Документ взят из кэша поисковой машины. Адрес оригинального документа : http://imaging.cs.msu.ru/pub/2012.Graphicon.Pavelyeva.Iris.ru.pdf Дата изменения: Mon Aug 11 15:26:58 2014 Дата индексирования: Sat Apr 9 23:25:08 2016 Кодировка:

.. .. , , E-mail: paveljeva@yandex.ru


. . . . . , , . , , . : , , , , .

, . , . . , .

2.
­ , , . (. 1) [4].

. 1.

1.
- , [1-4]. . [1] . . . , , . [4] . . , , . «» . , [5] . ,

, , . box-, .. 16 в 16 (. 2()). (. 2()), (leveling) (. 2()).
()

()

()

()

. 2. : () ; () ; () ; ( ) .


3.
, [4]. [6] :
( -1) e
n n x -
2

. y = 3 .

n ( x, ) =

2 n!

x H n ( ) , n = 0,1,2,3,... ,



H n ( x ) - :

H 0 ( x) = 1, H 1 ( x) = 2 x, H n ( x) = 2 x H n -1 ( x) - 2 (n - 1) H

n-2

( x).

(. 3) :



m, n

( x, y, x , y ) = m ( x, x ) n ( y, y ).

. 5. 2,0 ( x, y, x , y ) , y = 3 ,

x = 1 , x = 3 , x = 5 , x = 7 , x = 10 .
. 3.
1,0

2,0 :
( x, y )



2, 0

.

F ( x 0 , y 0 ) = I ( x, y )

(

2, 0

)

( x0 , y0 )

.

. m,0 .

2,0 ( x, y,3, 3) , k = 3 (. 6). N ( N 150 ) .



1,0

,

( OX), .. , . . 4 , 1,0 p = 10 , - , - p = -10 . () ( ) . 4: () ; () 1,0 ( x, y, x , y ) p = 10 - p = -10 , x = 3,
y

. 6. , 2, 0 ( x , y , x , y ) ,

x = 3, y = 3 .

4.



= 3.

[7, 8] «» . f ( x, y ) g ( x, y) , M в N F (u, v) G (u, v) . F (u, v) G (u, v)

R
( )
2,0

FG

(u , v) =

F (u , v) G (u , v) F (u , v) G (u , v)

=e

i ( F ( u ,v ) -G ( u ,v ))

,



. . 5 , 2,0 . . 5

.. , F G . ­ (POC-):


POC

fg

( x, y ) = F

-1

[R

FG

(u , v )] .

POC, , .

«» POC- , «» , . « », POC- . [5] L2 ( R2 )

5.
, . 8 x в 8 y , .. , 2,0 ( x, y, x , y ) . (1) i , j . ( m n ) x y .



m,n

( x, y ) ,







[9]. :
- x
2 2

n ( x, ) =

1 2n n!

e 2 H n ( ) , n = 0,1,2,3,... .

x



:

x = x , y = y . [10]
n ( x, )



m, n

( x, y, x , y ) = m ( x, x ) n ( y, y ).

f ( x, y ) g ( x, y ) D = [- A, A]в [- B, B] , R 2 \ D ij ( x, y ), i = 0, m, j = 0, n

[-

[-

2n + 1, 2n + 1 .

( 2 n + 1 + 1), ( 2 n + 1 + 1)

]

]







~ f ( x, y ) f ( x, y ) =


i =0 j =0

m

n

n ( x, ) . m ,

cij ij ( x, y, x , y ) ,

(1)

[-

2 ( 2n + 1 + 1), 2 ( 2n + 1 + 1) = - ( 2m + 1 + 1), ( 2m + 1 + 1)

][

]



c

i, j

=


R2

: m = 4n + 2 + 2 2n + 1 . , m = 0, 1,..., 15, n = 0, 1, 2, 3, 4 . 40 5 , .. , ±28°. . HPPOC- k=3, , . . 7-9.
()

f ( x, y )

i, j

( x, y , x , y ) dxdy.

