Point clouds in 3D applications frequently experience quality degradation
during processing, e.g., scanning and compression. Reliable point cloud quality
assessment (PCQA) is important for developing compression algorithms with good
bitrate-quality trade-offs and techniques for quality improvement (e.g.,
denoising). This paper introduces a full-reference (FR) PCQA method utilizing
spectral graph wavelets (SGWs). First, we propose novel SGW-based PCQA metrics
that compare SGW coefficients of coordinate and color signals between reference
and distorted point clouds. Second, we achieve accurate PCQA by integrating
several conventional FR metrics and our SGW-based metrics using support vector
regression. To our knowledge, this is the first study to introduce SGWs for
PCQA. Experimental results demonstrate the proposed PCQA metric is more
accurately correlated with subjective quality scores compared to conventional
PCQA metrics.

本研究介绍了一种基于谱图小波的全参考点云质量评估方法，利用新颖的基于谱图小波的度量标准对参考和失真点云之间的坐标和颜色信号进行比较，并通过支持向量回归将多个传统全参考度量标准和基于谱图小波的度量标准整合，从而实现准确的点云质量评估。实验结果表明，所提出的点云质量评估标准与主观质量评分更准确地相关联，相比传统点云质量评估标准效果更好。

基于谱图小波的全参考点云质量评估

Full-reference Point Cloud Quality Assessment Using Spectral Graph  Wavelets

Deriving meaningful representations from complex, high-dimensional data in
unsupervised settings is crucial across diverse machine learning applications.
This paper introduces a framework for multi-scale graph network embedding based
on spectral graph wavelets that employs a contrastive learning approach. A
significant feature of the proposed embedding is its capacity to establish a
correspondence between the embedding space and the input feature space which
aids in deriving feature importance of the original features. We theoretically
justify our approach and demonstrate that, in Paley-Wiener spaces on
combinatorial graphs, the spectral graph wavelets operator offers greater
flexibility and better control over smoothness properties compared to the
Laplacian operator. We validate the effectiveness of our proposed graph
embedding on a variety of public datasets through a range of downstream tasks,
including clustering and unsupervised feature importance.

本文介绍了一种基于谱图小波的多尺度图网络嵌入框架，采用对比学习方法，从复杂的高维数据中得出有意义的表示，从而在无监督设置下对各种机器学习应用具有重要意义。

MS-IMAP -- 一个用于可解释流形学习的多尺度图嵌入方法

MS-IMAP -- A Multi-Scale Graph Embedding Approach for Interpretable  Manifold Learning

We propose a novel method for constructing wavelet transforms of functions
defined on the vertices of an arbitrary finite weighted graph. Our approach is
based on defining scaling using the the graph analogue of the Fourier domain,
namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a
wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled
wavelet operator $T_g^t = g(t\L)$. The spectral graph wavelets are then formed
by localizing this operator by applying it to an indicator function. Subject to
an admissibility condition on $g$, this procedure defines an invertible
transform. We explore the localization properties of the wavelets in the limit
of fine scales. Additionally, we present a fast Chebyshev polynomial
approximation algorithm for computing the transform that avoids the need for
diagonalizing $\L$. We highlight potential applications of the transform
through examples of wavelets on graphs corresponding to a variety of different
problem domains.

本论文提出了一种新的方法来构建任意有限加权图的函数波形变换，基于以离散图拉普拉斯的频谱分解作为傅立叶域的图分析，并且探索了极细尺度下波形的局部化特性，提出了一个快速的切比雪夫多项式逼近算法来计算变换，并通过解决多种不同问题域图上的波形示例展示变换的潜在应用。