Möbius Convolutions for Spherical CNNs

Fig. 1. Equivariant convolutions require two ingredients: a frame operator and a density operator. Filters assign weights based on the relative positions of points and the frame operator T corrects for the deformation of the local “tangent space” under a Möbius transformation g. Similarly, the density operator ρ adjusts for the change in the area measure used for integration, proportional to the conformal scale factor λ2 g .