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International Journal of Computer Vision
Erschienen in: International Journal of Computer Vision 6/2020

21.12.2019

Representation Learning on Unit Ball with 3D Roto-translational Equivariance

verfasst von: Sameera Ramasinghe, Salman Khan, Nick Barnes, Stephen Gould

Erschienen in: International Journal of Computer Vision | Ausgabe 6/2020

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Abstract

Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces—such as a sphere (\(\mathbb {S}^2\)) or a unit ball (\(\mathbb {B}^3\))—entails unique challenges. In this work, we propose a novel ‘volumetric convolution’ operation that can effectively model and convolve arbitrary functions in \(\mathbb {B}^3\). We develop a theoretical framework for volumetric convolution based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer in deep networks. By construction, our formulation leads to the derivation of a novel formula to measure the symmetry of a function in \(\mathbb {B}^3\) around an arbitrary axis, that is useful in function analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on one viable use case i.e., 3D object recognition.
Vorheriger Artikel Real-Time Multi-person Motion Capture from Multi-view Video and IMUs
Nächster Artikel Scalable Person Re-Identification by Harmonious Attention

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Fußnoten
1
We refer the reader to (Cohen et al. 2018a) for an excellent review on group equivariant CNNs.
 
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Metadaten
Titel
Representation Learning on Unit Ball with 3D Roto-translational Equivariance
verfasst von
Sameera Ramasinghe
Salman Khan
Nick Barnes
Stephen Gould
Publikationsdatum
21.12.2019
Verlag
Springer US
Erschienen in
International Journal of Computer Vision / Ausgabe 6/2020
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI
https://doi.org/10.1007/s11263-019-01278-x

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