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。