Spoke-Darts for High-Dimensional Blue-Noise Sampling

TL;DR

This paper introduces spoke-dart sampling, a high-dimensional blue noise sampling technique that combines advantages of existing methods, with proven properties and applications in graphics, optimization, and robotics.

Contribution

We propose a novel high-dimensional blue noise sampling method, spoke-dart, with theoretical guarantees and broad applicability in graphics and robotics.

Findings

Sampling is saturated with high probability.

Bounds on distances between samples and domain points.

Effective in applications like Delaunay graph construction and motion planning.

Abstract

Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution and the adaptability of the intermediate processes of our method are useful in these applications.