Azimuthal Rotational Equivariance in Spherical Convolutional Neural Networks
Paper i proceeding, 2022

In this work, we analyze linear operators on the space of square integrable functions on the sphere. Specifically, we characterize the operators which are equivariant to azimuthal rotations, that is, rotations around the z-axis. Several high-performing neural networks defined on the sphere are equivariant to azimuthal rotations, but not to full SO(3) rotations. Our main result is to show that a linear operator acting on band-limited functions on the sphere is equivariant to azimuthal rotations if and only if it can be realized as a block-diagonal matrix acting on the spherical harmonic expansion coefficients of its input. Further, we show that such an operation can be interpreted as a convolution, or equivalently, a correlation in the spatial domain. Our theoretical findings are backed up with experimental results demonstrating that a state-of-the-art pipeline can be improved by making it equivariant to azimuthal rotations.

Författare

Carl Toft

Eigenvision AB

Digitala bildsystem och bildanalys

Georg Bokman

Eigenvision AB

Fredrik Kahl

Eigenvision AB

Proceedings - International Conference on Pattern Recognition

10514651 (ISSN)

Vol. 2022-August 3808-3814
9781665490627 (ISBN)

26th International Conference on Pattern Recognition, ICPR 2022
Montreal, Canada,

Ämneskategorier

Annan fysik

Signalbehandling

Matematisk analys

DOI

10.1109/ICPR56361.2022.9956611

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Senast uppdaterat

2024-05-23