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Extracting parametric edge curves from point clouds is a fundamental problemin 3D vision and geometry processing. Existing approaches mainly rely onkeypoint detection, a challenging procedure that tends to generate noisyoutput, making the subsequent edge extraction error-prone. To address thisissue, we propose to directly detect structured edges to circumvent thelimitations of the previous point-wise methods. We achieve this goal bypresenting NerVE, a novel neural volumetric edge representation that can beeasily learned through a volumetric learning framework. NerVE can be seamlesslyconverted to a versatile piece-wise linear (PWL) curve representation, enablinga unified strategy for learning all types of free-form curves. Furthermore, asNerVE encodes rich structural information, we show that edge extraction basedon NerVE can be reduced to a simple graph search problem. After convertingNerVE to the PWL representation, parametric curves can be obtained viaoff-the-shelf spline fitting algorithms. We evaluate our method on thechallenging ABC dataset. We show that a simple network based on NerVE canalready outperform the previous state-of-the-art methods by a great margin.Project page: https://dongdu3.github.io/projects/2023/NerVE/.

NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud