  This paper proposes a 3D shape descriptor network, which is a deep
convolutional energy-based model, for modeling volumetric shape patterns. The
maximum likelihood training of the model follows an "analysis by synthesis"
scheme and can be interpreted as a mode seeking and mode shifting process. The
model can synthesize 3D shape patterns by sampling from the probability
distribution via MCMC such as Langevin dynamics. The model can be used to train
a 3D generator network via MCMC teaching. The conditional version of the 3D
shape descriptor net can be used for 3D object recovery and 3D object
super-resolution. Experiments demonstrate that the proposed model can generate
realistic 3D shape patterns and can be useful for 3D shape analysis.
