Abstract
Neural implicit shape representation has drawn significant attention in recent years due to its smoothness, differentiability, and topological flexibility. However, directly modeling the shape of a neural implicit surface, especially as the zero-level set of a neural signed distance function (SDF), with sparse geometric control is still a challenging task. Sparse input shape control typically includes 3D curve networks or, more generally, 3D curve sketches, which are unstructured and cannot be connected to form a curve network, and therefore more difficult to deal with. While 3D curve networks or curve sketches provide intuitive shape control, their sparsity and varied topology pose challenges in generating high-quality surfaces to meet such curve constraints. In this paper, we propose NeuVAS, a variational approach to shape modeling using neural implicit surfaces constrained under sparse input shape control, including unstructured 3D curve sketches as well as connected 3D curve networks. Specifically, we introduce a smoothness term based on a functional of surface curvatures to minimize shape variation of the zero-level set surface of a neural SDF. We also develop a new technique to faithfully model G0 sharp feature curves as specified in the input curve sketches. Comprehensive comparisons with the state-of-the-art methods demonstrate the significant advantages of our method.
Abstract (translated)
近年来，神经隐式形状表示因其平滑性、可微性和拓扑灵活性而备受关注。然而，直接使用稀疏的几何控制来建模神经隐式曲面（尤其是作为神经符号距离函数(SDF)零等值集）的形状仍然是一个具有挑战性的任务。稀疏输入形状控制通常包括3D曲线网络或更一般的3D曲线草图，这些草图是无结构且不能连接成完整的曲线网络，因此更难以处理。虽然3D曲线网络或曲线草图可以提供直观的形状控制，但它们的稀疏性和不同的拓扑结构在生成满足这类曲线约束的高质量表面时带来了挑战。 本文中我们提出了NeuVAS，一种利用神经隐式曲面并受稀疏输入形状控制（包括无结构的3D曲线草图以及连接的3D曲线网络）限制的变分方法来进行形状建模。具体来说，我们引入了一个基于曲率泛函的平滑性项来最小化由神经SDF零等值集表面的形态变化，并且开发了一种新的技术以忠实于输入曲线草图中指定的G0锐利特征曲线进行模型构建。 与最先进的方法相比，我们的方法在综合比较中展示了显著的优势。
URL
https://arxiv.org/abs/2506.13050
