# Pairwise Alignment & Compatibility for Arbitrarily Irregular Image Fragments

arXiv: https://arxiv.org/abs/2507.09767 · HTML: https://mlsanity.com/paper/2507.09767/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 13 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [PuzzleFusion: Unleashing the Power of Diffusion Models for Spatial Puzzle Solving](https://mlsanity.com/paper/2211.13785/) (2022)
- [Solving Archaeological Puzzles](https://mlsanity.com/paper/1812.10553/) (2018)
- [Solving Jigsaw Puzzles with Eroded Boundaries](https://mlsanity.com/paper/1912.00755/) (2019)
- [Pictorial and apictorial polygonal jigsaw puzzles from arbitrary number of crossing cuts](https://mlsanity.com/paper/2008.07644/) (2020)
- [Multi-Phase Relaxation Labeling for Square Jigsaw Puzzle Solving](https://mlsanity.com/paper/2303.14793/) (2023)
- [Recognizing Artistic Style of Archaeological Image Fragments Using Deep Style Extrapolation](https://mlsanity.com/paper/2501.00836/) (2025)
- [Nash Meets Wertheimer: Using Good Continuation in Jigsaw Puzzles](https://mlsanity.com/paper/2410.16857/) (2024)
- [A Generic Hybrid Framework for 2D Visual Reconstruction](https://mlsanity.com/paper/2501.19325/) (2025)

## Built on by (most cited first, 6 of 6)

- [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)
- [Solving Convex Partition Visual Jigsaw Puzzles](https://mlsanity.com/paper/2511.04450/) (2025)
- [JigSync: Gauge-Resolved Synchronization for Jigsaw Reassembly under Unknown Piece Orientation](https://mlsanity.com/paper/2609.18379/) (2026)
- [An Invariant Tangent-Angle Descriptor and a Band U-Net for 2D Fragment Adjacency Prediction](https://mlsanity.com/paper/2610.09459/) (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)

Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to deal with fragments of realistic geometric properties one encounters in real-life puzzles. And in all other cases, compatibility methods rely strongly on the restricted shapes of the fragments. In this paper, we propose an efficient hybrid (geometric and pictorial) approach for computing the optimal alignment for pairs of fragments, without any assumptions about their shapes, dimensions, or pictorial content. We introduce a new image fragments dataset generated via a novel method for image fragmentation and a formal erosion model that mimics real-world archaeological erosion, along with evaluation metrics for the compatibility task. We then embed our proposed compatibility into an archaeological puzzle-solving framework and demonstrate state-of-the-art neighborhood-level precision and recall on the RePAIR 2D dataset, directly reflecting compatibility performance improvements.