VKSR: Scalable Kernel Surface Reconstruction Using Vecchia's Approximation

We propose Vecchia Kernel Surface Reconstruction (VKSR),an accurate implicit surface reconstruction method that efficiently scalesrecent kernel-based techniques to large point clouds with millions ofpoints. While existing (global) kernel methods work well in a sparsesetting, due to low-rank approximations, performance degrades quicklywhen presented with dense point clouds sampled from surfaces with highgeometric complexity or large-scale inputs with millions of points. Toovercome this limitation and inspired by the Gaussian Process litera-ture, VKSR uses Vecchia’s approximation instead of low-rank approx-imations, which naturally shifts computation from a global to a locallevel and allows reconstructing 14M+ points in minutes. VKSR achievesstate-of-the-art results on several challenging datasets while retainingkernel methods’ favorable properties when reconstructing sparse inputs.