Spectral Affine-Kernel Embeddings
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
In 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.
Description
@article{10.1111:cgf.13250,
journal = {Computer Graphics Forum},
title = {{Spectral Affine-Kernel Embeddings}},
author = {Budninskiy, Max and Liu, Beibei and Tong, Yiying and Desbrun, Mathieu},
year = {2017},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.13250}
}