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的通用连续表示方向发展。然而，尽管其具有众多吸引人的特性，但信号处理对其而言仍难以适用。为此，我们提出一种方法，利用神经场等通用连续信号实现通用连续卷积。我们发现分段多项式核在重复微分后会退化为一组稀疏的狄拉克Delta函数，进而利用卷积恒等式训练一个重复积分场，以高效执行大规模卷积运算。我们在多种数据模态和空间变化核上验证了该方法。