The mathematical representations of data in the Spherical Harmonic (SH)
domain has recently regained increasing interest in the machine learning
community. This technical report gives an in-depth introduction to the
theoretical foundation and practical implementation of SH representations,
summarizing works on rotation invariant and equivariant features, as well as
convolutions and exact correlations of signals on spheres. In extension, these
methods are then generalized from scalar SH representations to Vectorial
Harmonics (VH), providing the same capabilities for 3d vector fields on spheres

在这篇技术报告中，我们深入介绍了球谐（Spherical Harmonic）域中数据的数学表示的理论基础和实际实现，并总结了关于旋转不变性和等变特征、球面信号的卷积和精确相关性的作品。此外，我们还将这些方法从标量球谐表示推广到矢量谐波（Vectorial Harmonics），为球面上的三维矢量场提供了相同的能力。

关于球形调和表示对于标量和向量数据的不变性、等变性、相关性和卷积

On Invariance, Equivariance, Correlation and Convolution of Spherical  Harmonic Representations for Scalar and Vectorial Data

We present PPF-FoldNet for unsupervised learning of 3D local descriptors on
pure point cloud geometry. Based on the folding-based auto-encoding of well
known point pair features, PPF-FoldNet offers many desirable properties: it
necessitates neither supervision, nor a sensitive local reference frame,
benefits from point-set sparsity, is end-to-end, fast, and can extract powerful
rotation invariant descriptors. Thanks to a novel feature visualization, its
evolution can be monitored to provide interpretable insights. Our extensive
experiments demonstrate that despite having six degree-of-freedom invariance
and lack of training labels, our network achieves state of the art results in
standard benchmark datasets and outperforms its competitors when rotations and
varying point densities are present. PPF-FoldNet achieves $9\%$ higher recall
on standard benchmarks, $23\%$ higher recall when rotations are introduced into
the same datasets and finally, a margin of $>35\%$ is attained when point
density is significantly decreased.

本研究提出了 PPF-FoldNet，它基于基于折叠的自编码器计算点对特征，可以用于学习 3D 本地描述符，具有旋转不变性，并且在标准基准数据集上取得了最新的结果。

PPF-FoldNet：无监督学习旋转不变的三维局部描述符

PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local  Descriptors

This paper presents a new face identification system based on Graph Matching
Technique on SIFT features extracted from face images. Although SIFT features
have been successfully used for general object detection and recognition, only
recently they were applied to face recognition. This paper further investigates
the performance of identification techniques based on Graph matching topology
drawn on SIFT features which are invariant to rotation, scaling and
translation. Face projections on images, represented by a graph, can be matched
onto new images by maximizing a similarity function taking into account spatial
distortions and the similarities of the local features. Two graph based
matching techniques have been investigated to deal with false pair assignment
and reducing the number of features to find the optimal feature set between
database and query face SIFT features. The experimental results, performed on
the BANCA database, demonstrate the effectiveness of the proposed system for
automatic face identification.

本文提出了一种基于 SIFT 特征的图匹配技术的人脸识别系统，采用旋转不变的 SIFT 特征为基础来匹配代表人脸的图形的拓扑结构，并使用两种基于图形的匹配技术，以处理假匹配和减少找到数据库和查询脸 SIFT 特征之间最佳特征集的数量，实验结果表明了这种系统在自动人脸识别方面的有效性.