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
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.


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.


Paper (author version) / Source code / fast-forward video / summary video / talk video


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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