# A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts

arXiv: https://arxiv.org/abs/2410.14770 · HTML: https://mlsanity.com/paper/2410.14770/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 92 of its 321 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 30 of 92)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence](https://mlsanity.com/paper/2305.15347/) (2023)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Nonlinear 3D Face Morphable Model](https://mlsanity.com/paper/1804.03786/) (2018)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)

## Built on by (most cited first, 9 of 9)

- [GARF: Learning Generalizable 3D Reassembly for Real-World Fractures](https://mlsanity.com/paper/2504.05400/) (2025)
- [Assembler: Scalable 3D Part Assembly via Anchor Point Diffusion](https://mlsanity.com/paper/2506.17074/) (2025)
- [BiAssemble: Learning Collaborative Affordance for Bimanual Geometric Assembly](https://mlsanity.com/paper/2506.06221/) (2025)
- [TORA: Topological Representation Alignment for 3D Shape Assembly](https://mlsanity.com/paper/2604.04050/) (2026)
- [The Missing GAP: From Solving Square Jigsaw Puzzles to Handling Real World Archaeological Fragments](https://mlsanity.com/paper/2605.12077/) (2026)
- [CRAG: Can 3D Generative Models Help 3D Assembly?](https://mlsanity.com/paper/2602.22629/) (2026)
- [SARe: Structure-Aware Generative 3D Fragment Reassembly](https://mlsanity.com/paper/2603.21611/) (2026)
- [An Invariant Tangent-Angle Descriptor and a Band U-Net for 2D Fragment Adjacency Prediction](https://mlsanity.com/paper/2610.09459/) (2026)
- [LLM2R: From Large Language Models to 3D Reassemblers](https://mlsanity.com/paper/2610.18604/) (2026)

## Abstract (arXiv)

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes of individual pieces and establishing matches between different pieces. Many approaches also model priors of the underlying complete object. Existing approaches are tightly connected problems of shape segmentation, shape matching, and learning shape priors. We provide existing algorithms in this context and emphasize their similarities and differences to general-purpose approaches. We also survey the trends from early non-deep learning approaches to more recent deep learning approaches. In addition to algorithms, this survey will also describe existing datasets, open-source software packages, and applications. To the best of our knowledge, this is the first comprehensive survey on this topic in computer graphics.