Scalable Multi-class Sampling via Filtered Sliced Optimal Transport

Corentin Salaun1, Iliyan Georgiev2, Hans-Peter Seidel1, Gurprit Singh1
1Max Planck Institute for Informatics, Saarbrücken 2Autodesk, United Kingdom
SIGGRAPH Asia 2022 / ACM Transactions on Graphics, Volume 41 issue 6, December 2022
Snow
Demonstration of our multi-class sampling framework on three applications. Left: CMYK color stippling involves optimizing for 15 classes, each following a different, non-uniform density. Middle: 7 colors of trees and their union optimized jointly. Right: Distributing rendering error as blue noise, cast as a multi-class problem (4096 classes), showing improved visual fidelity over traditional uncorrelated-pixel sampling.

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 derive a multi-class error bound for perceptual rendering error which can be minimized using our optimization.

Material

Paper (author version)
Source code

Acknowledgements

We thank all the anonymous reviewers for their helpful comments in shaping the final version of the paper. We thank the following for scenes used in our experiments: julioras3d (chopper-titan), Mikael Hvidtfeldt Christensen (structuresynth), Greyscalegorilla (vw-van) and Eric Veach (Veach-mis). We also thanks Sponchia for the elephants image used in the supplemental.

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