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Blue noise through optimal transport

de Goes, Fernando and Breeden, Katherine and Ostromoukhov, Victor and Desbrun, Mathieu (2012) Blue noise through optimal transport. ACM Transactions on Graphics, 31 (6). Art. No. 171. ISSN 0730-0301. doi:10.1145/2366145.2366190.

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We present a fast, scalable algorithm to generate high-quality blue noise point distributions of arbitrary density functions. At its core is a novel formulation of the recently-introduced concept of capacity-constrained Voronoi tessellation as an optimal transport problem. This insight leads to a continuous formulation able to enforce the capacity constraints exactly, unlike previous work. We exploit the variational nature of this formulation to design an efficient optimization technique of point distributions via constrained minimization in the space of power diagrams. Our mathematical, algorithmic, and practical contributions lead to high-quality blue noise point sets with improved spectral and spatial properties.

Item Type:Article
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Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2012 ACM. We wish to thank the authors of [Chen et al. 2012] and [Fattal 2011] for providing data for comparisons, and Christian Lessig for proofreading. FdG, KB, and MD also acknowledge the support of NSF grants DGE-1147470 and CCF-1011944 throughout this project.
Funding AgencyGrant Number
Subject Keywords:Blue noise; power diagram; capacity constraints
Issue or Number:6
Record Number:CaltechAUTHORS:20130103-143514090
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Official Citation:de Goes, F., Breeden, K., Ostromoukhov, V., Desbrun, M. 2012. Blue Noise through Optimal Transport. ACM Trans. Graph. 31 6, Article 171 (November 2012), 11 pages. DOI = 10.1145/2366145.2366190
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36154
Deposited By: Tony Diaz
Deposited On:07 Jan 2013 23:20
Last Modified:09 Nov 2021 23:20

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