With uniformly sampled points, one can also easily perform importance sampling using curvature or other quantities like losses, and construct geometry-aware regularization terms to improve neural implicit optimization. (8/9)

Our white noise samples are also essential for enabling neural implicit deformation as proposed in [Yang et al. 2021]. (7/9)

A uniformly sampled set of points on implicit surfaces enables many downstream applications:

One can take our white noise samples and easily subsample to blue noise samples. (6/9)

More specifically, sampling on extracted meshes from isosurfacing algorithms like Marching Cubes requires expensive evaluation to a grid and easily aliases thin structures, while our method is both efficient and accurate. (5/9)

Our method is more efficient than the common alternatives: rejection sampling, sampling on extracted meshes via Marching Cubes, and a principled sampling algorithm using Markov chain Monte Carlo (e.g., Hamiltonian Monte Carlo). (4/9)

Our method exploits a classic mathematical relationship: to sample a point set, gather all intersections of randomly-cast rays against the surface — and intersecting rays with implicit surfaces is easy! (3/9)

Our #SGP25 work studies a simple and effective way to uniformly sample implicit surfaces by casting rays. (1/9)

“Uniform Sampling of Surfaces by Casting Rays” w/ @abhishekmadan.bsky.social @nmwsharp.bsky.social and Alec Jacobson