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Steerable 3D Spherical Neurons
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-6091-861X
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-6096-3648
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-0675-2794
2022 (English)In: Proceedings of the 39th International Conference on Machine Learning / [ed] Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, Sivan Sabato, PMLR , 2022, Vol. 162, p. 15330-15339Conference paper, Published paper (Refereed)
Abstract [en]

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

Place, publisher, year, edition, pages
PMLR , 2022. Vol. 162, p. 15330-15339
Series
Proceedings of Machine Learning Research, ISSN 2640-3498
National Category
Computer Vision and Robotics (Autonomous Systems)
Identifiers
URN: urn:nbn:se:liu:diva-187149ISI: 000900064905021OAI: oai:DiVA.org:liu-187149DiVA, id: diva2:1686024
Conference
International Conference on Machine Learning, Baltimore, Maryland, USA, 17-23 July 2022
Note

Funding: Wallenberg AI, Autonomous Systems and Software Program (WASP); Swedish Research Council [2018-04673]; strategic research environment ELLIIT

Available from: 2022-08-08 Created: 2022-08-08 Last updated: 2023-05-10

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Melnyk, PavloFelsberg, MichaelWadenbäck, Mårten

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