On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data
- The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exactThe mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation and practical implementation of SH representations, summarizing works on rotation invariant and equivariant features, as well as convolutions and exact correlations of signals on spheres. In extension, these methods are then generalized from scalar SH representations to Vectorial Harmonics (VH), providing the same capabilities for 3d vector fields on spheres.…
| Document Type: | Article (unreviewed) |
|---|---|
| Zitierlink: | https://opus.hs-offenburg.de/8235 | Bibliografische Angaben |
| Title (English): | On Invariance, Equivariance, Correlation and Convolution of Spherical Harmonic Representations for Scalar and Vectorial Data |
| Author: | Janis KeuperStaff MemberORCiDGND |
| Year of Publication: | 2023 |
| Publisher: | Arxiv |
| First Page: | 1 |
| Last Page: | 105 |
| DOI: | https://doi.org/10.48550/arXiv.2307.03311 |
| Language: | English | Inhaltliche Informationen |
| Institutes: | Fakultät Elektrotechnik, Medizintechnik und Informatik (EMI) (ab 04/2019) |
| Forschung / IMLA - Institute for Machine Learning and Analytics | |
| Institutes: | Bibliografie |
| Tag: | Deep Leaning | Formale Angaben |
| Relevance: | Wiss. Zeitschriftenartikel unreviewed |
| Open Access: | Open Access |
| Diamond | |
| Licence (German): |  Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International |
| ArXiv Id: | http://arxiv.org/abs/2307.03311v1 |