  Artificial data synthesis is currently a well studied topic with useful
applications in data science, computer vision, graphics and many other fields.
Generating realistic data is especially challenging since human perception is
highly sensitive to non realistic appearance. In recent times, new levels of
realism have been achieved by advances in GAN training procedures and
architectures. These successful models, however, are tuned mostly for use with
regularly sampled data such as images, audio and video. Despite the successful
application of the architecture on these types of media, applying the same
tools to geometric data poses a far greater challenge. The study of geometric
deep learning is still a debated issue within the academic community as the
lack of intrinsic parametrization inherent to geometric objects prohibits the
direct use of convolutional filters, a main building block of today's machine
learning systems. In this paper we propose a new method for generating
realistic human facial geometries coupled with overlayed textures. We
circumvent the parametrization issue by imposing a global mapping from our data
to the unit rectangle. We further discuss how to design such a mapping to
control the mapping distortion and conserve area within the mapped image. By
representing geometric textures and geometries as images, we are able to use
advanced GAN methodologies to generate new geometries. We address the often
neglected topic of relation between texture and geometry and propose to use
this correlation to match between generated textures and their corresponding
geometries. We offer a new method for training GAN models on partially
corrupted data. Finally, we provide empirical evidence demonstrating our
generative model's ability to produce examples of new identities independent
from the training data while maintaining a high level of realism, two traits
that are often at odds.
