  This paper explores the problem of effectively compressing 3D geometry sets
containing diverse categories. We make \textit{the first} attempt to tackle
this fundamental and challenging problem and propose NeCGS, a neural
compression paradigm, which can compress hundreds of detailed and diverse 3D
mesh models (~684 MB) by about 900 times (0.76 MB) with high accuracy and
preservation of detailed geometric details. Specifically, we first represent
each irregular mesh model/shape in a regular representation that implicitly
describes the geometry structure of the model using a 4D regular volume, called
TSDF-Def volume. Such a regular representation can not only capture local
surfaces more effectively but also facilitate the subsequent process. Then we
construct a quantization-aware auto-decoder network architecture to regress
these 4D volumes, which can summarize the similarity of local geometric
structures within a model and across different models for redundancy
limination, resulting in more compact representations, including an embedded
feature of a smaller size associated with each model and a network parameter
set shared by all models. We finally encode the resulting features and network
parameters into bitstreams through entropy coding. After decompressing the
features and network parameters, we can reconstruct the TSDF-Def volumes, where
the 3D surfaces can be extracted through the deformable marching
cubes.Extensive experiments and ablation studies demonstrate the significant
advantages of our NeCGS over state-of-the-art methods both quantitatively and
qualitatively.
