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

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 …

One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a
shape descriptor that would maintain invariance under a wide class of transformations the …

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

This paper introduces a method to extract 'Shape-DNA', a numerical fingerprint or signature,
of any 2d or 3d manifold (surface or solid) by taking the eigenvalues (ie the spectrum) of its …

Proof: Suppose two distinct points have equal GPS values. Then their eigenfunctions have
equal value at these points. Thus given any function f, the eigenfunction expansion of f will …

Most attempts to represent 3D shapes for deep learning have focused on volumetric grids,
multi-view images and point clouds. In this paper we look at the most popular representation …

We present an explicit method to compute a generalization of the Fourier Transform on a
mesh. It is well known that the eigenfunctions of the Laplace Beltrami operator (Manifold …

One of the core tasks in social network analysis is to predict the formation of links (ie various
types of relationships) over time. Previous research has generally represented the social …

We introduce a family of signatures for finite metric spaces, possibly endowed with real
valued functions, based on the persistence diagrams of suitable filtrations built on top of …