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Copyright 2012-2015 Manabu Kano. All rights reserved. 1
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Human Systems Lab., Dept. of Systems Science Graduate School of Informatics, Kyoto University
#1
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l l l l l l Computed Tomography l
Copyright 2012-2015 Manabu Kano. All rights reserved. 2
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Fourier 3
Jean Baptiste Joseph Fourier (17681830)
, 1822
1768 1795 1798 1802 1822 1827 1830 63
4
Copyright 2012-2015 Manabu Kano. All rights reserved. 3
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sin(1) 5
-2
-1
0
1
2 N=2
-2
-1
0
1
2
N=5
-2
-1
0
1
2
N=10
-2
-1
0
1
2
M=2
sin(2) 6
-2
-1
0
1
2
M=5
-2
-1
0
1
2
M=10
Copyright 2012-2015 Manabu Kano. All rights reserved. 4
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7
2 f(x)
(1) 8
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(2) 9
(3) 10
Copyright 2012-2015 Manabu Kano. All rights reserved. 6
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-2
-1
0
1
2 M=10
(4) 11
12
Copyright 2012-2015 Manabu Kano. All rights reserved. 7
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Outline 13
l l l l l l Computed Tomography l
(1) 14
Copyright 2012-2015 Manabu Kano. All rights reserved. 8
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(2) 15
(3) 16
Copyright 2012-2015 Manabu Kano. All rights reserved. 9
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(4) 17
18
2 f (x) g(x)
f (x) g(x)
a b aTb = 0
ab
Copyright 2012-2015 Manabu Kano. All rights reserved. 10
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1. 0 2. 0
19
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l l l l l l Computed Tomography l
Copyright 2012-2015 Manabu Kano. All rights reserved. 11
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(1) 21
f (x) cos mx
(2) 22
Copyright 2012-2015 Manabu Kano. All rights reserved. 12
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Outline 23
l l l l l l Computed Tomography l
24
2L f(x)
an =1
L
Z 2L
0f(x) cos
nx
L
dx
bn =1
L
Z 2L
0f(x) sin
nx
L
dx
Copyright 2012-2015 Manabu Kano. All rights reserved. 13
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25
f (x)
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l l l l l l Computed Tomography l
Copyright 2012-2015 Manabu Kano. All rights reserved. 14
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Computed Tomography CT 27
CT
CTXX
http://www.toshiba-medical.co.jp/tmd/products/ct/index.html
CT 28
X),( yxf
),( XR
f (x,y)
R(X,)
),( wvG
X y
x
Copyright 2012-2015 Manabu Kano. All rights reserved. 15
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Outline 29
l l l l l l Computed Tomography l
30
1. M = 2, 5, 10 f (x)
2.
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