  3D-aware GANs aim to synthesize realistic 3D scenes such that they can be
rendered in arbitrary perspectives to produce images. Although previous methods
produce realistic images, they suffer from unstable training or degenerate
solutions where the 3D geometry is unnatural. We hypothesize that the 3D
geometry is underdetermined due to the insufficient constraint, i.e., being
classified as real image to the discriminator is not enough. To solve this
problem, we propose to approximate the background as a spherical surface and
represent a scene as a union of the foreground placed in the sphere and the
thin spherical background. It reduces the degree of freedom in the background
field. Accordingly, we modify the volume rendering equation and incorporate
dedicated constraints to design a novel 3D-aware GAN framework named BallGAN.
BallGAN has multiple advantages as follows. 1) It produces more reasonable 3D
geometry; the images of a scene across different viewpoints have better
photometric consistency and fidelity than the state-of-the-art methods. 2) The
training becomes much more stable. 3) The foreground can be separately rendered
on top of different arbitrary backgrounds.
