Spectral Affine-Kernel Embeddings

dc.contributor.authorBudninskiy, Maxen_US
dc.contributor.authorLiu, Beibeien_US
dc.contributor.authorTong, Yiyingen_US
dc.contributor.authorDesbrun, Mathieuen_US
dc.contributor.editorBærentzen, Jakob Andreas and Hildebrandt, Klausen_US
dc.date.accessioned2017-07-02T17:37:52Z
dc.date.available2017-07-02T17:37:52Z
dc.date.issued2017
dc.description.abstractIn this paper, we propose a controllable embedding method for high- and low-dimensional geometry processing through sparse matrix eigenanalysis. Our approach is equally suitable to perform non-linear dimensionality reduction on big data, or to offer non-linear shape editing of 3D meshes and pointsets. At the core of our approach is the construction of a multi-Laplacian quadratic form that is assembled from local operators whose kernels only contain locally-affine functions. Minimizing this quadratic form provides an embedding that best preserves all relative coordinates of points within their local neighborhoods. We demonstrate the improvements that our approach brings over existing nonlinear dimensionality reduction methods on a number of datasets, and formulate the first eigen-based as-rigid-as-possible shape deformation technique by applying our affine-kernel embedding approach to 3D data augmented with user-imposed constraints on select vertices.en_US
dc.description.number5
dc.description.sectionheadersSpectra and Kernels
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13250
dc.identifier.issn1467-8659
dc.identifier.pages117-129
dc.identifier.urihttps://doi.org/10.1111/cgf.13250
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13250
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleSpectral Affine-Kernel Embeddingsen_US
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