  Point-clouds are a popular choice for vision and graphics tasks due to their
accurate shape description and direct acquisition from range-scanners. This
demands the ability to synthesize and reconstruct high-quality point-clouds.
Current deep generative models for 3D data generally work on simplified
representations (e.g., voxelized objects) and cannot deal with the inherent
redundancy and irregularity in point-clouds. A few recent efforts on 3D
point-cloud generation offer limited resolution and their complexity grows with
the increase in output resolution. In this paper, we develop a principled
approach to synthesize 3D point-clouds using a spectral-domain Generative
Adversarial Network (GAN). Our spectral representation is highly structured and
allows us to disentangle various frequency bands such that the learning task is
simplified for a GAN model. As compared to spatial-domain generative
approaches, our formulation allows us to generate arbitrary number of points
high-resolution point-clouds with minimal computational overhead. Furthermore,
we propose a fully differentiable block to transform from {the} spectral to the
spatial domain and back, thereby allowing us to integrate knowledge from
well-established spatial models. We demonstrate that Spectral-GAN performs well
for point-cloud generation task. Additionally, it can learn {a} highly
discriminative representation in an unsupervised fashion and can be used to
accurately reconstruct 3D objects.
