“Neural Representations: Coordinate Based Networks for Fitting Signals, Derivatives, and Integrals”
Julien Martel
(Stanford)
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Date: April 28, 2021
Description:
Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal’s spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. In this talk, we describe how sinusoidal representation networks or SIREN, are ideally suited for representing complex natural signals and their derivatives. Using SIREN, we demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how SIRENs can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. While SIREN can be used to fit signals and their derivatives, we also introduce a new framework for solving integral equations using implicit neural representation networks. Our automatic integration framework, AutoInt, enables the calculation of any definite integral with two evaluations of a neural network. We apply our approach for efficient integration to the problem of neural volume rendering. Finally we present a novel architecture and training procedure able to fit data such as gigapixel images or fine-detailed 3D geometry, demonstrating those neural representations are now ready to be used in large scale scenarios.
Further Information:
Julien Martel (http://www.jmartel.net/) is a postdoctoral scholar in the Stanford Computational Imaging Lab. His research interests are in unconventional visual sensing and computing. More specifically, his current topics of research include the co-design of hardware and algorithms for visual sensing, the design of methods for vision sensors with in-pixel computing capabilities, and the use of novel neural representations to store and compute on visual data.
Created: Wednesday, May 5th, 2021