  Point clouds are characterized by irregularity and unstructuredness, which
pose challenges in efficient data exploitation and discriminative feature
extraction. In this paper, we present an unsupervised deep neural architecture
called Flattening-Net to represent irregular 3D point clouds of arbitrary
geometry and topology as a completely regular 2D point geometry image (PGI)
structure, in which coordinates of spatial points are captured in colors of
image pixels. \mr{Intuitively, Flattening-Net implicitly approximates a locally
smooth 3D-to-2D surface flattening process while effectively preserving
neighborhood consistency.} \mr{As a generic representation modality, PGI
inherently encodes the intrinsic property of the underlying manifold structure
and facilitates surface-style point feature aggregation.} To demonstrate its
potential, we construct a unified learning framework directly operating on PGIs
to achieve \mr{diverse types of high-level and low-level} downstream
applications driven by specific task networks, including classification,
segmentation, reconstruction, and upsampling. Extensive experiments demonstrate
that our methods perform favorably against the current state-of-the-art
competitors. We will make the code and data publicly available at
https://github.com/keeganhk/Flattening-Net.
