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.
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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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