# A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis

arXiv: https://arxiv.org/abs/2605.16779 · HTML: https://mlsanity.com/paper/2605.16779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 59 references that are in the map.
- First posted on arXiv 16 May 2026.

## Builds on (most cited first, 15 of 15)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [A Large Dataset of Object Scans](https://mlsanity.com/paper/1602.02481/) (2016)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Robust and Accurate Superquadric Recovery: a Probabilistic Approach](https://mlsanity.com/paper/2111.14517/) (2021)
- [3Doodle: Compact Abstraction of Objects with 3D Strokes](https://mlsanity.com/paper/2402.03690/) (2024)
- [SuperDec: 3D Scene Decomposition with Superquadric Primitives](https://mlsanity.com/paper/2504.00992/) (2025)
- [Joint Alignment of Multiple Point Sets with Batch and Incremental Expectation-Maximization](https://mlsanity.com/paper/1609.01466/) (2016)
- [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)
- [Efficient Path Planning in Narrow Passages for Robots with Ellipsoidal Components](https://mlsanity.com/paper/2104.04658/) (2021)
- [SQ-SLAM: Monocular Semantic SLAM Based on Superquadric Object Representation](https://mlsanity.com/paper/2209.10817/) (2022)
- [Segmentation and Recovery of Superquadric Models using Convolutional Neural Networks](https://mlsanity.com/paper/2001.10504/) (2020)
- [A Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting](https://mlsanity.com/paper/2407.19269/) (2024)

## Abstract (arXiv)

This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively focus on fitting rigid or deformable superquadrics, or suffer from robustness and numerical instability issues, our method redefines the problem from a new unsupervised clustering perspective, enabling the holistic fitting of both rigid and deformable superquadrics within a unified framework. Central to our approach is a stable optimization function inspired by unsupervised clustering analysis, where we formulate the point cloud data and samples from the potential parametric surface as clustering members and centroids, respectively. Then, the clustering process with dynamic updates to centroid locations serves as a direct proxy for optimizing superquadric parameters, establishing a principled link between geometric fitting and clustering dynamics. We further derive the relationship between pairwise computations of clustering centroids and clustering members to orthogonal distances, effectively eliminating the need for the time-consuming surface sampling process. Moreover, our formulation provides closed-form analytical solutions for both the fuzzy membership degree vector and the covariance matrix, ensuring efficient iteration optimization and enabling more effective handling of geometric deformations. In addition, we provide a theoretical certificate of convergence analysis and demonstrate that the clustering-inspired fitting method can escape local minima by inherently increasing the convexity of the objective function. The implementation is publicly available at https://github.com/zikai1/SuperquadricFitting.