# Robust and Accurate Superquadric Recovery: a Probabilistic Approach

arXiv: https://arxiv.org/abs/2111.14517 · HTML: https://mlsanity.com/paper/2111.14517/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [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)
- [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)
- [Im2Struct: Recovering 3D Shape Structure from a Single RGB Image](https://mlsanity.com/paper/1804.05469/) (2018)
- [Segmentation and Recovery of Superquadric Models using Convolutional Neural Networks](https://mlsanity.com/paper/2001.10504/) (2020)
- [Closed-Form Minkowski Sums of Convex Bodies with Smooth Positively Curved Boundaries](https://mlsanity.com/paper/2012.15461/) (2020)

## Built on by (most cited first, 29 of 29)

- [Part123: Part-aware 3D Reconstruction from a Single-view Image](https://mlsanity.com/paper/2405.16888/) (2024)
- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)
- [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)
- [Primitive-based Shape Abstraction via Nonparametric Bayesian Inference](https://mlsanity.com/paper/2203.14714/) (2022)
- [Iterative Superquadric Recomposition of 3D Objects from Multiple Views](https://mlsanity.com/paper/2309.02102/) (2023)
- [Self-supervised Learning of Hybrid Part-aware 3D Representations of 2D Gaussians and Superquadrics](https://mlsanity.com/paper/2408.10789/) (2024)
- [GaussianBlock: Building Part-Aware Compositional and Editable 3D Scene by Primitives and Gaussians](https://mlsanity.com/paper/2410.01535/) (2024)
- [Learnable Earth Parser: Discovering 3D Prototypes in Aerial Scans](https://mlsanity.com/paper/2304.09704/) (2023)
- [DPA-Net: Structured 3D Abstraction from Sparse Views via Differentiable Primitive Assembly](https://mlsanity.com/paper/2404.00875/) (2024)
- [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)
- [SuperFlex: Deformable Superquadrics for Point Cloud Decomposition](https://mlsanity.com/paper/2607.01015/) (2026)
- [Efficient Representations of Object Geometry for Reinforcement Learning of Interactive Grasping Policies](https://mlsanity.com/paper/2211.10957/) (2022)
- [Aligning Instance-Semantic Sparse Representation towards Unsupervised Object Segmentation and Shape Abstraction with Repeatable Primitives](https://mlsanity.com/paper/2503.06947/) (2025)
- [A Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting](https://mlsanity.com/paper/2407.19269/) (2024)
- [Articulation in Prime: Primitive-Based Articulated Object Understanding from a Single Casual Video](https://mlsanity.com/paper/2605.18645/) (2026)
- [ShapeShift: Superquadric-based Object Pose Estimation for Robotic Grasping](https://mlsanity.com/paper/2304.04861/) (2023)
- [Deep Polycuboid Fitting for Compact 3D Representation of Indoor Scenes](https://mlsanity.com/paper/2503.14912/) (2025)
- [SAR2Struct: Extracting 3D Semantic Structural Representation of Aircraft Targets from Single-View SAR Image](https://mlsanity.com/paper/2506.06757/) (2025)
- [A Multi-Level Similarity Approach for Single-View Object Grasping: Matching, Planning, and Fine-Tuning](https://mlsanity.com/paper/2507.11938/) (2025)
- [A 3D Generation Framework from Cross Modality to Parameterized Primitive](https://mlsanity.com/paper/2510.08656/) (2025)
- [DualPrim: Compact 3D Reconstruction with Positive and Negative Primitives](https://mlsanity.com/paper/2603.16133/) (2026)
- [D-Prism: Differentiable Primitives for Structured Dynamic Modeling](https://mlsanity.com/paper/2604.17082/) (2026)
- [A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2605.16779/) (2026)
- [Rethinking 3D Shape Generation: Diffusion over Superquadrics](https://mlsanity.com/paper/2606.08957/) (2026)
- [Prompting Image Generators for Training-free Primitive Shape Abstraction](https://mlsanity.com/paper/2607.05568/) (2026)
- [Hi-TOPS: Hierarchical Topology-aware Scoring Prior for 3D Part Decomposition](https://mlsanity.com/paper/2608.00767/) (2026)
- [Superquadric Primitive Decomposition of 3D point clouds via Geometric-Aware Inlier Refinement](https://mlsanity.com/paper/2609.35725/) (2026)

## Abstract (arXiv)

Interpreting objects with basic geometric primitives has long been studied in computer vision. Among geometric primitives, superquadrics are well known for their ability to represent a wide range of shapes with few parameters. However, as the first and foremost step, recovering superquadrics accurately and robustly from 3D data still remains challenging. The existing methods are subject to local optima and sensitive to noise and outliers in real-world scenarios, resulting in frequent failure in capturing geometric shapes. In this paper, we propose the first probabilistic method to recover superquadrics from point clouds. Our method builds a Gaussian-uniform mixture model (GUM) on the parametric surface of a superquadric, which explicitly models the generation of outliers and noise. The superquadric recovery is formulated as a Maximum Likelihood Estimation (MLE) problem. We propose an algorithm, Expectation, Maximization, and Switching (EMS), to solve this problem, where: (1) outliers are predicted from the posterior perspective; (2) the superquadric parameter is optimized by the trust-region reflective algorithm; and (3) local optima are avoided by globally searching and switching among parameters encoding similar superquadrics. We show that our method can be extended to the multi-superquadrics recovery for complex objects. The proposed method outperforms the state-of-the-art in terms of accuracy, efficiency, and robustness on both synthetic and real-world datasets. The code is at http://github.com/bmlklwx/EMS-superquadric_fitting.git.