  We present a new and general framework for convolutional neural network
operations on spherical (or omnidirectional) images. Our approach represents
the surface as a graph of connected points that doesn't rely on a particular
sampling strategy. Additionally, by using an interpolated version of
SelectionConv, we can operate on the sphere while using existing 2D CNNs and
their weights. Since our method leverages existing graph implementations, it is
also fast and can be fine-tuned efficiently. Our method is also general enough
to be applied to any surface type, even those that are topologically
non-simple. We demonstrate the effectiveness of our technique on the tasks of
style transfer and segmentation for spheres as well as stylization for 3D
meshes. We provide a thorough ablation study of the performance of various
spherical sampling strategies.
