Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the discretized sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of pixels and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibility of this formulation. Perhaps surprisingly, comparison with previous work suggests that anisotropic filters might be an unnecessary price to pay.
A graph-based spherical CNN that strikes an interesting balance of trade-offs for a wide variety of applications. Combines existing CNN frameworks based on the discretization of a sphere as a graph to show a convergence result which is related to the rotation equivalence on a sphere. The authors use the existing graph CNN formulation and a pooling strategy that exploits hierarchical pixelations of the sphere to learn from the discretized sphere.