Neural Fields as Learnable Kernels for 3D Reconstruction

TL;DR

Neural Kernel Fields introduce a new approach combining neural networks and kernel ridge regression for accurate 3D shape reconstruction from sparse data, excelling in generalization and detail preservation.

Contribution

The paper presents Neural Kernel Fields, a novel method that integrates learned kernels with neural networks for improved 3D shape reconstruction, especially from sparse data.

Findings

Achieves state-of-the-art results on 3D reconstruction tasks.

Generalizes well to unseen shape categories and scenes.

Maintains interpolatory behavior with increasing data density.

Abstract

We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse oriented points, and can reconstruct shape categories outside the training set with almost no drop in accuracy. The core insight of our approach is that kernel methods are extremely effective for reconstructing shapes when the chosen kernel has an appropriate inductive bias. We thus factor the problem of shape reconstruction into two parts: (1) a backbone neural network which learns kernel parameters from data, and (2) a kernel ridge regression that fits the input points on-the-fly by solving a simple positive definite linear system using the learned kernel. As a result of this factorization, our reconstruction gains the benefits of data-driven methods under sparse point density while maintaining interpolatory behavior, which converges to the ground truth shape as input sampling density increases. Our experiments demonstrate a strong generalization capability to objects outside the train-set category and scanned scenes. Source code and pretrained models are available at https://nv-tlabs.github.io/nkf.