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 https://github.com/ChirikjianLab/Marching-Primitives.git.

翻译：用基本几何基元表示复杂物体一直是计算机视觉领域的研究课题。基于基元的表示在高层次任务（如物理模拟、碰撞检测和机器人操作）中具有紧凑性和计算效率的优势。与以往从符号距离函数（SDF）提取多边形网格的方法不同，本文提出了一种名为Marching-Primitives的新方法，可直接从SDF获得基于基元的抽象表示。该方法通过分析体素在符号距离不同层级行进时的连通性，迭代生成几何基元（如超二次曲面）。针对每个有效的感兴趣连通体，我们在可概率性提取基元的体素范围内行进，同时求解基元参数以捕捉局部几何特征。我们在合成数据集和真实数据集上评估了该方法的性能。结果表明，所提方法在精度上优于现有最新技术，并可直接泛化至不同类别和尺度。代码已在 https://github.com/ChirikjianLab/Marching-Primitives.git 开源。