用可参数化球面迭代收缩，从SDF重建连续可微的显式曲面。
Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields
- 以参数化球面为初始形状，通过迭代收缩逼近目标SDF
- 重建结果保持光滑与可微性，适合纹理映射与动画等应用
- 适用于需要精确几何表示的图形学与深度学习任务
我们提出一种新方法，从符号距离场（SDF）重建显式参数化曲面，这是一种广泛使用的3D曲面隐式神经表示（INR）。传统方法如Marching Cubes生成离散网格，会丢失INR的连续性和可微性。我们的方法通过迭代收缩一个参数化初始球面，使其贴合目标SDF形状，全程保持可微性与表面参数化。该特性支持纹理映射、几何处理、动画及有限元分析等下游应用。在ABC数据集的典型几何体和部件上评估，本方法实现具有竞争力的重建质量，保持了对高级计算机图形学与几何深度学习至关重要的平滑性与可微性。
原文摘要 · Abstract (English)
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.
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