  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/.
