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.

翻译：神经场正朝着视觉计算通用连续表示的方向发展。然而，尽管神经场具有众多吸引人的特性，但其在信号处理中的应用仍面临挑战。为此，我们提出一种方法，能够对神经场等通用连续信号执行广义连续卷积。通过观察发现，分段多项式核经过重复微分后会退化为稀疏的狄拉克δ函数集，我们利用卷积恒等式训练一个重复积分场，从而高效执行大规模卷积。我们在多种数据模态和空间变化核上验证了本方法的有效性。