IEEE Trans Image Process. 2017 Jul;26(7):3507-3517. doi: 10.1109/TIP.2017.2699922. Epub 2017 Apr 28.
We propose using stationary Gaussian processes (GPs) to model the statistics of the signal on points in a point cloud, which can be considered samples of a GP at the positions of the points. Furthermore, we propose using Gaussian process transforms (GPTs), which are Karhunen-Loève transforms of the GP, as the basis of transform coding of the signal. Focusing on colored 3D point clouds, we propose a transform coder that breaks the point cloud into blocks, transforms the blocks using GPTs, and entropy codes the quantized coefficients. The GPT for each block is derived from both the covariance function of the GP and the locations of the points in the block, which are separately encoded. The covariance function of the GP is parameterized, and its parameters are sent as side information. The quantized coefficients are sorted by the eigenvalues of the GPTs, binned, and encoded using an arithmetic coder with bin-dependent Laplacian models, whose parameters are also sent as side information. Results indicate that transform coding of 3D point cloud colors using the proposed GPT and entropy coding achieves superior compression performance on most of our data sets.
我们提出使用固定的高斯过程（Gaussian processes，GP）来模拟点云中各点信号的统计特性，这些点可以被视为 GP 在这些点位置上的样本。此外，我们提出使用高斯过程变换（Gaussian process transforms，GPT）作为信号变换编码的基础，GPT 是 GP 的 Karhunen-Loève 变换。聚焦于彩色 3D 点云，我们提出了一种变换编码器，它将点云分成块，使用 GPT 对块进行变换，并对量化系数进行熵编码。每个块的 GPT 由 GP 的协方差函数和块中各点的位置导出，这两者都被单独编码。GP 的协方差函数被参数化，其参数作为辅助信息发送。量化系数按照 GPT 的特征值排序、分组，然后使用具有分组相关拉普拉斯模型的算术编码器进行编码，其参数也作为辅助信息发送。结果表明，使用所提出的 GPT 和熵编码对 3D 点云颜色进行变换编码，在我们的大多数数据集上都能实现卓越的压缩性能。
