Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks
This provides a novel kernel-based method for 3D surface reconstruction, offering improved accuracy and analytical tractability for researchers in computer vision and graphics.
The paper tackles 3D surface reconstruction by introducing Neural Splines, a technique based on random feature kernels from infinitely-wide shallow ReLU networks, achieving state-of-the-art results and outperforming recent neural network methods and Poisson Surface Reconstruction.
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural network-based techniques and widely used Poisson Surface Reconstruction (which, as we demonstrate, can also be viewed as a type of kernel method). Because our approach is based on a simple kernel formulation, it is easy to analyze and can be accelerated by general techniques designed for kernel-based learning. We provide explicit analytical expressions for our kernel and argue that our formulation can be seen as a generalization of cubic spline interpolation to higher dimensions. In particular, the RKHS norm associated with Neural Splines biases toward smooth interpolants.