Neural Gaussian Scale-Space Fields

TL;DR

This paper introduces a self-supervised neural method to efficiently learn continuous, anisotropic Gaussian scale spaces for various signals, enabling multiscale analysis without manual filtering.

Contribution

It presents a novel neural approach that models Gaussian scale spaces continuously and anisotropically, trained without manual supervision, applicable across multiple data modalities.

Findings

Faithfully captures multiscale representations across diverse modalities

Supports applications like anti-aliasing and multiscale optimization

Operates efficiently without manual filtering

Abstract

Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in particular for continuous representations such as neural fields. We present an efficient and lightweight method to learn the fully continuous, anisotropic Gaussian scale space of an arbitrary signal. Based on Fourier feature modulation and Lipschitz bounding, our approach is trained self-supervised, i.e., training does not require any manual filtering. Our neural Gaussian scale-space fields faithfully capture multiscale representations across a broad range of modalities, and support a diverse set of applications. These include images, geometry, light-stage data, texture anti-aliasing, and multiscale optimization.