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arXiv · 2304.01834

Neural Field Convolutions by Repeated Differentiation

Ntumba Elie Nsampi·Adarsh Djeacoumar·Hans-Peter Seidel·Tobias Ritschel·Thomas Leimkühler
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Abstract

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.

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Ntumba Elie Nsampi, Adarsh Djeacoumar, Hans-Peter Seidel, Tobias Ritschel, Thomas Leimkühler. 2023-04-04. Neural Field Convolutions by Repeated Differentiation. https://doi.org/10.1145/3618340

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