# JigSync: Gauge-Resolved Synchronization for Jigsaw Reassembly under Unknown Piece Orientation

arXiv: https://arxiv.org/abs/2609.18379 · HTML: https://mlsanity.com/paper/2609.18379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 49 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Iterative Reorganization with Weak Spatial Constraints: Solving Arbitrary Jigsaw Puzzles for Unsupervised Representation Learning](https://mlsanity.com/paper/1812.00329/) (2018)
- [The Met Dataset: Instance-level Recognition for Artworks](https://mlsanity.com/paper/2202.01747/) (2022)
- [Jigsaw-R1: A Study of Rule-based Visual Reinforcement Learning with Jigsaw Puzzles](https://mlsanity.com/paper/2505.23590/) (2025)
- [Masked Jigsaw Puzzle: A Versatile Position Embedding for Vision Transformers](https://mlsanity.com/paper/2205.12551/) (2022)
- [DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly](https://mlsanity.com/paper/2402.19302/) (2024)
- [Tightness of the maximum likelihood semidefinite relaxation for angular synchronization](https://mlsanity.com/paper/1411.3272/) (2014)
- [Jigsaw-ViT: Learning Jigsaw Puzzles in Vision Transformer](https://mlsanity.com/paper/2207.11971/) (2022)
- [Deepzzle: Solving Visual Jigsaw Puzzles with Deep Learning andShortest Path Optimization](https://mlsanity.com/paper/2005.12548/) (2020)
- [Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving](https://mlsanity.com/paper/2410.24010/) (2024)
- [JigsawGAN: Auxiliary Learning for Solving Jigsaw Puzzles with Generative Adversarial Networks](https://mlsanity.com/paper/2101.07555/) (2021)
- [Solving Archaeological Puzzles](https://mlsanity.com/paper/1812.10553/) (2018)
- [Solving Jigsaw Puzzles with Eroded Boundaries](https://mlsanity.com/paper/1912.00755/) (2019)
- [A Genetic Algorithm-Based Solver for Very Large Jigsaw Puzzles](https://mlsanity.com/paper/1711.06769/) (2017)
- [Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers](https://mlsanity.com/paper/2404.07292/) (2024)
- [Solving Jigsaw Puzzles with Linear Programming](https://mlsanity.com/paper/1511.04472/) (2015)
- [Pictorial and apictorial polygonal jigsaw puzzles from arbitrary number of crossing cuts](https://mlsanity.com/paper/2008.07644/) (2020)
- [GANzzle: Reframing jigsaw puzzle solving as a retrieval task using a generative mental image](https://mlsanity.com/paper/2207.05634/) (2022)
- [Jigsaw-Puzzles: From Seeing to Understanding to Reasoning in Vision-Language Models](https://mlsanity.com/paper/2505.20728/) (2025)
- [Multi-Phase Relaxation Labeling for Square Jigsaw Puzzle Solving](https://mlsanity.com/paper/2303.14793/) (2023)
- [DNN-Buddies: A Deep Neural Network-Based Estimation Metric for the Jigsaw Puzzle Problem](https://mlsanity.com/paper/1711.08762/) (2017)
- [Pairwise Alignment & Compatibility for Arbitrarily Irregular Image Fragments](https://mlsanity.com/paper/2507.09767/) (2025)
- [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)
- [TEN: Twin Embedding Networks for the Jigsaw Puzzle Problem with Eroded Boundaries](https://mlsanity.com/paper/2203.06488/) (2022)
- [PuzLM: Solving Jigsaw Puzzles with Sequence-to-Sequence Language Models](https://mlsanity.com/paper/2511.06315/) (2025)
- [The Missing GAP: From Solving Square Jigsaw Puzzles to Handling Real World Archaeological Fragments](https://mlsanity.com/paper/2605.12077/) (2026)

## Abstract (arXiv)

Square jigsaw reassembly requires recovering the spatial arrangement of shuffled fragments from their visual content and pairwise relationships. While recent studies have made substantial progress, existing benchmarks typically assume that all fragments are provided upright, reducing reassembly to a permutation problem. We study the generalized problem in which each fragment may also have gone through an unknown rotation. For this setting we establish a gauge-unobservability theorem: the minimum of the weighted least-squares objective is exactly invariant under a uniform global rotation of arbitrary magnitude, so no residual-based criterion can recover the global orientation. The theorem further identifies how the issue of global orientation can be resolved: an orientation anchor estimated from the content of a single fragment, lying outside its scope, suffices. To address the above, we propose JigSync, which attains 63.8% and 31.8% absolute accuracy (AA) on GAP-3 and GAP-5, respectively, the highest reported on both, while additionally recovering a rotation per piece that neither benchmark requires. We release JigSync, a degradation protocol that sweeps shape, erosion, photometry, grid size, and rotation independently.