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dc.contributor.authorCorman, Etienne
dc.contributor.authorOvsjanikov, Maks
dc.date.accessioned2021-03-11T08:28:09Z
dc.date.available2021-03-11T08:28:09Z
dc.date.issued2019-02-20
dc.identifier.citationCorman, E., & Ovsjanikov, M. (2019). Functional Characterization of Deformation Fields. ACM Transactions on Graphics, 38(1), 1–19. doi:10.1145/3292480
dc.identifier.issn0730-0301
dc.identifier.issn1557-7368
dc.identifier.doi10.1145/3292480
dc.identifier.urihttp://hdl.handle.net/10754/668068
dc.description.abstractIn this article, we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows one to represent a deformation field in a coordinate-free way as a linear operator acting on real-valued functions defined on the shape. Such a representation provides both a way to relate deformation fields to other classical functional operators and enables analysis and processing of deformation fields using standard linear-algebraic tools. This opens the door to a wide variety of applications such as explicitly adding extrinsic information into the computation of functional maps, intrinsic shape symmetrization, joint deformation design through precise control of metric distortion, and coordinate-free deformation transfer without requiring pointwise correspondences. Our method is applicable to both surface and volumetric shape representations and we guarantee the equivalence between the operator-based and standard deformation field representation under mild genericity conditions in the discrete setting. We demonstrate the utility of our approach by comparing it with existing techniques and show how our representation provides a powerful toolbox for a wide variety of challenging problems.
dc.description.sponsorshipParts of this work were supported by a Competitive Research Grant CRG6 2017 3426 from KAUST, a Google Focused Research Award, and the ERC Starting Grant No. 758800 (EXPROTEA).
dc.publisherAssociation for Computing Machinery (ACM)
dc.relation.urlhttps://dl.acm.org/doi/10.1145/3292480
dc.rights© ACM, 2019. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Graphics, {38, 1, (2019-02-20)} http://doi.acm.org/10.1145/3292480
dc.titleFunctional Characterization of Deformation Fields
dc.typeArticle
dc.identifier.journalACM Transactions on Graphics
dc.eprint.versionPost-print
dc.contributor.institutionUniversity of Toronto, Canada
dc.contributor.institutionLIX, École Polytechnique, CNRS, France
dc.identifier.volume38
dc.identifier.issue1
dc.identifier.pages1-19
dc.identifier.arxivid1709.09701
kaust.grant.number2017 3426
dc.identifier.eid2-s2.0-85061256682
kaust.acknowledged.supportUnitCompetitive Research
kaust.acknowledged.supportUnitCRG


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