Polynomial Neural Fields for Subband Decomposition and ManipulationDownload PDF

Published: 31 Oct 2022, 18:00, Last Modified: 12 Jan 2023, 10:03NeurIPS 2022 AcceptReaders: Everyone
Keywords: Neural Fields, Signal Processing, Subband Decomposition, Signal Manipulation
TL;DR: We propose Polynomial Neural Fields (PNF), a novel neural field architecture that enables decomposing and manipulating signals in terms of subbands.
Abstract: Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like a black box, which precludes many signal manipulation tasks. In this paper, we propose a new class of neural fields called basis-encoded polynomial neural fields (PNFs). The key advantage of a PNF is that it can represent a signal as a composition of a number of manipulable and interpretable components without losing the merits of neural fields representation. We develop a general theoretical framework to analyze and design PNFs. We use this framework to design Fourier PNFs, which match state-of-the-art performance in signal representation tasks that use neural fields. In addition, we empirically demonstrate that Fourier PNFs enable signal manipulation applications such as texture transfer and scale-space interpolation. Code is available at https://github.com/stevenygd/PNF.
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