# Learning elementary structures for 3D shape generation and matching

arXiv: https://arxiv.org/abs/1908.04725 · HTML: https://mlsanity.com/paper/1908.04725/

## Key facts

- Cited by 98 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 13 Aug 2019.

## Built on by (most cited first, 30 of 98)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [The Power of Points for Modeling Humans in Clothing](https://mlsanity.com/paper/2109.01137/) (2021)
- [SCALE: Modeling Clothed Humans with a Surface Codec of Articulated Local Elements](https://mlsanity.com/paper/2104.07660/) (2021)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Learning Implicit Templates for Point-Based Clothed Human Modeling](https://mlsanity.com/paper/2207.06955/) (2022)
- [Towards High-Fidelity Single-view Holistic Reconstruction of Indoor Scenes](https://mlsanity.com/paper/2207.08656/) (2022)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Learned Vertex Descent: A New Direction for 3D Human Model Fitting](https://mlsanity.com/paper/2205.06254/) (2022)
- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)
- [PartNeRF: Generating Part-Aware Editable 3D Shapes without 3D Supervision](https://mlsanity.com/paper/2303.09554/) (2023)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes](https://mlsanity.com/paper/2201.07788/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow](https://mlsanity.com/paper/2211.14020/) (2022)
- [OctField: Hierarchical Implicit Functions for 3D Modeling](https://mlsanity.com/paper/2111.01067/) (2021)
- [Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Space](https://mlsanity.com/paper/2207.04161/) (2022)
- [Learning 3D Dense Correspondence via Canonical Point Autoencoder](https://mlsanity.com/paper/2107.04867/) (2021)
- [CloSET: Modeling Clothed Humans on Continuous Surface with Explicit Template Decomposition](https://mlsanity.com/paper/2304.03167/) (2023)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis](https://mlsanity.com/paper/2212.08892/) (2022)
- [SE-ORNet: Self-Ensembling Orientation-aware Network for Unsupervised Point Cloud Shape Correspondence](https://mlsanity.com/paper/2304.05395/) (2023)
- [NeuForm: Adaptive Overfitting for Neural Shape Editing](https://mlsanity.com/paper/2207.08890/) (2022)
- [Shape-Pose Disentanglement using SE(3)-equivariant Vector Neurons](https://mlsanity.com/paper/2204.01159/) (2022)

## Abstract (arXiv)

We propose to represent shapes as the deformation and combination of learnable elementary 3D structures, which are primitives resulting from training over a collection of shape. We demonstrate that the learned elementary 3D structures lead to clear improvements in 3D shape generation and matching. More precisely, we present two complementary approaches for learning elementary structures: (i) patch deformation learning and (ii) point translation learning. Both approaches can be extended to abstract structures of higher dimensions for improved results. We evaluate our method on two tasks: reconstructing ShapeNet objects and estimating dense correspondences between human scans (FAUST inter challenge). We show 16% improvement over surface deformation approaches for shape reconstruction and outperform FAUST inter challenge state of the art by 6%.