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1 Introduction
Lie Groups for Computer Vision
Ethan Eade
1
Introduction
2
General Properties
2
.
1
Matrix Groups
2
.
2
Lie Algebra
2
.
3
Exponential Map and Logarithm
2
.
4
Interpolation on the Manifold
2
.
5
Adjoint Representation
2
.
6
Group Action on
3
SO(2)
3
.
1
Description
3
.
2
Lie Algebra
3
.
3
Exponential Map
3
.
4
Adjoint Representation
4
SE(2)
4
.
1
Description
4
.
2
Lie Algebra
4
.
3
Exponential Map
4
.
4
Adjoint Representation
5
Sim(2)
5
.
1
Description
5
.
2
Lie Algebra
5
.
3
Exponential Map
5
.
4
Adjoint Representation
6
Aff(2)
6
.
1
Description
6
.
2
Lie Algebra
6
.
3
Exponential Map
6
.
4
Adjoint Representation
7
SL(3)
7
.
1
Description
7
.
2
Lie Algebra
7
.
3
Exponential Map
7
.
4
Adjoint Representation
8
SO(3)
8
.
1
Description
8
.
2
Lie Algebra
8
.
3
Exponential Map
8
.
4
Adjoint Representation
9
SE(3)
9
.
1
Description
9
.
2
Lie Algebra
9
.
3
Exponential Map
9
.
4
Adjoint Representation
10
Sim(3)
10
.
1
Description
10
.
2
Lie Algebra
10
.
3
Exponential Map
10
.
4
Adjoint Representation
About this document ...
Ethan Eade 2012-02-16
