Kernel methods on Riemannian manifolds
Richard Hartley, Sadeep Jayasumana, Mehrtash Harandi, Mathieu Salzmann
Hongdong Li, Khurrum Aftab
Oxford, March 2014
Image from http://en.wikipedia.org/wiki/File:Tangentialvektor.svg
Exponential map. Set out in a given direction and see where you get to.
Logarithm map. What direction do I need to go to get from X to Y ?
xy
Kernels on Positive Definite Matrices
Example: Kernel Dictionary Learning on Manifolds
Harandi et al (ICCV 2013)
Planes through the origin
Projective space – lines through the origin
Atul Kanaujia
Guillaume Charpiat
Shape Manifold.Captures the configuration of a set of points, allowing for rotation, translation and scaling.
The Hopf Fibration – the realization of CP1 as a fibration
Leaf Database
Acknowledgements.
This talk deals with work done by myself and my collaborators, particularly
1. Mehrtash Harandi2. Sadeep Jayasumana3. Mathieu Salzmann4. Hongdong Li5. Brian Lovell
The End