Deep Scale-spaces: Equivariance Over Scale

2019/05/28 by Daniel E. Worrall, Max Welling, Worrall, Daniel E. +1 · 10 citations
Computer Science · Engineering · #3D Shape Modeling and Analysis #Computer Graphics and Visualization Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Image Segmentation Techniques

paper · pdf · doi:10.48550/arxiv.1905.11697

openalex publication_date 2019/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Gradient-based learning applied to document recognition
• DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Cited by

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• On sources to variabilities of simple cells in the primary visual cortex: A principled theory for the interaction between geometric image transformations and receptive field responses
• CLIPSym: Delving into Symmetry Detection with CLIP
• Local Scale Equivariance with Latent Deep Equilibrium Canonicalizer
• Graph Lineages and Skeletal Graph Products
• Flow Equivariant Recurrent Neural Networks
• AdS-GNN -- a Conformally Equivariant Graph Neural Network
• Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurring

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