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1 Introduction
Lie Groups for 2D and 3D Transformations
Ethan Eade
1
Introduction
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Why use Lie groups for robotics or computer vision?
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Lie algebras and other general properties
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SO(3): Rotations in 3D space
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Representation
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Exponential Map
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Adjoint
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Jacobians
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Gaussians in SO(3)
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Sampling
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Composition of uncertain rotations
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Bayesian combination of rotation estimates
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Extended Kalman Filtering in SO(3)
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SE(3): Rigid transformations in 3D space
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Representation
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Exponential Map
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Adjoint
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Jacobians
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SO(2): Rotations in 2D space
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Representation
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Exponential Map
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Adjoint
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SE(2): Rigid transformations in 2D space
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Representation
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Exponential Map
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Adjoint
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Sim(3): Similarity Transformations in 3D space
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Representation
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Exponential Map
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Adjoint
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Interpolation
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Uncertain Transformations
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Sampling
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Transforming
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Distribution of Inverse
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Projection through Group Actions
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Computing Moments from Samples
About this document ...
Ethan Eade 2012-02-16
