Scalable multi-class sampling via filtered sliced optimal transport

TL;DR

This paper introduces a scalable multi-class sampling method based on filtered sliced optimal transport, enabling efficient handling of numerous objectives for applications like stippling, object placement, and Monte Carlo integration.

Contribution

It presents a novel multi-class point optimization framework using continuous Wasserstein barycenters with a practical optimization scheme for large-scale problems.

Findings

Effective sampling for high-objective scenarios

Reduced perceptual rendering error through optimization

Open-source implementation available

Abstract

We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We demonstrate the effectiveness of our framework on various sampling applications like stippling, object placement, and Monte-Carlo integration. We a derive multi-class error bound for perceptual rendering error which can be minimized using our optimization. We provide source code at https://github.com/iribis/filtered-sliced-optimal-transport.