# Learning Convex Decomposition via Feature Fields

arXiv: https://arxiv.org/abs/2603.09285 · HTML: https://mlsanity.com/paper/2603.09285/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 62 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 27 of 27)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [SAMPart3D: Segment Any Part in 3D Objects](https://mlsanity.com/paper/2411.07184/) (2024)
- [PARTFIELD: Learning 3D Feature Fields for Part Segmentation and Beyond](https://mlsanity.com/paper/2504.11451/) (2025)
- [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [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)
- [Label-Efficient Learning on Point Clouds using Approximate Convex Decompositions](https://mlsanity.com/paper/2003.13834/) (2020)
- [SuperDec: 3D Scene Decomposition with Superquadric Primitives](https://mlsanity.com/paper/2504.00992/) (2025)
- [Marching-Primitives: Shape Abstraction from Signed Distance Function](https://mlsanity.com/paper/2303.13190/) (2023)
- [Self-supervised Learning of Hybrid Part-aware 3D Representations of 2D Gaussians and Superquadrics](https://mlsanity.com/paper/2408.10789/) (2024)
- [Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes](https://mlsanity.com/paper/2509.24986/) (2025)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [Residual Primitive Fitting of 3D Shapes with SuperFrusta](https://mlsanity.com/paper/2512.09201/) (2025)
- [GenAnalysis: Joint Shape Analysis by Learning Man-Made Shape Generators with Deformation Regularizations](https://mlsanity.com/paper/2503.00807/) (2025)

## Built on by (most cited first, 2 of 2)

- [FACT: Fidelity-Aware Construction of Articulated Twins](https://mlsanity.com/paper/2609.37067/) (2026)
- [I2CD: Direct Image-to-Convex Decomposition for Simulation-Ready Collision Geometry](https://mlsanity.com/paper/2610.03453/) (2026)

## Abstract (arXiv)

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality decompositions of 3D shapes into a union of convex bodies, which are essential to accelerate collision detection in physical simulation, amongst many other applications. The key insight is to adopt a feature learning approach and learn a continuous feature field that can later be clustered to yield a good convex decomposition via our self-supervised, purely-geometric objective derived from the classical definition of convexity. Our formulation can be used for single shape optimization, but more importantly, feature prediction unlocks scalable, self-supervised learning on large datasets resulting in the first learned open-world model for convex decomposition. Experiments show that our decompositions are higher-quality than alternatives and generalize across open-world objects as well as across representations to meshes, CAD models, and even Gaussian splats. https://research.nvidia.com/labs/sil/projects/learning-convex-decomp/