Neural Field Convolutions by Repeated Differentiation
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914741404827648 |
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| author | Nsampi, Ntumba Elie Djeacoumar, Adarsh Seidel, Hans-Peter Ritschel, Tobias Leimkühler, Thomas |
| author_facet | Nsampi, Ntumba Elie Djeacoumar, Adarsh Seidel, Hans-Peter Ritschel, Tobias Leimkühler, Thomas |
| contents | Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to perform general continuous convolutions with general continuous signals such as neural fields. Observing that piecewise polynomial kernels reduce to a sparse set of Dirac deltas after repeated differentiation, we leverage convolution identities and train a repeated integral field to efficiently execute large-scale convolutions. We demonstrate our approach on a variety of data modalities and spatially-varying kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neural Field Convolutions by Repeated Differentiation Nsampi, Ntumba Elie Djeacoumar, Adarsh Seidel, Hans-Peter Ritschel, Tobias Leimkühler, Thomas Computer Vision and Pattern Recognition Graphics Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to perform general continuous convolutions with general continuous signals such as neural fields. Observing that piecewise polynomial kernels reduce to a sparse set of Dirac deltas after repeated differentiation, we leverage convolution identities and train a repeated integral field to efficiently execute large-scale convolutions. We demonstrate our approach on a variety of data modalities and spatially-varying kernels. |
| title | Neural Field Convolutions by Repeated Differentiation |
| topic | Computer Vision and Pattern Recognition Graphics |
| url | https://arxiv.org/abs/2304.01834 |