We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

翻译：我们提出了一种从符号距离场（SDF）重建显式参数化曲面的新方法，SDF是三维曲面广泛使用的隐式神经表示（INR）。传统重建方法（如移动立方体法）提取的是离散网格，会丢失INR的连续性和可微性；而我们的方法通过迭代收缩一个参数化的初始球体，使其贴合目标SDF形状，在整个过程中保持了可微性和曲面参数化。这使得下游应用如纹理映射、几何处理、动画和有限元分析成为可能。在典型几何形状和ABC数据集部分模型上的评估表明，我们的方法实现了有竞争力的重建质量，保持了对于高级计算机图形学和几何深度学习应用至关重要的平滑性和可微性。