Deep Scale-spaces: Equivariance Over Scale

TL;DR

This paper introduces deep scale-spaces, a novel extension of convolutional neural networks that achieves scale equivariance by leveraging the mathematical structure of scale-spaces, improving recognition tasks across varying image scales.

Contribution

The paper presents a new class of scale-equivariant cross-correlations based on scale-space theory, which can be integrated into existing deep learning architectures for better scale invariance.

Findings

Effective on Patch Camelyon and Cityscapes datasets

Demonstrates improved robustness to scale variations

Provides insights into scale-equivariance properties

Abstract

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.