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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. https://resolver.caltech.edu/CaltechAUTHORS:20130103-143514090

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Abstract

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2366145.2366190 DOIUNSPECIFIED
http://dl.acm.org/citation.cfm?doid=2366145.2366190PublisherUNSPECIFIED
ORCID:
AuthorORCID
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.
Funders:
Funding AgencyGrant Number
NSFDGE-1147470
NSFCCF-1011944
Subject Keywords:Blue noise; power diagram; capacity constraints
Issue or Number:6
DOI:10.1145/2366145.2366190
Record Number:CaltechAUTHORS:20130103-143514090
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130103-143514090
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 http://doi.acm.org/10.1145/2366145.2366190
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36154
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Jan 2013 23:20
Last Modified:09 Nov 2021 23:20

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