  3D data that contains rich geometry information of objects and scenes is
valuable for understanding 3D physical world. With the recent emergence of
large-scale 3D datasets, it becomes increasingly crucial to have a powerful 3D
generative model for 3D shape synthesis and analysis. This paper proposes a
deep 3D energy-based model to represent volumetric shapes. The maximum
likelihood training of the model follows an "analysis by synthesis" scheme. The
benefits of the proposed model are six-fold: first, unlike GANs and VAEs, the
model training does not rely on any auxiliary models; second, the model can
synthesize realistic 3D shapes by Markov chain Monte Carlo (MCMC); third, the
conditional model can be applied to 3D object recovery and super resolution;
fourth, the model can serve as a building block in a multi-grid modeling and
sampling framework for high resolution 3D shape synthesis; fifth, the model can
be used to train a 3D generator via MCMC teaching; sixth, the unsupervisedly
trained model provides a powerful feature extractor for 3D data, which is
useful for 3D object classification. Experiments demonstrate that the proposed
model can generate high-quality 3D shape patterns and can be useful for a wide
variety of 3D shape analysis.
