Neural Field Convolutions by Repeated Differentiation

arXiv:2304.01834v3 Announce Type: replace
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 …

abstract arxiv computing continuous cs.cv cs.gr differentiation fields general polynomial processing representation signal type visual