Abstract The Gromov-Hausdorff (GH) distance is traditionally used for measuring distances
between metric spaces. It was adapted for non-rigid shape comparison and matching of …

In this work, we propose computational models and algorithms for point cloud registration
with nonrigid transformation. First, point clouds sampled from manifolds originally embedded …

In this paper, we propose a spectral method for deriving functions that are jointly smooth on
multiple observed manifolds. This allows us to register measurements of the same …

Given a set of signals, a classical construction of an optimal truncatable basis for optimally
representing the signals, is the principal component analysis (PCA for short) approach …

Representing a signal as a linear combination of a set of basis functions is central in a wide
range of applications, such as approximation, de-noising, compression, shape …

We propose a method to simultaneously compute scalar basis functions with an associated
functional map for a given pair of triangle meshes. Unlike previous techniques that put …

A classical approach for surface classification is to find a compact algebraic representation
for each surface that would be similar for objects within the same class and preserve …

During the last decade the trend in image analysis has been to shift from axiomatically
derived measures into ones that are extracted empirically from data samples. The problem is …

We discuss optimal L 2-approximations of functions controlled in the H 1-norm. We prove
that the basis of eigenfunctions of the Laplace operator with Dirichlet boundary condition is …

In this chapter, we give an overview of part of our previous work based on the minimal
geodesic path framework and the Eikonal partial differential equation (PDE). We show that …