A Holistic Method for Superquadric Fitting Using Unsupervised Clustering Analysis.

Area of Science:

• Computer Vision
• Geometric Modeling
• Machine Learning

Background:

• Superquadric fitting is crucial for shape modeling but challenged by noise and outliers.
• Existing methods often struggle with robustness, numerical stability, or fitting both rigid and deformable superquadrics.

Purpose of the Study:

• To develop a novel, robust, and stable method for fitting superquadrics to noisy point clouds.
• To unify the fitting of rigid and deformable superquadrics within a single framework.
• To improve accuracy and avoid local minima in superquadric fitting.

Main Methods:

• A new unsupervised clustering perspective is employed, treating point cloud data and surface samples as clustering members and centroids.
• A stable optimization function inspired by clustering analysis dynamically updates centroid locations to optimize superquadric parameters.
• Closed-form analytical solutions for fuzzy membership and covariance matrices ensure efficient optimization and handling of deformations.

Main Results:

• The method demonstrates superior accuracy, robustness, and stability compared to state-of-the-art approaches.
• It effectively avoids convergence to local minima, achieving smaller point-to-surface distances, especially for tapered shapes.
• Experimental results validate improvements in fitting noisy and outlier-contaminated point clouds.

Conclusions:

• The proposed clustering-inspired method offers a principled and efficient approach to superquadric fitting.
• It successfully addresses limitations of prior methods, providing a unified framework for diverse superquadric fitting tasks.
• The method's versatility is shown in applications like multiple superquadric representation, geometry editing, and medical modeling.