Synthesizing facial photometries and corresponding geometries using generative adversarial networks 
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. This mapping enables the representation of our geometric data as regularly sampled 2D images. 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. In addition, we widen the scope of our discussion and offer a new method for training GAN models on partially corrupted data. Finally, we provide empirical evidence demonstrating our generative modelâĂŹs is 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.