Learning Localized Representations of Point Clouds with Graph-Convolutional Generative Adversarial Networks

Point clouds are an important type of geometric data generated by 3D acquisition devices, and have widespread use in computer graphics and vision. However, learning representations for point clouds is particularly challenging due to their nature as being an unordered collection of points irregularly distributed in 3D space. Recently, supervised and semisupervised problems for point clouds leveraged graph convolution, a generalization of the convolution operation for data defined over graphs. This operation has been shown to be very successful at extracting localized features from point clouds. In this paper, we study the unsupervised problem of a generative model exploiting graph convolution. Employing graph convolution operations in generative models is not straightforward and it poses some unique challenges. In particular, we focus on the generator of a GAN, where the graph is not known in advance as it is the very output of the generator. We show that the proposed architecture can learn to generate the graph and the features simultaneously. We also study the problem of defining an upsampling layer in the graph-convolutional generator, proposing two methods that respectively learn to exploit a multi-resolution or self-similarity prior to sample the data distribution.