This paper presents a novel framework to learn a concise geometric primitive representation for 3D point clouds. Different from representing each type of primitive individually, we focus on the challenging problem of how to achieve a concise and uniform representation robustly. We employ quadrics to represent diverse primitives with only 10 parameters and propose the first end-to-end learning-based framework, namely QuadricsNet, to parse quadrics in point clouds. The relationships between quadrics mathematical formulation and geometric attributes, including the type, scale and pose, are insightfully integrated for effective supervision of QuaidricsNet. Besides, a novel pattern-comprehensive dataset with quadrics segments and objects is collected for training and evaluation. Experiments demonstrate the effectiveness of our concise representation and the robustness of QuadricsNet. Our code is available at \url{https://github.com/MichaelWu99-lab/QuadricsNet}

翻译：本文提出了一种新颖框架，用于学习三维点云中简洁的几何基元表示。与传统方法分别表示每种基元类型不同，本文聚焦于如何鲁棒地实现统一且简洁表示这一挑战性问题。我们采用二次曲面（quadrics）表示多种基元，仅需10个参数，并提出了首个端到端学习框架QuadricsNet，用于解析点云中的二次曲面。该框架洞悉地整合了二次曲面数学表达与几何属性（包括类型、尺度与位姿）之间的关系，从而实现对QuadricsNet的有效监督。此外，我们构建了一个包含二次曲面片段与物体的全新模式综合数据集，用于训练与评估。实验结果表明，本研究的简洁表示方法及QuadricsNet均具有有效性与鲁棒性。本代码开源地址为：\url{https://github.com/MichaelWu99-lab/QuadricsNet}