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Basic Mathematical Toolsfor
Imaging and Visualization
Dr. Tobias Lasser
November 3rd, 2011
http://campar.in.tum.de/Chair/TeachingWs11BasicMathTools
Computer Aided Medical Procedures (I-16)
Technische Universitt Mnchen
http://campar.in.tum.de/Chair/TeachingWs11BasicMathToolshttp://campar.in.tum.de/Chair/TeachingWs11BasicMathToolshttp://campar.in.tum.de/Chair/TeachingWs11BasicMathTools
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Basic Mathematical Tools for Imaging and Visualization - Tobias
Lasser
Admin Mid-term exam
- Tuesday, December 13th, 2011, start:16:15- duration: 60 or 90
minutes
- location: MW 0350
Final exam- Thursday, February 9th, 2012, start: 17:15
- duration: 90 minutes- location: tba
allowed material: one handwritten DIN A4 page (or US letter)
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Basic Mathematical Tools for Imaging and Visualization - Tobias
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So far...0. Introduction
1. Linear Algebra
1.1. Three-dimensional space
1.2. Linear spaces
1.3. Bases
1.4. Linear mappings and matrices
1.5. Linear systems and matrices
1.6. Application: Series Expansion Method
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Original
Measurements
Reconstruction
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Basic Mathematical Tools for Imaging and Visualization - Tobias
Lasser
Today0. Introduction
1. Linear Algebra
1.1. ...
1.4. Linear mappings and matrices
1.5. Linear systems and matrices
1.6. Application: Series Expansion Method
1.7. Orthogonality
1.8. Change of basis1.9. Solving linear systems
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R N)
,
:R
R
R
,
,
:=
=
= (),= () R
: R R, :=,.
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= . . .
() =
=, . . . ,
(+) = ()
=
a3x=y
3
a2x=y
2
a1x=y
1
x0=0
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R
= cos sin sin cos
,
=
cos sin sin cos
cos sin sin cos
=
= ,
(cos ) + (sin ) = det() =
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R , > R = R
=
.
= = = =
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R ||
=|| = , . . . ,
= ,
R R
= = = =
R
= ,
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R R
R
= .
= =
R > R R
= =
R
=
=
R
R()
,
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Thank you for your attention!
