  We present a learning framework for abstracting complex shapes by learning to
assemble objects using 3D volumetric primitives. In addition to generating
simple and geometrically interpretable explanations of 3D objects, our
framework also allows us to automatically discover and exploit consistent
structure in the data. We demonstrate that using our method allows predicting
shape representations which can be leveraged for obtaining a consistent parsing
across the instances of a shape collection and constructing an interpretable
shape similarity measure. We also examine applications for image-based
prediction as well as shape manipulation.
