Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare
in a geometrically faithful way point clouds and more generally probability distributions. The …

This monograph reviews both the theory and practice of the numerical computation of
geodesic distances on Riemannian manifolds. The notion of Riemannian manifold allows …

Training on large-scale graphs has achieved remarkable results in graph representation
learning, but its cost and storage have attracted increasing concerns. Existing graph …

We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a
novel and theoretically-supported paradigm for large-scale graph analysis. The proposed …

This paper discusses certain modifications of the ideas concerning the Gromov–Hausdorff
distance which have the goal of modeling and tackling the practical problems of object …

The computer vision and pattern recognition communities have recently witnessed a surge
of feature-based methods in object recognition and image retrieval applications. These …

Many shape and image processing tools rely on computation of correspondences between
geometric domains. Efficient methods that stably extract" soft" matches in the presence of …

A common operation in many geometry processing algorithms consists of finding
correspondences between pairs of shapes by finding structure‐preserving maps between …

Informative and discriminative feature descriptors play a fundamental role in deformable
shape analysis. For example, they have been successfully employed in correspondence …

In this paper, the problem of non-rigid shape recognition is studied from the perspective of
metric geometry. In particular, we explore the applicability of diffusion distances within the …