an advanced CM model (based on modified embeddings and a new loss function, called hard batch triplet loss) for closing the above gap between speed and accuracy; namely a CM model that achieves SOTA results in terms of performance and efficiency combined. We evaluated our newly derived CM on three commonly used datasets, and obtained a reconstruction improvement of 5.8% and 19.5% for so-called Type-1 and Type-2 problem variants, respectively, compared to best known results due to previous CMs.