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