# Pictorial and apictorial polygonal jigsaw puzzles from arbitrary number of crossing cuts

arXiv: https://arxiv.org/abs/2008.07644 · HTML: https://mlsanity.com/paper/2008.07644/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

## Built on by (most cited first, 10 of 10)

- [Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving](https://mlsanity.com/paper/2410.24010/) (2024)
- [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)
- [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)
- [ReassembleNet: Learnable Keypoints and Diffusion for 2D Fresco Reconstruction](https://mlsanity.com/paper/2505.21117/) (2025)
- [Solving Convex Partition Visual Jigsaw Puzzles](https://mlsanity.com/paper/2511.04450/) (2025)
- [Benchmarking Content-Based Puzzle Solvers on Corrupted Jigsaw Puzzles](https://mlsanity.com/paper/2507.07828/) (2025)
- [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)

Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered visual fragments, is fundamental to numerous applications, and yet most of the literature of the last two decades has focused thus far on less realistic puzzles whose pieces are identical squares. Here, we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results on both apictorial and pictorial puzzles to show that they are solvable completely automatically.