Compression of Currents and Varifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915868694282240 |
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| author | Paul, Allen Campbell, Neill Shardlow, Tony |
| author_facet | Paul, Allen Campbell, Neill Shardlow, Tony |
| contents | We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster than existing compression techniques and comes with theoretical guarantees on the rate of decay of the compression error as a function of the smoothness of the associated shape representation. The obtained compressions are shown to be useful for accelerating downstream tasks such as nonlinear shape registration in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework without loss of quality, even for very high compression ratios. The performance of our algorithm is demonstrated on large-scale shape data from modern geometry processing datasets, and is shown to be fast and scalable with rapid error decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compression of Currents and Varifolds Paul, Allen Campbell, Neill Shardlow, Tony Numerical Analysis 65D18, 65D15, 68W20, 68W25 We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster than existing compression techniques and comes with theoretical guarantees on the rate of decay of the compression error as a function of the smoothness of the associated shape representation. The obtained compressions are shown to be useful for accelerating downstream tasks such as nonlinear shape registration in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework without loss of quality, even for very high compression ratios. The performance of our algorithm is demonstrated on large-scale shape data from modern geometry processing datasets, and is shown to be fast and scalable with rapid error decay. |
| title | Compression of Currents and Varifolds |
| topic | Numerical Analysis 65D18, 65D15, 68W20, 68W25 |
| url | https://arxiv.org/abs/2406.09932 |