mlsanityData to 7 Oct 2026

M"obius Convolutions for Spherical CNNs

arXiv 2201.12212 ↗First posted 28 Jan 2022cs.CV cs.GR cs.LGcited by 13

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Abstract (arXiv)

M"obius transformations play an important role in both geometry and spherical image processing - they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel, M"obius-equivariant spherical convolution operator which we call M"obius convolution, and with it, develop the foundations for M"obius-equivariant spherical CNNs. Our approach is based on a simple observation: to achieve equivariance, we only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors. To efficiently compute M"obius convolutions at scale we derive an approximation of the action of the transformations on spherical filters, allowing us to compute our convolutions in the spectral domain with the fast Spherical Harmonic Transform. The resulting framework is both flexible and descriptive, and we demonstrate its utility by achieving promising results in both shape classification and image segmentation tasks.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 36 of its 64 references that are in the map. First posted on arXiv 28 Jan 2022.

Builds on

36 of 64 references.

References · 36

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  12. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
24 more
  1. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  2. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  3. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
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  5. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  6. 2019Deep Scale-spaces: Equivariance Over Scalecited by 113
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 4; 2025: 1; 2026: 2.

13 papers.

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  1. 2023Towards Stability of Autoregressive Neural Operatorscited by 54
  2. 2022Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutionscited by 23
  3. 2023Scaling Spherical CNNscited by 21
  4. 2023Single Mesh Diffusion Models with Field Latents for Texture Generationcited by 11
  5. 2023Multi-body SE(3) Equivariance for Unsupervised Rigid Segmentation and Motion Estimationcited by 7
  6. 2023OmniZoomer: Learning to Move and Zoom in on Sphere at High-Resolutioncited by 7
  7. 2024Neural Isometries: Taming Transformations for Equivariant MLcited by 6
  8. 2024M"obius Transform for Mitigating Perspective Distortions in Representation Learningcited by 2
  9. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  10. 2024Learning High-Quality Navigation and Zooming on Omnidirectional Images in Virtual Realitycited by 1
  11. 2026AdapToPASS: Ambiguity-aware Adaptive Spherical Transformer for Panoramic Semantic Segmentationcited by 1
  12. 2025Algebraic Priors for Approximately Equivariant Networkscited by 0
1 more
  1. 2026Smoothness Errors in Dynamics Models and How to Avoid Themcited by 0