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dc.contributor.authorWang, Larryen_US
dc.contributor.authorGehre, Anneen_US
dc.contributor.authorBronstein, Michael M.en_US
dc.contributor.authorSolomon, Justinen_US
dc.contributor.editorJu, Tao and Vaxman, Amiren_US
dc.date.accessioned2018-07-27T12:54:30Z
dc.date.available2018-07-27T12:54:30Z
dc.date.issued2018
dc.identifier.issn1467-8659
dc.identifier.urihttps://doi.org/10.1111/cgf.13488
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13488
dc.description.abstractFunctional maps provide a means of extracting correspondences between surfaces using linear-algebraic machinery. While the functional framework suggests efficient algorithms for map computation, the basic technique does not incorporate the intuition that pointwise modifications of a descriptor function (e.g. composition of a descriptor and a nonlinearity) should be preserved under the mapping; the end result is that the basic functional maps problem can be underdetermined without regularization or additional assumptions on the map. In this paper, we show how this problem can be addressed through kernelization, in which descriptors are lifted to higher-dimensional vectors or even infinite-length sequences of values. The key observation is that optimization problems for functional maps only depend on inner products between descriptors rather than descriptor values themselves. These inner products can be evaluated efficiently through use of kernel functions. In addition to deriving a kernelized version of functional maps including a recent extension in terms of pointwise multiplication operators, we provide an efficient conjugate gradient algorithm for optimizing our generalized problem as well as a strategy for low-rank estimation of kernel matrices through the Nyström approximation.en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]
dc.subjectComputer graphics
dc.subjectComputational Geometry and Object Modeling
dc.titleKernel Functional Mapsen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersFunctional Maps
dc.description.volume37
dc.description.number5
dc.identifier.doi10.1111/cgf.13488
dc.identifier.pages27-36


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  • 37-Issue 5
    Geometry Processing 2018 - Symposium Proceedings

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