In this work, we present a novel learning-based framework that combines the
local accuracy of contrastive learning with the global consistency of geometric
approaches, for robust non-rigid matching. We first observe that while
contrastive learning can lead to powerful point-wise features, the learned
correspondences commonly lack smoothness and consistency, owing to the purely
combinatorial nature of the standard contrastive losses. To overcome this
limitation we propose to boost contrastive feature learning with two types of
smoothness regularization that inject geometric information into correspondence
learning. With this novel combination in hand, the resulting features are both
highly discriminative across individual points, and, at the same time, lead to
robust and consistent correspondences, through simple proximity queries. Our
framework is general and is applicable to local feature learning in both the 3D
and 2D domains. We demonstrate the superiority of our approach through
extensive experiments on a wide range of challenging matching benchmarks,
including 3D non-rigid shape correspondence and 2D image keypoint matching.

本研究提出了一个新的基于学习的框架，将对比学习的局部准确性与几何方法的全局一致性相结合，用于强健性非刚性匹配。

SRFeat：学习局部精确和全局一致的非刚性形状对应

SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid  Shape Correspondence

Geometric approaches to network analysis combine simply defined models with
great descriptive power. In this work we provide a method for embedding
directed acyclic graphs into Minkowski spacetime using Multidimensional scaling
(MDS). First we generalise the classical MDS algorithm, defined only for
metrics with a Euclidean signature, to manifolds of any metric signature. We
then use this general method to develop an algorithm to be used on networks
which have causal structure allowing them to be embedded in Lorentzian
manifolds. The method is demonstrated by calculating embeddings for both causal
sets and citation networks in Minkowski spacetime. We finally suggest a number
of applications in citation analysis such as paper recommendation, identifying
missing citations and fitting citation models to data using this geometric
approach.

该研究提供了一种将有向无环图嵌入到闵可夫斯基时空中的方法，使用了多维标度（MDS）技术进行几何分析，并探讨了在引用网络分析中的应用， 如论文推荐和识别缺失引用。