  This paper introduces a 3D shape generative model based on deep neural
networks. A new image-like (i.e., tensor) data representation for genus-zero 3D
shapes is devised. It is based on the observation that complicated shapes can
be well represented by multiple parameterizations (charts), each focusing on a
different part of the shape. The new tensor data representation is used as
input to Generative Adversarial Networks for the task of 3D shape generation.
The 3D shape tensor representation is based on a multi-chart structure that
enjoys a shape covering property and scale-translation rigidity.
Scale-translation rigidity facilitates high quality 3D shape learning and
guarantees unique reconstruction. The multi-chart structure uses as input a
dataset of 3D shapes (with arbitrary connectivity) and a sparse correspondence
between them. The output of our algorithm is a generative model that learns the
shape distribution and is able to generate novel shapes, interpolate shapes,
and explore the generated shape space. The effectiveness of the method is
demonstrated for the task of anatomic shape generation including human body and
bone (teeth) shape generation.
