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 out-put, 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 lin-ear (PWL) curve representation, enabling a unified strategy for learning all types offree-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 [19]. We show that a sim-ple network based on NerVE can already outperform the previous state-of-the-art methods by a great margin.

Transformer with its underlying attention mechanism and the ability to capture long-range dependencies makes it become a natural choice for unordered point cloud data. However, local regions separated from the general sampling architecture corrupt the structural information of the instances, and the inherent relationships between adjacent local regions lack exploration. In other words, the transformer only focuses on the long-range dependence, while local structural information is still crucial in a transformer-based 3D point cloud model. To enable transformers to incorporate local structural information, we proposed a straightforward solution based on the natural structure of the point clouds to exploit the message passing between neighboring local regions, thus making their representations more comprehensive and discriminative. Concretely, the proposed module, named Local Context Propagation (LCP), is inserted between two transformer layers. It takes advantage of the overlapping points of adjacent local regions (statistically shown to be prevalent) as intermediaries, then re-weighs the features of these shared points from different local regions before passing them to the next layers. Finally, we design a flexible LCPFormer architecture equipped with the LCP module, which is applicable to several different tasks. Experimental results demonstrate that our proposed LCPFormer outperforms various transformer-based methods in benchmarks including 3D shape classification and dense prediction tasks such as 3D object detection and semantic segmentation. Code will be released for reproduction.