RBF 你的 SDF：带隐含切点的符号距离场的径向基函数插值
RBF Your SDF: Radial Basis Function Interpolation of Signed Distance Fields with Implied Tangent Points
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中文总结 AI 辅助
提出一种结合切球观察与径向基函数插值所有数据的方法，通过检测受限切点保留表面角点，利用单位分解扩展至大网格，在多个分辨率下提升重建精度。
中文摘要 AI 辅助
符号距离场（SDF）是一种流行的几何隐式表示。将一组离散的 SDF 样本转换为显式表面是几何处理中的一个基本问题。传统的重建方法，如移动立方体（marching cubes）和双重轮廓法（dual contouring），忽略了远离表面的样本所携带的几何信息。最近，Sellán 等人 [2023] 及若干后续工作利用了 SDF 的切球结构；每个样本都隐含了切于表面的球上的一个点。然而，这些方法通过表面重建来提取零水平集，仅考虑表面上的点和法线，而忽略了其余样本。我们提出了一种方法，将切球观察与所有数据（隐含表面点和原始数据）的径向基函数插值相结合。通过检测具有极度受限切点的球（一种在尖锐表面特征处几何上被迫出现的构型），我们识别并保留了表面重建方法系统性磨圆的表面角点。一种单位分解（partition-of-unity）分解使我们的方法能够高效扩展到大的网格分辨率。我们的重建在每个测试分辨率下都提高了倒角（Chamfer）和豪斯多夫（Hausdorff）精度。
英文摘要
Signed distance fields (SDFs) are a popular implicit representation of geometry. Converting a discrete set of SDF samples into an explicit surface is a fundamental problem in geometry processing. Traditional reconstruction methods such as marching cubes and dual contouring ignore the geometric information carried by samples far from the surface. Recently, Sellán et al.[2023] and several follow-up works leveraged the tangent-sphere structure of SDFs; every sample implies a point on a sphere tangent to the surface. However, these approaches extract the zero-level set via surface reconstruction, which considers only points and normals on the surface and ignores the remaining samples. We propose an approach that marries the tangent-sphere observation with radial basis function interpolation of all data, the implied surface points and the original data. By detecting spheres with extremely constrained tangent points, a configuration geometrically forced at sharp surface features, we identify and preserve surface corners that surface reconstruction-based methods systematically round. A partition-of-unity decomposition allows our method to scale efficiently to large grid resolutions. Our reconstructions improve both Chamfer and Hausdorff accuracy at every tested resolution.
发表机构
- George Mason University（乔治梅森大学）
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