  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.
