This study develops a unified Point Cloud Geometry (PCG) compression method
through the processing of multiscale sparse tensor-based voxelized PCG. We call
this compression method SparsePCGC. The proposed SparsePCGC is a low complexity
solution because it only performs the convolutions on sparsely-distributed
Most-Probable Positively-Occupied Voxels (MP-POV). The multiscale
representation also allows us to compress scale-wise MP-POVs by exploiting
cross-scale and same-scale correlations extensively and flexibly. The overall
compression efficiency highly depends on the accuracy of estimated occupancy
probability for each MP-POV. Thus, we first design the Sparse Convolution-based
Neural Network (SparseCNN) which stacks sparse convolutions and voxel sampling
to best characterize and embed spatial correlations. We then develop the
SparseCNN-based Occupancy Probability Approximation (SOPA) model to estimate
the occupancy probability either in a single-stage manner only using the
cross-scale correlation, or in a multi-stage manner by exploiting stage-wise
correlation among same-scale neighbors. Besides, we also suggest the SparseCNN
based Local Neighborhood Embedding (SLNE) to aggregate local variations as
spatial priors in feature attribute to improve the SOPA. Our unified approach
not only shows state-of-the-art performance in both lossless and lossy
compression modes across a variety of datasets including the dense object PCGs
(8iVFB, Owlii, MUVB) and sparse LiDAR PCGs (KITTI, Ford) when compared with
standardized MPEG G-PCC and other prevalent learning-based schemes, but also
has low complexity which is attractive to practical applications.

本研究提出了一种基于多尺度稀疏张量的点云几何压缩方法，称为 SparsePCGC，使用 Sparse Convolution-based Neural Network 和 Occupancy Probability Approximation 模型计算不同尺度的空间相关性来提高估计空间占用概率的准确性和压缩效率。在各种数据集中，该方法在无损和有损压缩模式下均表现出与标准化的 MPEG G-PCC 以及流行的基于学习的方案相比的最先进性能，同时具有低复杂度的优势。

基于稀疏张量的点云几何多尺度表示压缩

Sparse Tensor-based Multiscale Representation for Point Cloud Geometry  Compression

We describe a framework for defining high-order image models that can be used
in a variety of applications. The approach involves modeling local patterns in
a multiscale representation of an image. Local properties of a coarsened image
reflect non-local properties of the original image. In the case of binary
images local properties are defined by the binary patterns observed over small
neighborhoods around each pixel. With the multiscale representation we capture
the frequency of patterns observed at different scales of resolution. This
framework leads to expressive priors that depend on a relatively small number
of parameters. For inference and learning we use an MCMC method for block
sampling with very large blocks. We evaluate the approach with two example
applications. One involves contour detection. The other involves binary
segmentation.

该研究提出了一种基于多尺度表示、局部模式建模的高阶图像模型框架，使用 MCMC 方法进行采样，并利用其进行轮廓检测和图像二值分割。

多尺度模式场

Multiscale Fields of Patterns

We present a probabilistic model for natural images which is based on
Gaussian scale mixtures and a simple multiscale representation. In contrast to
the dominant approach to modeling whole images focusing on Markov random
fields, we formulate our model in terms of a directed graphical model. We show
that it is able to generate images with interesting higher-order correlations
when trained on natural images or samples from an occlusion based model. More
importantly, the directed model enables us to perform a principled evaluation.
While it is easy to generate visually appealing images, we demonstrate that our
model also yields the best performance reported to date when evaluated with
respect to the cross-entropy rate, a measure tightly linked to the average
log-likelihood.

提出了一种基于高斯混合模型和简单的多尺度表示的自然图像的概率模型，并展示了这种模型能够生成具有有趣的高阶相关性的图像，并在评估方面表现出到目前为止最好的性能，这是基于平均对数似然度高度相关的一种衡量方式。