A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis

2026-05-15

AI Summary

This work addresses the limitations of existing superquadric fitting methods, which often suffer from poor robustness, numerical instability, and an inability to uniformly handle both rigid and deformable cases under noise and outliers. The authors propose an unsupervised clustering framework that treats point cloud data as observations and surface samples as dynamic cluster centers, optimizing superquadric parameters through clustering dynamics. For the first time, this approach unifies the modeling of rigid and deformable superquadrics within a single formulation. By incorporating an orthogonal distance approximation and a fuzzy membership mechanism, the method yields closed-form parameter updates, enhances the convexity of the objective function to avoid local minima, and provides theoretical convergence guarantees. Experiments demonstrate its efficiency and robustness in noisy and outlier-contaminated scenarios, and the implementation is publicly released.

Abstract

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.

Problem

• superquadric fitting
• point cloud
• noise and outliers
• shape modeling
• unsupervised clustering

Innovation

• superquadric fitting
• unsupervised clustering
• geometric modeling
• closed-form solution
• robust optimization