# Relaxation Labeling Meets GANs: Solving Jigsaw Puzzles with Missing Borders

arXiv: https://arxiv.org/abs/2203.14428 · HTML: https://mlsanity.com/paper/2203.14428/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Free-Form Image Inpainting with Gated Convolution](https://mlsanity.com/paper/1806.03589/) (2018)
- [Boundless: Generative Adversarial Networks for Image Extension](https://mlsanity.com/paper/1908.07007/) (2019)
- [Deepzzle: Solving Visual Jigsaw Puzzles with Deep Learning andShortest Path Optimization](https://mlsanity.com/paper/2005.12548/) (2020)
- [Solving Archaeological Puzzles](https://mlsanity.com/paper/1812.10553/) (2018)
- [Solving Jigsaw Puzzles with Eroded Boundaries](https://mlsanity.com/paper/1912.00755/) (2019)
- [A Generalized Genetic Algorithm-Based Solver for Very Large Jigsaw Puzzles of Complex Types](https://mlsanity.com/paper/1711.06768/) (2017)

## Built on by (most cited first, 2 of 2)

- [ERL-MPP: Evolutionary Reinforcement Learning with Multi-head Puzzle Perception for Solving Large-scale Jigsaw Puzzles of Eroded Gaps](https://mlsanity.com/paper/2504.09608/) (2025)
- [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 proposes JiGAN, a GAN-based method for solving Jigsaw puzzles with eroded or missing borders. Missing borders is a common real-world situation, for example, when dealing with the reconstruction of broken artifacts or ruined frescoes. In this particular condition, the puzzle's pieces do not align perfectly due to the borders' gaps; in this situation, the patches' direct match is unfeasible due to the lack of color and line continuations. JiGAN, is a two-steps procedure that tackles this issue: first, we repair the eroded borders with a GAN-based image extension model and measure the alignment affinity between pieces; then, we solve the puzzle with the relaxation labeling algorithm to enforce consistency in pieces positioning, hence, reconstructing the puzzle. We test the method on a large dataset of small puzzles and on three commonly used benchmark datasets to demonstrate the feasibility of the proposed approach.