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.

翻译：在计算机视觉中，用基本几何基元解释对象已被长期研究。在几何基元中，超二次曲面因其能用少量参数表示广泛形状而闻名。然而，作为首要且最关键的一步，从三维数据中准确且鲁棒地恢复超二次曲面仍具挑战性。现有方法易陷入局部最优，并在真实世界场景中对噪声和异常值敏感，导致频繁无法捕捉几何形状。本文提出了首个从点云中恢复超二次曲面的概率方法。该方法在超二次曲面的参数曲面上构建高斯-均匀混合模型（GUM），明确建模异常值和噪声的生成过程。超二次曲面恢复被形式化为最大似然估计（MLE）问题。我们提出了一种名为期望-最大化-切换（EMS）的算法来解决该问题，其中：(1) 从后验角度预测异常值；(2) 通过置信域反射算法优化超二次曲面参数；(3) 通过全局搜索并在编码相似超二次曲面的参数间切换来避免局部最优。我们展示了该方法可扩展至复杂对象的多超二次曲面恢复。所提方法在合成数据集和真实世界数据集上的精度、效率和鲁棒性均优于现有最优技术。代码见 http://github.com/bmlklwx/EMS-superquadric_fitting.git。