Superquadric Primitive Decomposition of 3D point clouds via Geometric-Aware Inlier Refinement

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.

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.

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete observations of the underlying scene geometry. This makes reliable geometric reasoning challenging and degrades downstream perception performance. Existing approaches attempt to compensate for these limitations by estimating local geometry, but often rely on hand-crafted statistics or end-to-end supervised learning, which can suffer from limited scalability or require large amounts of accurately labeled data. To address these challenges, we explicitly model point cloud geometry under a principled mathematical formulation. We represent local geometry as a statistical manifold induced by a family of Gaussian distributions, where each point is associated with a Gaussian capturing its local geometric structure. Based on this formulation, we introduce Point-to-Ellipsoid (POLI), a deep neural estimator that predicts per-point Gaussian geometry. POLI learns a mapping from point cloud observations to their underlying geometry in a self-supervised manner, removing the need for labeled data while preserving strong geometric inductive biases. The resulting representation integrates seamlessly into existing robotic perception pipelines without architectural modifications. Extensive experiments show that POLI enables accurate and robust geometry estimation and consistently improves performance across diverse robotic perception tasks.