Matérn Kernels for Tunable Implicit Surface Reconstruction
This work addresses 3D surface reconstruction for computer graphics and vision, offering a tunable and efficient kernel-based method that is incremental but provides practical improvements in speed and simplicity.
The paper tackles implicit surface reconstruction from oriented point clouds by proposing Matérn kernels, which outperform state-of-the-art arc-cosine kernel methods while being easier to implement, faster to compute, and scalable, with the Laplace kernel achieving near state-of-the-art performance in noise-free cases and reducing training time by more than five times.
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.