# SuperFlex: Deformable Superquadrics for Point Cloud Decomposition

arXiv: https://arxiv.org/abs/2607.01015 · HTML: https://mlsanity.com/paper/2607.01015/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [ABO: Dataset and Benchmarks for Real-World 3D Object Understanding](https://mlsanity.com/paper/2110.06199/) (2021)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Details](https://mlsanity.com/paper/2507.02546/) (2025)
- [SAM 3D: 3Dfy Anything in Images](https://mlsanity.com/paper/2511.16624/) (2025)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Aria Digital Twin: A New Benchmark Dataset for Egocentric 3D Machine Perception](https://mlsanity.com/paper/2306.06362/) (2023)
- [Omni3D: A Large Benchmark and Model for 3D Object Detection in the Wild](https://mlsanity.com/paper/2207.10660/) (2022)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [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)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [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)
- [Robust and Accurate Superquadric Recovery: a Probabilistic Approach](https://mlsanity.com/paper/2111.14517/) (2021)
- [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)
- [SpaceControl: Introducing Test-Time Spatial Control to 3D Generative Modeling](https://mlsanity.com/paper/2512.05343/) (2025)
- [Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes](https://mlsanity.com/paper/2509.24986/) (2025)
- [Residual Primitive Fitting of 3D Shapes with SuperFrusta](https://mlsanity.com/paper/2512.09201/) (2025)
- [Prox-E: Fine-Grained 3D Shape Editing via Primitive-Based Abstractions](https://mlsanity.com/paper/2604.23774/) (2026)
- [SQ-CBF: Signed Distance Functions for Reliable Superquadric-Based Safety Filtering](https://mlsanity.com/paper/2602.11049/) (2026)

## Built on by (most cited first, 3 of 3)

- [Prompting Image Generators for Training-free Primitive Shape Abstraction](https://mlsanity.com/paper/2607.05568/) (2026)
- [An overview of 3D Vision-Language Models](https://mlsanity.com/paper/2609.05583/) (2026)
- [FACT: Fidelity-Aware Construction of Articulated Twins](https://mlsanity.com/paper/2609.37067/) (2026)

## Abstract (arXiv)

Superquadrics have proven to provide a compact, geometrically meaningful representation for 3D objects. However, existing methods suffer from limited reconstruction accuracy, are restricted to rigid primitives, and lack robustness to partial point clouds. In this work, we present SuperFlex, an enhanced framework that expands the expressive power and applicability of superquadric decompositions. First, we introduce a novel loss formulation which significantly improves reconstruction accuracy. Second, we include bending and tapering deformations, enabling high-fidelity representation of curved and asymmetric geometries. Finally, we leverage these high-quality decompositions as supervision to train a model that is robust to partial real-world point clouds. Experiments demonstrate substantial improvements in reconstruction accuracy over both optimization- and learning-based baselines while maintaining a highly compact primitive representation.