# DeepMend: Learning Occupancy Functions to Represent Shape for Repair

arXiv: https://arxiv.org/abs/2210.05728 · HTML: https://mlsanity.com/paper/2210.05728/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 63 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 30 of 42)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [Complete & Label: A Domain Adaptation Approach to Semantic Segmentation of LiDAR Point Clouds](https://mlsanity.com/paper/2007.08488/) (2020)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans](https://mlsanity.com/paper/1712.10215/) (2017)
- [High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference](https://mlsanity.com/paper/1709.07599/) (2017)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations](https://mlsanity.com/paper/2008.01639/) (2020)
- [SG-NN: Sparse Generative Neural Networks for Self-Supervised Scene Completion of RGB-D Scans](https://mlsanity.com/paper/1912.00036/) (2019)
- [SDF-SRN: Learning Signed Distance 3D Object Reconstruction from Static Images](https://mlsanity.com/paper/2010.10505/) (2020)
- [Improved Adversarial Systems for 3D Object Generation and Reconstruction](https://mlsanity.com/paper/1707.09557/) (2017)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [RL-GAN-Net: A Reinforcement Learning Agent Controlled GAN Network for Real-Time Point Cloud Shape Completion](https://mlsanity.com/paper/1904.12304/) (2019)

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

- [Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving](https://mlsanity.com/paper/2410.24010/) (2024)
- [Fantastic Breaks: A Dataset of Paired 3D Scans of Real-World Broken Objects and Their Complete Counterparts](https://mlsanity.com/paper/2303.14152/) (2023)
- [Cultural Heritage 3D Reconstruction with Diffusion Networks](https://mlsanity.com/paper/2410.10927/) (2024)
- [Occupancy-Based Dual Contouring](https://mlsanity.com/paper/2409.13418/) (2024)
- [Pix2Repair: Implicit Shape Restoration from Images](https://mlsanity.com/paper/2305.18273/) (2023)
- [3D Shape Completion with Test-Time Training](https://mlsanity.com/paper/2410.18668/) (2024)

## Abstract (arXiv)

We present DeepMend, a novel approach to reconstruct restorations to fractured shapes using learned occupancy functions. Existing shape repair approaches predict low-resolution voxelized restorations, or require symmetries or access to a pre-existing complete oracle. We represent the occupancy of a fractured shape as the conjunction of the occupancy of an underlying complete shape and the fracture surface, which we model as functions of latent codes using neural networks. Given occupancy samples from an input fractured shape, we estimate latent codes using an inference loss augmented with novel penalty terms that avoid empty or voluminous restorations. We use inferred codes to reconstruct the restoration shape. We show results with simulated fractures on synthetic and real-world scanned objects, and with scanned real fractured mugs. Compared to the existing voxel approach and two baseline methods, our work shows state-of-the-art results in accuracy and avoiding restoration artifacts over non-fracture regions of the fractured shape.