Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the parameters for accurate and robust reconstructions remains a challenge, especially when the input data is noisy or incomplete. In this work, we develop a hybrid neural surface representation that allows us to impose geometry-aware sampling and regularization, which significantly improves the fidelity of reconstructions. We propose to use \emph{iso-points} as an explicit representation for a neural implicit function. These points are computed and updated on-the-fly during training to capture important geometric features and impose geometric constraints on the optimization. We demonstrate that our method can be adopted to improve state-of-the-art techniques for reconstructing neural implicit surfaces from multi-view images or point clouds. Quantitative and qualitative evaluations show that, compared with existing sampling and optimization methods, our approach allows faster convergence, better generalization, and accurate recovery of details and topology.

本文提出了一种用于改进神经隐函数 3D 表示中采样和正则化的混合模型，利用 iso-points 作为神经隐函数的显式表示，使训练时能够实时计算并更新采样点，以捕获重要的几何特征和优化几何约束，提高重建质量和拓扑准确性。实验结果表明，相比现有方法，该方法可以更快地收敛、更好地泛化、更准确地恢复细节和拓扑结构。

Iso-Points: 用混合表征优化神经隐式曲面