Keynote lecture 2: “Riemannian manifolds, kernels and learning”

Summary form only given. I will talk about recent results from a number of people in my group on Riemannian manifolds in computer vision. In many Vision problems Riemannian manifolds come up as a natural model. Data related to a problem can be naturally represented as a point on a Riemannian manifold. This talk will give an intuitive introduction to Riemannian manifolds, and show how they can be applied in many situations. Manifolds of interest include the manifold of Positive Definite matrices and the Grassman Manifolds, which have a role in object recognition and classification, and the Kendall shape manifold, which represents the shape of 2D objects. Of particular interest is the question of when one can define positive-definite kernels on Riemannian manifolds. This would allow the application of kernel techniques of SVMs, Kernel FDA, dictionary learning etc directly on the manifold.