Deep Scale-spaces: Equivariance Over Scale

By Daniel E. Worrall, Max Welling. 2019

194 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

Group Equivariant Stand-Alone Self-Attention For Vision (2020, background): “…2020) to spherical rotations (Cohen et al., 2018; Worrall & Brostow, 2018; Weiler et al., 2018a; Cohen et al., 2019b), scaling (Marcos et al., 2018; Worrall & Welling, 2019; Sosnovik et al., 2020; Romero et al., 2020b) and more general symmetry groups (Cohen & Welling, 2016; Kondor & Trivedi,…”
SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2020, methodology): “Similar to [27, 39], we measure the exactness of equivariance by applying uniformly sampled SO(3)transformations to input and output.”
Alias-Free Generative Adversarial Networks (2021, neutral): “, rotation [16, 62, 60, 59] and scale [61].”
Attentive Group Equivariant Convolutional Networks (2020, background): “2): Resultantly, the computational cost of a group convolution is roughly equivalent to that of a spatial convolution with a ﬁlter bank of size N ˜ c × | H | (Cohen & Welling, 2016a; Worrall & Welling, 2019; Cohen et al., 2019b).”
Wavelet Networks: Scale Equivariant Learning From Raw Waveforms (2020, methodology): “Motivated by this observation, we propose to induce translation and scale equivariance in neural architectures for time-series, in a manner similar to Worrall and Welling [78], Sosnovik et al.”
Scale-Equivariant Steerable Networks (2019, methodology): “For SiCNN, DSS, SEVF and our model, we additionally train counterparts where after each convolution, an extra projection layer is inserted.”
Co-Attentive Equivariant Neural Networks: Focusing Equivariance On Transformations Co-Occurring In Data (2019, background): “…et al., 2018; Li et al., 2018), spherical rotations (Cohen et al., 2018; Worrall & Brostow, 2018; Cohen et al., 2019), scaling (Marcos et al., 2018; Worrall & Welling, 2019) and general transformation groups (Cohen & Welling, 2016), such that transformed copies of a single entity are not required…”