Extracting parametric edge curves from point clouds is a fundamental problem in 3D vision and geometry processing. Existing approaches mainly rely on keypoint detection, a challenging procedure that tends to generate noisy output, making the subsequent edge extraction error-prone. To address this issue, we propose to directly detect structured edges to circumvent the limitations of the previous point-wise methods. We achieve this goal by presenting NerVE, a novel neural volumetric edge representation that can be easily learned through a volumetric learning framework. NerVE can be seamlessly converted to a versatile piece-wise linear (PWL) curve representation, enabling a unified strategy for learning all types of free-form curves. Furthermore, as NerVE encodes rich structural information, we show that edge extraction based on NerVE can be reduced to a simple graph search problem. After converting NerVE to the PWL representation, parametric curves can be obtained via off-the-shelf spline fitting algorithms. We evaluate our method on the challenging ABC dataset. We show that a simple network based on NerVE can already outperform the previous state-of-the-art methods by a great margin. Project page: https://dongdu3.github.io/projects/2023/NerVE/.

翻译：摘要：从点云中提取参数边缘曲线是三维视觉与几何处理中的基本问题。现有方法主要依赖关键点检测，这一过程易产生噪声输出，导致后续边缘提取误差较大。为解决该问题，我们提出直接检测结构化边缘，从而规避以往逐点方法的局限性。通过提出NerVE——一种可经由体积学习框架轻松习得的新型神经体积边缘表示，我们实现了这一目标。NerVE可无缝转换为通用的分段线性曲线表示，为学习所有类型自由曲线提供了统一策略。此外，由于NerVE编码了丰富的结构信息，我们证明基于NerVE的边缘提取可简化为简单的图搜索问题。将NerVE转换为分段线性表示后，可通过现成的样条拟合算法获得参数曲线。我们在具有挑战性的ABC数据集上评估了该方法，结果表明基于NerVE的简易网络已能以显著优势超越先前最先进方法。项目页面：https://dongdu3.github.io/projects/2023/NerVE/。