# Learning Shape Abstractions by Assembling Volumetric Primitives

arXiv: https://arxiv.org/abs/1612.00404 · HTML: https://mlsanity.com/paper/1612.00404/

## Key facts

- Cited by 181 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2016.

## Built on by (most cited first, 30 of 181)

- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenes](https://mlsanity.com/paper/2311.13384/) (2023)
- [ATISS: Autoregressive Transformers for Indoor Scene Synthesis](https://mlsanity.com/paper/2110.03675/) (2021)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [SceneScript: Reconstructing Scenes With An Autoregressive Structured Language Model](https://mlsanity.com/paper/2403.13064/) (2024)
- [Semantic Abstraction: Open-World 3D Scene Understanding from 2D Vision-Language Models](https://mlsanity.com/paper/2207.11514/) (2022)
- [What's in your hands? 3D Reconstruction of Generic Objects in Hands](https://mlsanity.com/paper/2204.07153/) (2022)
- [Real2Code: Reconstruct Articulated Objects via Code Generation](https://mlsanity.com/paper/2406.08474/) (2024)
- [Deep Implicit Moving Least-Squares Functions for 3D Reconstruction](https://mlsanity.com/paper/2103.12266/) (2021)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [LASSIE: Learning Articulated Shapes from Sparse Image Ensemble via 3D Part Discovery](https://mlsanity.com/paper/2207.03434/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [High-fidelity 3D GAN Inversion by Pseudo-multi-view Optimization](https://mlsanity.com/paper/2211.15662/) (2022)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Control-NeRF: Editable Feature Volumes for Scene Rendering and Manipulation](https://mlsanity.com/paper/2204.10850/) (2022)
- [Part123: Part-aware 3D Reconstruction from a Single-view Image](https://mlsanity.com/paper/2405.16888/) (2024)
- [KeypointDeformer: Unsupervised 3D Keypoint Discovery for Shape Control](https://mlsanity.com/paper/2104.11224/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Towards High-Fidelity Single-view Holistic Reconstruction of Indoor Scenes](https://mlsanity.com/paper/2207.08656/) (2022)
- [Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priors](https://mlsanity.com/paper/2205.14886/) (2022)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [ExtrudeNet: Unsupervised Inverse Sketch-and-Extrude for Shape Parsing](https://mlsanity.com/paper/2209.15632/) (2022)
- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)

## Abstract (arXiv)

We present a learning framework for abstracting complex shapes by learning to assemble objects using 3D volumetric primitives. In addition to generating simple and geometrically interpretable explanations of 3D objects, our framework also allows us to automatically discover and exploit consistent structure in the data. We demonstrate that using our method allows predicting shape representations which can be leveraged for obtaining a consistent parsing across the instances of a shape collection and constructing an interpretable shape similarity measure. We also examine applications for image-based prediction as well as shape manipulation.