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dc.contributor.authorBonneel, Nicolas
HAL ID: 4159
ORCID: 0000-0001-5243-4810
*
hal.structure.identifier
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
*
hal.structure.identifier
dc.contributor.authorCuturi, Marco
HAL ID: 3354
*
dc.date.accessioned2017-03-15T15:12:09Z
dc.date.available2017-03-15T15:12:09Z
dc.date.issued2016
dc.identifier.issn0730-0301
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16364
dc.descriptionProceedings of ACM SIGGRAPH 2016en
dc.language.isoenen
dc.subjectSinkhorn algorithmen
dc.subjectbarycentric coordinatesen
dc.subjectWasserstein distanceen
dc.subjectoptimal transporten
dc.subjectfittingen
dc.subject.ddc006.3en
dc.titleWasserstein barycentric coordinates: histogram regression using optimal transporten
dc.typeCommunication / Conférence
dc.description.abstractenThis article defines a new way to perform intuitive and geometrically faithful regressions on histogram-valued data. It leverages the theory of optimal transport, and in particular the definition of Wasserstein barycenters, to introduce for the first time the notion of barycentric coordinates for histograms. These coordinates take into account the underlying geometry of the ground space on which the histograms are defined, and are thus particularly meaningful for applications in graphics to shapes, color or material modification. Beside this abstract construction, we propose a fast numerical optimization scheme to solve this backward problem (finding the barycentric coordinates of a given histogram) with a low computational overhead with respect to the forward problem (computing the barycenter). This scheme relies on a backward algorithmic differentiation of the Sinkhorn algorithm which is used to optimize the entropic regularization of Wasserstein barycenters. We showcase an illustrative set of applications of these Wasserstein coordinates to various problems in computer graphics: shape approximation, BRDF acquisition and color editing.en
dc.relation.isversionofjnlnameACM Transactions on Graphics
dc.relation.isversionofjnlvol35en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpagesn°71en
dc.relation.isversionofdoi10.1145/2897824.2925918en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01303148en
dc.relation.isversionofjnlpublisherAssociation for Computing Machineryen
dc.subject.ddclabelIntelligence artificielleen
dc.relation.conftitle43rd international conference and exhibition on Computer Graphics & Interactive Techniques (SIGGRAPH 2016)
dc.relation.confdate2016-07
dc.relation.confcityAnaheim
dc.relation.confcountryEtats-Unis
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-09T14:14:17Z
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