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.
@article{arxiv.2304.01834,
title = {Neural Field Convolutions by Repeated Differentiation},
author = {Ntumba Elie Nsampi and Adarsh Djeacoumar and Hans-Peter Seidel and Tobias Ritschel and Thomas Leimkühler},
journal= {arXiv preprint arXiv:2304.01834},
year = {2024}
}