Paper ID: 2304.01834

Neural Field Convolutions by Repeated Differentiation

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

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.

Submitted: Apr 4, 2023