# TEN: Twin Embedding Networks for the Jigsaw Puzzle Problem with Eroded Boundaries

arXiv: https://arxiv.org/abs/2203.06488 · HTML: https://mlsanity.com/paper/2203.06488/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 12 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [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)
- [Deepzzle: Solving Visual Jigsaw Puzzles with Deep Learning andShortest Path Optimization](https://mlsanity.com/paper/2005.12548/) (2020)
- [JigsawGAN: Auxiliary Learning for Solving Jigsaw Puzzles with Generative Adversarial Networks](https://mlsanity.com/paper/2101.07555/) (2021)
- [Solving Jigsaw Puzzles with Eroded Boundaries](https://mlsanity.com/paper/1912.00755/) (2019)
- [Solving Jigsaw Puzzles with Linear Programming](https://mlsanity.com/paper/1511.04472/) (2015)
- [A Novel Hybrid Scheme Using Genetic Algorithms and Deep Learning for the Reconstruction of Portuguese Tile Panels](https://mlsanity.com/paper/1912.02707/) (2019)

## Built on by (most cited first, 4 of 4)

- [The Missing GAP: From Solving Square Jigsaw Puzzles to Handling Real World Archaeological Fragments](https://mlsanity.com/paper/2605.12077/) (2026)
- [Edge2Vec: A High Quality Embedding for the Jigsaw Puzzle Problem](https://mlsanity.com/paper/2211.07771/) (2022)
- [JigSync: Gauge-Resolved Synchronization for Jigsaw Reassembly under Unknown Piece Orientation](https://mlsanity.com/paper/2609.18379/) (2026)
- [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)

This paper introduces the novel CNN-based encoder Twin Embedding Network (TEN), for the jigsaw puzzle problem (JPP), which represents a puzzle piece with respect to its boundary in a latent embedding space. Combining this latent representation with a simple distance measure, we demonstrate improved accuracy levels of our newly proposed pairwise compatibility measure (CM), compared to that of various classical methods, for degraded puzzles with eroded tile boundaries. We focus on this problem instance for our case study, as it serves as an appropriate testbed for real-world scenarios. Specifically, we demonstrated an improvement of up to 8.5% and 16.8% in reconstruction accuracy, for so-called Type-1 and Type-2 problem variants, respectively. Furthermore, we also demonstrated that TEN is faster by a few orders of magnitude, on average, than a typical deep neural network (NN) model, i.e., it is as fast as the classical methods. In this regard, the paper makes a significant first attempt at bridging the gap between the relatively low accuracy (of classical methods and the intensive computational complexity (of NN models), for practical, real-world puzzle-like problems.