バイオメトリクス授業資料 iwatawiki lec01 s

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2016/9/26 13:00-14:45

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h0p://www.new-fukushima.jp/archives/4992.html

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“On Growth and Form” D’Arcy Thompson

…

→

– 

– 

– 

8

…

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→

9

10

y(t) = c

_n

cos ^2nπt

T ^{+ d}

ⁿ

^sin

2nπt

T

#

$ % ^&

' (

i= 0

∑

N

= →

t y

11

∑

∞

=

+

+

=

1

0

( cos sin )

) 2

(

n

n

n

^{nx b nx}

a a

x

f

∫

∫

=

=

π π

π

π

2 0

2 0

sin ) 1 (

cos ) 1 (

nxdx x f b

nxdx x

f a

n n

12

) ( ) 2 (

) 2 ( 1

) 0 ( ) 1 (

x f x f

x x x

f

= +

⎩⎨

⎧

≤ <

−

≤ <

= π

π π

π

0 2 4 6 8 10

-1.00.01.0

x

f(x)

0 2 4 6 8 10

-1.00.01.0

x

f1(x)

x x f1( ) ⁴sin

=π

0 2 4 6 8 10

-1.00.01.0

x

f3(x)

x x

f sin5

5 ) 4

3( = _π

0 2 4 6 8 10

-1.00.01.0

x

f2(x)

x x

f sin3

3 ) 4

2(

= π

0 2 4 6 8 10

-1.00.01.0

x

f4(x)

x x

f sin7

7 ) 4

4( = _π

0 2 4 6 8 10

-1.00.01.0

x

f1(x)+f2(x)

0 2 4 6 8 10

-1.00.01.0

x

f1(x)+f2(x)+f3(x)+f4(x)

0 2 4 6 8 10

-1.00.01.0

x

f1(x)+f2(x)+f3(x)

f (x) =⁴ π^{sin x +}

4 3π^{sin 3x +}

4 5π^{sin5x +}

4

7πsin 7x + ... = ⁴

(2k−1)π^{sin(2k−1)π}

k =1

∞

∑

●

●

y(t) = c₁cos^2πt T ^{+ d1sin}

2πt T

y(t) = c1cos^2πt T^{+ d1sin}

2πt T +....+ c5cos^10πt

T ^{+ d5sin} 10πt

T

y(t) = c₁cos^2πt T^{+ d1sin}

2πt T +....+ c10cos^20πt

T ^{+ d10sin} 20πt

T

y(t) = c₁cos^2πt T^{+ c1sin}

2πt T +....+ c40cos^80πt

T ^{+ d40sin} 80πt

T

  2 =7 2

( 2 ( 2

2 8

N = 1 N = 5 N = 10

N = 20 N = 40 N = 80

●

●

15

3 a₁=1, b₁=0, c₁¹⁶ =0

a

_n

b

_n

c

_n

(

17

a_n

b_n c_n

77

PC1 PC2

PC1=1.2 PC2=0.8

18

PC1=1.2 PC2=0.8 PC2

PC1

19

Pictured by Dr. Satoshi Niikura

20

6×6

∑

=

⎟⎠

⎜ ⎞

⎝

⎛ +

= N

i n

n T

nt b T nt a t x

0 sin2 cos2 )

( ^{π π}

∑₌^⎜_⎝^{⎛ + ⎟}_⎠^⎞

= N

i n

n T

d nt T c nt t y

0 sin2 cos2 )

( ^{π π}

SHAPE

h0p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/

21

RGB 256 2

22

∑

=

= Δ

p

i i

p

^t

t

1

t

K

T ₌

→

∑

^∞

=

⎟ ⎠

⎜ ⎞

⎝

⎛ +

=

1

sin 2

cos 2

)

(

n

n

n

T

t

d n

T

t

c n

t

y ^{π π}

2 )

2 cos

2

₁

(cos

1 2

2

∑

=

−

−

Δ

Δ

=

K

p

p p

p p

n

T

t

n

T

t

n

t

y

n

c T ^{π π}

π

2 )

2 sin

2

1

(sin

1 2

2

∑

=

−

−

Δ

Δ

=

K

p

p p

p p

n

T

t

n

T

t

n

t

y

n

d T ^{π π}

π

Kuhl and Giardina (1982)

... ²³

1

⎥ ⎦

⎢ ⎤

⎣

⎡

−

+ −

= +

₂

1 2 1 2 1 2 1

1 1 1 1 1

)

