用马特恩核实现可调的隐式表面重建，更快更准还易用。
Matérn Kernels for Tunable Implicit Surface Reconstruction
- 采用马特恩核替代传统弧余弦核，提升表面重建精度。
- 无噪声情况下性能接近顶尖方法，训练速度提升五倍以上。
- 适合需要快速高效重建的3D建模与几何学习场景。
我们提出使用马特恩核族进行隐式表面重建，基于核方法在有向点云三维重建中的最新成功。从理论和实践角度分析表明，马特恩核具备优越特性，不仅优于基于弧余弦核的现有方法，且实现更简单、计算更快、更具可扩展性。由于其平稳性，马特恩核能像傅里叶特征映射一样实现可调表面重建，克服坐标基MLP的频谱偏差问题。我们进一步理论分析了其与SIREN网络及先前使用的弧余弦核的关系。基于近期提出的神经核场，我们引入数据依赖型马特恩核，发现其中的拉普拉斯核（属于马特恩族）表现极为出色：在无噪声情况下性能几乎与最先进方法相当，训练时间却缩短超过五倍。
原文摘要 · Abstract (English)
We propose to use the family of Matérn kernels for implicit surface reconstruction, building upon the recent success of kernel methods for 3D reconstruction of oriented point clouds. As we show from a theoretical and practical perspective, Matérn kernels have some appealing properties which make them particularly well suited for surface reconstruction -- outperforming state-of-the-art methods based on the arc-cosine kernel while being significantly easier to implement, faster to compute, and scalable. Being stationary, we demonstrate that Matérn kernels allow for tunable surface reconstruction in the same way as Fourier feature mappings help coordinate-based MLPs overcome spectral bias. Moreover, we theoretically analyze Matérn kernels' connection to SIREN networks as well as their relation to previously employed arc-cosine kernels. Finally, based on recently introduced Neural Kernel Fields, we present data-dependent Matérn kernels and conclude that especially the Laplace kernel (being part of the Matérn family) is extremely competitive, performing almost on par with state-of-the-art methods in the noise-free case while having a more than five times shorter training time.
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