  A signed distance function (SDF) as the 3D shape description is one of the
most effective approaches to represent 3D geometry for rendering and
reconstruction. Our work is inspired by the state-of-the-art method DeepSDF
that learns and analyzes the 3D shape as the iso-surface of its shell and this
method has shown promising results especially in the 3D shape reconstruction
and compression domain. In this paper, we consider the degeneration problem of
reconstruction coming from the capacity decrease of the DeepSDF model, which
approximates the SDF with a neural network and a single latent code. We propose
Local Geometry Code Learning (LGCL), a model that improves the original DeepSDF
results by learning from a local shape geometry of the full 3D shape. We add an
extra graph neural network to split the single transmittable latent code into a
set of local latent codes distributed on the 3D shape. Mentioned latent codes
are used to approximate the SDF in their local regions, which will alleviate
the complexity of the approximation compared to the original DeepSDF.
Furthermore, we introduce a new geometric loss function to facilitate the
training of these local latent codes. Note that other local shape adjusting
methods use the 3D voxel representation, which in turn is a problem highly
difficult to solve or even is insolvable. In contrast, our architecture is
based on graph processing implicitly and performs the learning regression
process directly in the latent code space, thus make the proposed architecture
more flexible and also simple for realization. Our experiments on 3D shape
reconstruction demonstrate that our LGCL method can keep more details with a
significantly smaller size of the SDF decoder and outperforms considerably the
original DeepSDF method under the most important quantitative metrics.
