Neural Field Convolutions by Repeated Differentiation

Fuente: arXiv
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Hauptverfasser: Nsampi, Ntumba Elie, Djeacoumar, Adarsh, Seidel, Hans-Peter, Ritschel, Tobias, Leimkühler, Thomas
Format: Preprint
Veröffentlicht: 2023
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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