Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an SDF, traditional isosurfacing methods, such as Marching Cubes and and its variants, are typically used. However, these methods overlook fundamental properties of SDFs, resulting in reconstructions that exhibit severe oversmoothing and feature loss. To address this shortcoming, we propose a novel method based on a key insight: each SDF sample corresponds to a spherical region that must lie fully inside or outside the surface, depending on its sign, and that must be tangent to the surface at some point. Leveraging this understanding, we formulate an energy that gauges the degree of violation of tangency constraints by a proposed surface. We then employ a gradient flow that minimizes our energy, starting from an initial triangle mesh that encapsulates the surface. This algorithm yields superior reconstructions to previous methods, even with sparsely sampled SDFs. Our approach provides a more nuanced understanding of SDFs and offers significant improvements in surface reconstruction.

翻译：[translated abstract in Chinese] 有符号距离场（SDF）是一种广泛使用的隐式曲面表示方法，在计算机图形学、计算机视觉和应用数学中具有广泛应用。为了重建与SDF对应的显式三角形网格曲面，传统等值面提取方法（如Marching Cubes及其变体）通常被采用。然而，这些方法忽略了SDF的基本属性，导致重建结果出现严重的过度平滑和特征丢失问题。为解决这一缺陷，我们提出了一种基于关键洞察的新方法：每个SDF样本对应一个球体区域，该区域必须根据其符号完全位于曲面内部或外部，并且必须在某点与曲面相切。基于这一理解，我们构建了一个能量函数，用于度量候选曲面违反切向约束的程度。随后，我们采用梯度流方法最小化该能量，从包裹曲面的初始三角形网格出发。即使使用稀疏采样的SDF，该算法也能获得优于以往方法的重建结果。我们的方法为理解SDF提供了更细致的视角，并在曲面重建方面实现了显著改进。