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，尽管具有诸多诱人特性，它们却难以应用于信号处理领域。为此，我们提出了一种方法，能够利用神经场等通用连续信号执行通用连续卷积。通过观察分段多项式核在反复微分后简化为稀疏狄拉克δ函数集这一特性，我们利用卷积恒等式并训练重复积分场，从而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的有效性。