  Although convolutional neural networks have achieved remarkable success in
analyzing 2D images/videos, it is still non-trivial to apply the well-developed
2D techniques in regular domains to the irregular 3D point cloud data. To
bridge this gap, we propose ParaNet, a novel end-to-end deep learning
framework, for representing 3D point clouds in a completely regular and nearly
lossless manner. To be specific, ParaNet converts an irregular 3D point cloud
into a regular 2D color image, named point geometry image (PGI), where each
pixel encodes the spatial coordinates of a point. In contrast to conventional
regular representation modalities based on multi-view projection and
voxelization, the proposed representation is differentiable and reversible.
Technically, ParaNet is composed of a surface embedding module, which
parameterizes 3D surface points onto a unit square, and a grid resampling
module, which resamples the embedded 2D manifold over regular dense grids. Note
that ParaNet is unsupervised, i.e., the training simply relies on
reference-free geometry constraints. The PGIs can be seamlessly coupled with a
task network established upon standard and mature techniques for 2D
images/videos to realize a specific task for 3D point clouds. We evaluate
ParaNet over shape classification and point cloud upsampling, in which our
solutions perform favorably against the existing state-of-the-art methods. We
believe such a paradigm will open up many possibilities to advance the progress
of deep learning-based point cloud processing and understanding.
