kernel methods on manifolds - australian national...
TRANSCRIPT
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Kernel Methods on Manifolds
Richard Hartley, Sadeep Jayasumana, Mehrtash Harandi, Mathieu Salzmann
Hongdong Li, Khurrum Aftab, Fatih Porikli Conrad Sanderson
CVPR-2017
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Optimization methods on Manifolds. • Rotation averaging (SO3) • Weiszfeld Algorithm on Riemannian
manifolds • General IRLS algorithms on manifolds
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Kernel SVM
Linear and Kernel SVM
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Flatten out the meridians
(longitude lines)
Azimuthal Equidistant Projection
Angle-axis representation of Rotations
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Azimuthal Equidistant Projection
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Tissot Indicatrix – shows distortion
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Kernels on Positive Definite Matrices
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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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Leaf Database
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Radial kernels on n-sphere
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Schoenberg’s result
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Radial kernels on n-sphere
• As i increases ki rapidly approaches either k-1 or k-2. • Therefore, the infinite series can be closely approximated with
a finite sum. • Readily fits in to a Multiple Kernel Learning (MKL) framework!
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Extending to other manifolds • Grassmann manifold with Projection
distance
• Shape manifold with full Procrustes distance
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Hand sketch recognition
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Face & action recognition
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Shape recognition
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Acknowledgements. This talk deals with work done by myself and my collaborators, particularly
• Mehrtash Harandi • Sadeep Jayasumana • Mathieu Salzmann • Hongdong Li • Brian Lovell • Fatih Porikli
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NICTA : 9 Maryland : 7 Florida state : 6 University of Florida : 6 John Hopkins : 2 INRIA : 1
Papers in the last 3 years at top 3 vision conferences on Riemannian manifolds.
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The End