  Representing complex 3D objects as simple geometric primitives, known as
shape abstraction, is important for geometric modeling, structural analysis,
and shape synthesis. In this paper, we propose an unsupervised shape
abstraction method to map a point cloud into a compact cuboid representation.
We jointly predict cuboid allocation as part segmentation and cuboid shapes and
enforce the consistency between the segmentation and shape abstraction for
self-learning. For the cuboid abstraction task, we transform the input point
cloud into a set of parametric cuboids using a variational auto-encoder
network. The segmentation network allocates each point into a cuboid
considering the point-cuboid affinity. Without manual annotations of parts in
point clouds, we design four novel losses to jointly supervise the two branches
in terms of geometric similarity and cuboid compactness. We evaluate our method
on multiple shape collections and demonstrate its superiority over existing
shape abstraction methods. Moreover, based on our network architecture and
learned representations, our approach supports various applications including
structured shape generation, shape interpolation, and structural shape
clustering.
