Uniform Sampling of Surfaces by Casting Rays

2025-06-05

AI Summary

This work addresses the challenge of directly generating uniform surface samples from implicit representations (e.g., signed distance functions). We propose a general surface sampling method based on stochastic ray–surface intersections. First, we establish a rigorous theoretical connection between the distribution of ray intersection points and geometrically uniform surface sampling, guaranteeing uniformity in the sense of surface-area probability measure. Second, we extend the framework to support blue-noise sampling and stratified sampling, while enabling seamless integration with dynamically deforming neural implicit surfaces. Crucially, our method bypasses meshing entirely—ensuring efficiency, mesh-freeness, and differentiability. Experiments demonstrate substantial improvements over state-of-the-art techniques across diverse implicit representations, including neural SDFs and radiance fields. The approach has been successfully deployed in neural implicit deformation modeling and geometric moment estimation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used implicit surfaces. This work studies a simple and general scheme for sampling points on a surface, which is derived from a connection to the intersections of random rays with the surface. Concretely, given a subroutine to cast a ray against a surface and find all intersections, we can use that subroutine to uniformly sample white noise points on the surface. This approach is particularly effective in the context of implicit signed distance functions, where sphere marching allows us to efficiently cast rays and sample points, without needing to extract an intermediate mesh. We analyze the basic method to show that it guarantees uniformity, and find experimentally that it is significantly more efficient than alternative strategies on a variety of representations. Furthermore, we show extensions to blue noise sampling and stratified sampling, and applications to deform neural implicit surfaces as well as moment estimation.

Problem

• Uniformly sample points on implicit surfaces efficiently
• Use random ray intersections for surface sampling
• Extend method to blue noise and stratified sampling

Innovation

• Uniform sampling via random ray casting
• Efficient sphere marching for implicit surfaces
• Extensions to blue noise and stratified sampling