  Recently researchers have been shifting their focus towards learned 3D shape
descriptors from hand-craft ones to better address challenging issues of the
deformation and structural variation inherently present in 3D objects. 3D
geometric data are often transformed to 3D Voxel grids with regular format in
order to be better fed to a deep neural net architecture. However, the
computational intractability of direct application of 3D convolutional nets to
3D volumetric data severely limits the efficiency (i.e. slow processing) and
effectiveness (i.e. unsatisfied accuracy) in processing 3D geometric data. In
this paper, powered with a novel design of adversarial networks (3D-A-Nets), we
have developed a novel 3D deep dense shape descriptor (3D-DDSD) to address the
challenging issues of efficient and effective 3D volumetric data processing. We
developed new definition of 2D multilayer dense representation (MDR) of 3D
volumetric data to extract concise but geometrically informative shape
description and a novel design of adversarial networks that jointly train a set
of convolution neural network (CNN), recurrent neural network (RNN) and an
adversarial discriminator. More specifically, the generator network produces 3D
shape features that encourages the clustering of samples from the same category
with correct class label, whereas the discriminator network discourages the
clustering by assigning them misleading adversarial class labels. By addressing
the challenges posed by the computational inefficiency of direct application of
CNN to 3D volumetric data, 3D-A-Nets can learn high-quality 3D-DSDD which
demonstrates superior performance on 3D shape classification and retrieval over
other state-of-the-art techniques by a great margin.
