Neural Fields (NFs) have gained momentum as a tool for compressing various
data modalities - e.g. images and videos. This work leverages previous advances
and proposes a novel NF-based compression algorithm for 3D data. We derive two
versions of our approach - one tailored to watertight shapes based on Signed
Distance Fields (SDFs) and, more generally, one for arbitrary non-watertight
shapes using Unsigned Distance Fields (UDFs). We demonstrate that our method
excels at geometry compression on 3D point clouds as well as meshes. Moreover,
we show that, due to the NF formulation, it is straightforward to extend our
compression algorithm to compress both geometry and attribute (e.g. color) of
3D data.

本研究提出了一种基于神经场的三维数据压缩算法，能够优秀地进行几何压缩以及属性（例如颜色）压缩。

神经场的 3D 压缩

3D Compression Using Neural Fields

We study 3D point cloud attribute compression using a volumetric approach:
given a target volumetric attribute function $f : \mathbb{R}^3 \rightarrow
\mathbb{R}$, we quantize and encode parameter vector $\theta$ that
characterizes $f$ at the encoder, for reconstruction
$f_{\hat{\theta}}(\mathbf{x})$ at known 3D points $\mathbf{x}$'s at the
decoder. Extending a previous work Region Adaptive Hierarchical Transform
(RAHT) that employs piecewise constant functions to span a nested sequence of
function spaces, we propose a feedforward linear network that implements
higher-order B-spline bases spanning function spaces without
eigen-decomposition. Feedforward network architecture means that the system is
amenable to end-to-end neural learning. The key to our network is space-varying
convolution, similar to a graph operator, whose weights are computed from the
known 3D geometry for normalization. We show that the number of layers in the
normalization at the encoder is equivalent to the number of terms in a matrix
inverse Taylor series. Experimental results on real-world 3D point clouds show
up to 2-3 dB gain over RAHT in energy compaction and 20-30% bitrate reduction.

通过使用体积法进行 3D 点云属性压缩，本研究介绍了一种新的前馈线性网络方法 ——B 样条基的非特征值分解实现，利用空间变化的卷积和编码器中表示矩阵逆泰勒级数的项的数目等因素，能够在真实的 3D 点云场景下，具有比区域自适应分层变换（RAHT）更好的能量压缩效果，并能减少 20-30% 的比特率。