Fast quasi-harmonic weights for geometric data interpolation
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 o...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Association for Computing Machinery (ACM)
2022
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| Online Access: | https://hdl.handle.net/1721.1/143890 |
| _version_ | 1811074433984495616 |
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| author | Wang, Yu Solomon, Justin |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Wang, Yu Solomon, Justin |
| author_sort | Wang, Yu |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:49:24Z |
| format | Article |
| id | mit-1721.1/143890 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:49:24Z |
| publishDate | 2022 |
| publisher | Association for Computing Machinery (ACM) |
| record_format | dspace |
| spelling | mit-1721.1/1438902023-04-14T18:30:47Z Fast quasi-harmonic weights for geometric data interpolation Wang, Yu Solomon, Justin Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory 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. 2022-07-20T15:57:20Z 2022-07-20T15:57:20Z 2021 2022-07-20T15:51:16Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/143890 Wang, Yu and Solomon, Justin. 2021. "Fast quasi-harmonic weights for geometric data interpolation." ACM Transactions on Graphics, 40 (4). en 10.1145/3450626.3459801 ACM Transactions on Graphics Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Association for Computing Machinery (ACM) ACM |
| spellingShingle | Wang, Yu Solomon, Justin Fast quasi-harmonic weights for geometric data interpolation |
| title | Fast quasi-harmonic weights for geometric data interpolation |
| title_full | Fast quasi-harmonic weights for geometric data interpolation |
| title_fullStr | Fast quasi-harmonic weights for geometric data interpolation |
| title_full_unstemmed | Fast quasi-harmonic weights for geometric data interpolation |
| title_short | Fast quasi-harmonic weights for geometric data interpolation |
| title_sort | fast quasi harmonic weights for geometric data interpolation |
| url | https://hdl.handle.net/1721.1/143890 |
| work_keys_str_mv | AT wangyu fastquasiharmonicweightsforgeometricdatainterpolation AT solomonjustin fastquasiharmonicweightsforgeometricdatainterpolation |