# Edge2Vec: A High Quality Embedding for the Jigsaw Puzzle Problem

arXiv: https://arxiv.org/abs/2211.07771 · HTML: https://mlsanity.com/paper/2211.07771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 14 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [The 2018 PIRM Challenge on Perceptual Image Super-resolution](https://mlsanity.com/paper/1809.07517/) (2018)
- [Solving Jigsaw Puzzles with Eroded Boundaries](https://mlsanity.com/paper/1912.00755/) (2019)
- [A Novel Hybrid Scheme Using Genetic Algorithms and Deep Learning for the Reconstruction of Portuguese Tile Panels](https://mlsanity.com/paper/1912.02707/) (2019)
- [TEN: Twin Embedding Networks for the Jigsaw Puzzle Problem with Eroded Boundaries](https://mlsanity.com/paper/2203.06488/) (2022)

## Built on by (most cited first, 1 of 1)

- [Fix the Match, Not the Solver: STITCH -- a Self-Supervised Compatibility Measure for Eroded Visual Puzzles](https://mlsanity.com/paper/2610.13176/) (2026)

## Abstract (arXiv)

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.