Fast quasi-harmonic weights for geometric data interpolation
Name
3450626.3459801.pdf
Description
Published version
Size
53.96 MB
Format
Adobe PDF
Checksum (MD5)
e8de48d1728654bb9766ca4e7f872198
Author(s)
Wang, Yu
Solomon, Justin
Date Issued
2021
Journal
ACM Transactions on Graphics
Publisher
Association for Computing Machinery (ACM)
Citation
Wang, Yu and Solomon, Justin. 2021. "Fast quasi-harmonic weights for geometric data interpolation." ACM Transactions on Graphics, 40 (4).
Version
Final published version
Abstract
We propose quasi-harmonic weights for interpolating geometric data, which
are orders of magnitude faster to compute than state-of-the-art. Currently,
interpolation (or, skinning) weights are obtained by solving large-scale
constrained optimization problems with explicit constraints to suppress
oscillative patterns, yielding smooth weights only after a substantial amount
of computation time. As an alternative, our weights are obtained as minima
of an unconstrained problem that can be optimized quickly using straightforward numerical techniques. We consider weights that can be obtained as
solutions to a parameterized family of second-order elliptic partial differential equations. By leveraging the maximum principle and careful parameterization, we pose weight computation as an inverse problem of recovering
optimal anisotropic diffusivity tensors. In addition, we provide a customized
ADAM solver that significantly reduces the number of gradient steps; our
solver only requires inverting tens of linear systems that share the same
sparsity pattern. Overall, our approach achieves orders of magnitude acceleration compared to previous methods, allowing weight computation in
near real-time.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.1145/3450626.3459801
