Robust and Accurate Superquadric Recovery: a Probabilistic Approach (2111.14517v3)

Abstract: 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.

Robust and Accurate Superquadric Recovery: A Probabilistic Approach

This paper presents a novel method for recovering superquadrics from 3D point clouds using a probabilistic framework. Superquadrics are a class of geometric primitives characterized by a small set of parameters, capable of representing a wide array of shapes including cuboids, cylinders, and ellipsoids. Although potentially powerful, accurately recovering superquadrics from noisy 3D data remains a challenge due to issues such as sensitivity to initialization and local optima in optimization problems. The authors propose a tangible solution through the development of the Expectation, Maximization, and Switching (EMS) algorithm.

The EMS algorithm tackles superquadric recovery by framing it as a Maximum Likelihood Estimation (MLE) task within a Gaussian-uniform mixture model. Here, Gaussian models reflect inlier points on the superquadric surface while uniform distributions handle outliers and noise. The EMS algorithm comprises three phases: Expectation, Maximization, and geometric Switching, which together form a robust approach capable of surpassing local optima pitfalls. Notably, the approach proves effective in modeling complex shapes that involve multiple superquadrics, pushing the boundaries of expressive, geometric abstraction in various applications.

Key Results and Contributions

• High Accuracy and Robustness: The method outperformed existing state-of-the-art techniques in recovering superquadrics in synthetic and real-world datasets, showing strong resilience against outliers and noise. Quantitatively, the approach achieved lower average point-to-surface errors and faster convergence times.
• Probabilistic Formulation: By establishing a Gaussian-uniform mixture model, the authors deliver a probabilistic framework that captures the relationship between observed data and potential underlying geometric forms, enabling robust recovery even in challenging scenarios with partial data.
• Geometric Switching Strategy: The introduction of geometric switching in the EMS algorithm effectively circumvents local optima by leveraging geometric properties and symmetries inherent in the superquadrics, refining recovery precision.

Implications and Future Directions

The implications of this research span both practical applications and theoretical inquiry. Practically, improved superquadric recovery has immediate benefits for robotics, 3D modeling, and computer-aided design, where accurate shape abstraction is beneficial for object recognition, manipulation, and interaction. Theoretically, the probabilistic framework could catalyze further exploration into geometric primitive recovery, driving advancements in intelligent system design.

Future work could extend the approach to encompass broader classes of volumetric primitives. Researchers might consider incorporating deformation models or exploring the dynamics of hierarchical structure recovery, as hinted at in the paper's discussion of multi-superquadrics. Such advancements could refine interaction models between AI-driven systems and their environments, potentially leading to innovations in automated reasoning and robotic manipulation.

Overall, this paper contributes significantly to the understanding and advancement of geometric primitive recovery in computer vision. The authors provide a compelling approach to tackle long-standing issues in superquadric recovery with the EMS algorithm, setting a precedent for further development in 3D shape representation and abstraction.