Signal Processing for Implicit Neural Representations
This work addresses a bottleneck in INR manipulation for computer vision applications, offering a novel approach to maintain compactness and continuity, though it appears incremental as it builds on existing INR frameworks.
The paper tackles the problem of editing and processing Implicit Neural Representations (INRs) without explicit decoding, which is intractable due to their latent parameter representation, by proposing INSP-Net, a method using differential operators to directly modify INRs, and builds INSP-ConvNet, the first CNN operating implicitly on INRs, with experiments validating expressiveness in tasks like blurring, denoising, and image classification.
Implicit Neural Representations (INRs) encoding continuous multi-media data via multi-layer perceptrons has shown undebatable promise in various computer vision tasks. Despite many successful applications, editing and processing an INR remains intractable as signals are represented by latent parameters of a neural network. Existing works manipulate such continuous representations via processing on their discretized instance, which breaks down the compactness and continuous nature of INR. In this work, we present a pilot study on the question: how to directly modify an INR without explicit decoding? We answer this question by proposing an implicit neural signal processing network, dubbed INSP-Net, via differential operators on INR. Our key insight is that spatial gradients of neural networks can be computed analytically and are invariant to translation, while mathematically we show that any continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators. With these two knobs, INSP-Net instantiates the signal processing operator as a weighted composition of computational graphs corresponding to the high-order derivatives of INRs, where the weighting parameters can be data-driven learned. Based on our proposed INSP-Net, we further build the first Convolutional Neural Network (CNN) that implicitly runs on INRs, named INSP-ConvNet. Our experiments validate the expressiveness of INSP-Net and INSP-ConvNet in fitting low-level image and geometry processing kernels (e.g. blurring, deblurring, denoising, inpainting, and smoothening) as well as for high-level tasks on implicit fields such as image classification.