When generalizing schemes for real-valued data approximation or decomposition to data
living in Riemannian manifolds, tangent space-based schemes are very attractive for the …

We consider the classification problem and focus on nonlinear methods for classification on
manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold …

We propose a variational formulation for dimension reduction on Riemannian manifolds.
The algorithm is developed based on the level set method together with a recently …

This thesis develops theory and algorithms for a Riemannian geometric approach to inverse
problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated …

In this thesis, we propose new methods for dimension reduction based on differ-ential
geometry, that is, finding a representation of a set of observations in a space of lower …

The primary goal of this thesis is development of an algorithm for accurate object recognition
in a given image based on its statistical model of shape. A common approach to this …