(

arctan 2

2

1

d

b

c

a

d

c

b

θ a

⎥ ⎦

⎢ ⎤

⎣

⎥ ⎡

⎦

⎢ ⎤

⎣

⎡

= −

⎥ ⎦

⎢ ⎤

⎣

⎡

1 1

1 1

1 1

1 1

* 1

* 1

* 1

* 1

cos

sin

sin

cos

d b

c a d

b c a

θ

θ

θ

θ

* 1

* 1 1

^arctan

a

= c

ψ

1

1

E*

2

* 1 2

*

* ^a

1

^c

E _{= +}

⎥ ⎦

⎢ ⎤

⎣

⎡

⎥ −

⎦

⎢ ⎤

⎣

⎥ ⎡

⎦

⎢ ⎤

⎣

⎡

= −

⎥ ⎦

⎢ ⎤

⎣

⎡

1 1

1 1

1 1

1 1

*

*

*

*

*

*

*

*

cos

sin

sin

cos

cos

sin

sin

cos

*

1

θ

θ

θ

θ

ψ

ψ

ψ

ψ

n

n

n

n

d

b

c

a

d E

b

c

a

n n

n n

n n

n n

... ²⁴

h0p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/ 25

73.9%

14.2%

3.9%

1.9%

78.9%

10.3%

5.6%

3.8%

h0p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/ 26

27

28

↓ ↓

0

2

2 2 0 ) 2 2 ₂₉

30

… T ... C ... T ... A ... G ... C ... T ...

… A ... G ... C ... A ... G ... T ... T ...

… T ... C ... C ... A ... A ... C ... G ...

… A ... C ... C ... A ... G ... C ... G ...

… T ... C ... T ... C ... A ... C ... G ...

… T ... C ... T ... C ... A ... T ... T ...

… A ... C ... C ... C ... G ... C ... T ...

… A ... G ... T ... C ... A ... C ... T ...

•  ^DNA

8

• 

DNA

31

−0.20 −0.15 −0.10 −0.05 ^{0.00 0.05 0.10 0.15}

−0.02−0.010.000.010.02

PC1

PC2

2

=7

( 2 2 ³²

1

DNA

DNA

33

x

y = f (x)

\\\

_x

y

273 142

304

423 173 373 234 138

203133 223

y = _{f (x)}

GS

PLS

x ₁

x ₂

x ₃

x ₄

y ₁

t ₁

t ₂

y ₂

y ₃

y ₄

s ₁

s ₂

77

DNA

36,901

PLS

φ

1

x ^y

1

t₁

t₂

y

₂

y

₃

y

₄

s₁

s₂

φ

2

_x

φ

3

x

φ

4

x

x

PLS

input space)

x

feature space)

φ

x

y

_i

= x

_i^T

^w + e

_i

y

_i

= φ _(x

_i

)

^T

^w + e

_i

∞ 77

• 

• 

HP

(Yoshioka 2004)

(Goto 2005)

38

(Goto et al. 2005)

→

39

8.3 m tower

40

•  ^{3 4 AP3 AP5}

3 BP3

•  ^{70% 1 2}

AP1 AP2 AP3, AP5,

BP3 9.5%

• 

Table 4. Estimation of parameters in regresssion models.

Variables Estimate SE t P(Prob>|t|)

AP3 -21.214 5.549 -3.820 0.0003

AP5 -41.990 14.138 -2.970 0.0040

BP3 -38.009 18.649 -2.040 0.0452

Area 0.013 0.002 5.250 <0.0001

Weight -16.181 5.998 -2.700 0.0087

41

42

43

CG

PC1 (42.09%) PC2 (37.81%)

CG

-2 s.d. +2 s.d.

PC1:

PC :

44

0

100

0

100

P = 0.31, n = 24

P = 0.57, n = 28

0

100

0

100

P < 0.02, n = 45

P = 0.33, n = 26 PC1: mean-2s.d. vs. mean+2s.d. PC2: mean-2s.d. vs. mean+2s.d.

Training Training

±2 95

PC1 PC2

Results of two-tailed binomial tests

45

0

100 P = 1, n = 28

P = 0.52, n = 22

0

100

P < 0.02, n = 38

P < 0.04, n = 25

0

100

0

100

PC1: mean-4s.d. vs. mean+4s.d. PC2: mean-4s.d. vs. mean+4s.d.

Training Training

±4

PC1

PC2

Results of two-tailed binomial tests

46

Contour density /

Dafni and Neal, 1997; Dafni et al., 1997

Contour density

Contour Density P < 0.02, n = 38

0

100

P < 0.04, n = 25

0

100 PC1: mean-4s.d. vs. mean+4s.d.

Training Training

Contour density 7.468 1.876

47

• 

―

•  ^{( )}

•  ^(2003/06)

•  ISBN-10: 4320017382

•  ISBN-13: 978-4320017382

www.amazon.co.jp

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