Representing complex objects with basic geometric primitives has long been a
topic in computer vision. Primitive-based representations have the merits of
compactness and computational efficiency in higher-level tasks such as physics
simulation, collision checking, and robotic manipulation. Unlike previous works
which extract polygonal meshes from a signed distance function (SDF), in this
paper, we present a novel method, named Marching-Primitives, to obtain a
primitive-based abstraction directly from an SDF. Our method grows geometric
primitives (such as superquadrics) iteratively by analyzing the connectivity of
voxels while marching at different levels of signed distance. For each valid
connected volume of interest, we march on the scope of voxels from which a
primitive is able to be extracted in a probabilistic sense and simultaneously
solve for the parameters of the primitive to capture the underlying local
geometry. We evaluate the performance of our method on both synthetic and
real-world datasets. The results show that the proposed method outperforms the
state-of-the-art in terms of accuracy, and is directly generalizable among
different categories and scales. The code is open-sourced at
this https URL

该论文提出了 Marching-Primitives 方法，通过分析体素的连接性，以及在不同的有符号距离级别上行进，在概率意义下从体素范围上生长几何基元（例如超椭球），并同时解决基元参数问题，以捕捉基本局部几何信息。研究人员在合成数据集和真实世界数据集上评估该方法，结果表明该方法在准确性方面优于现有技术，可在不同类别和尺度之间直接泛化。

从有符号距离函数中抽象出形状

Marching-Primitives: Shape Abstraction from Signed Distance Function

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
this http URL

本文提出了一种用于从点云数据中恢复超椭球体的概率方法，该方法建立了一个高斯均匀混合模型，明确地对噪声与异常值进行建模，并通过最大似然估计问题的期望最大化与切换算法解决了这一问题。我们证明了我们的方法可以扩展到用于恢复复杂物体的多超椭球体，并在综合数据集上的实验中显著优于现有技术。

鲁棒和准确的超立方恢复：一种概率方法

Robust and Accurate Superquadric Recovery: a Probabilistic Approach

Abstracting complex 3D shapes with parsimonious part-based representations
has been a long standing goal in computer vision. This paper presents a
learning-based solution to this problem which goes beyond the traditional 3D
cuboid representation by exploiting superquadrics as atomic elements. We
demonstrate that superquadrics lead to more expressive 3D scene parses while
being easier to learn than 3D cuboid representations. Moreover, we provide an
analytical solution to the Chamfer loss which avoids the need for computational
expensive reinforcement learning or iterative prediction. Our model learns to
parse 3D objects into consistent superquadric representations without
supervision. Results on various ShapeNet categories as well as the SURREAL
human body dataset demonstrate the flexibility of our model in capturing fine
details and complex poses that could not have been modelled using cuboids.

本文提出了一种基于学习的解决方案，将超椭球作为原子元素来代替传统的 3D 长方体表示方法，从而在不需要监督的情况下将三维对象分解成一致的超椭球表示，并能够更易于学习地表达更多细节和复杂姿态。