~ ~ f ( x, y ) g ( x, y ) . ±1, ± i :
F ( n ) = (-i ) n n . , :
~ F[ f ] = F


i =0 j =0

m

n

c ij ij ( x, y) =


i = 0 j =0

m

n

c ij (-i )

i+ j

ij ( x, y).

HPPOC fg ( x, y ) = F-1[ RFG (u , v)] : f ( x, y ) = F
-1

()

[F

(u , v)] = F [F ( -u,-v)] .

[5] , , . , HPPOC ( POC), HPPOC ( ).

()

()

()

. 7. : (), () . ; () () ; () ; () HPPOC- .


(. 7) HPPOC. (. 8) HPPOC.

. 8. ( ) .

. 10 , . 9, - . , ­ . , . ( ). , , .

. 9 . , . ­ , . , k HPPOC- , .

. 10. .

6.
CASIA-IrisV3 [11]. CASIA, 20 : 224 , 40 M 1 ,...M 40 ( 20 ). . «» ( ) . 1 . 11. · ­ «» d , .. . () ­ ( ), . () ­ I (II) , , «» d .
d inner outer
FAR (%) FRR (%)

k =2

k = 3 - 6.

·

k =4
. 9. k .

·

[4] . , , , (. 10). , , .

0
0 42615 0 10.7

1
0 4771 0 0.8

2
4 362 0.18 0.05

3
2 22 0.27 0.004

4
15 2 0.96 0

5
13 0 1.5 0

...
0

0

1. .


EER (Equal Error Rate), EER ­ , I II . EER 0.1% «» d = 2 . . 11 OX «» d , OY ­ , «» ( ) [12].

[7] K. Miyazawa, K. Ito, T. Aoki, K. Kobayashi, H. Nakajima. A Phase-Based Iris Recognition Algorithm, LNCS (ICB 2006), No. 3832, p. 356--365, 2006. [8] S. Nagashima, K. Ito, T. Aoki, H. Ishii, K. Kobayashi. High Accuracy Estimation of Image Rotation using 1D PhaseOnly Correlation, IEICE Trans. Fund. v.E92-A, p.235 243,2009. [9] A. Krylov, D.Korchagin. Fast Hermite Projection Method, LNCS, v.4141, p.329-338, 2006. [10] .. . , . , , . 2, 1979. [11] CASIA-IrisV3 database. http://www.cbsr.ia.ac.cn/IrisDatabase.htm. [12] J. Daugman. How iris recognition works, IEEE Transactions on Circuits and Systems for Video Technology, Vol. 14. No. 1. P. 21­30, 2004.

Hermite Projection Phase-Only Correlation Method in Iris Key Points Abstract
. 11. .

7.
. , . , . , , . -72.2001.9 10-07-00433.

The Hermite projection phase-only correlation method in iris key points has been proposed. The local information of areas around key points is used for key points matching. The iris key points are selected using the Hermite transform. The Hermite projection phase-only correlation of areas around taken key points is calculated for key points matching. The correlation is calculated using Hermite projection method of expansion of intensity functions into series of Hermite functions. In case of small local images the proposed method allows avoid errors of Phase-Only Correlation method like Gibbs effect. The proposed method is robust to eyelids, eyelashes, glares and local shifts of parts of images.
Keywords: iris recognition, phase only correlation, Hermite functions, key points, biometrics.

8.
[1] L. Yu, D. Zhang, K. Wang. The relative distance of key point based iris recognition, Pattern Recognition, vol. 40, 2, p. 423-430, 2007. [2] K. Hollingsworth, K. Bowyer, P. Flynn. The Best Bits in an Iris Code, IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 31, no. 6, pp. 964-973, June 2009. [3] L. Ma, T. Tan, Y. Wang, and D. Zhang. Efficient iris recognition by characterizing key local variations, IEEE Transaction on Image Processing, vol. 13, no. 6, p. 739­750, 2004. [4] . . , . . . , , .5, .1, 2011, .68-72 [5] . . , . . . , GraphiCon'2011, , 2011, . 188-191. [6] J.-B. Martens. The Hermite transform-theory, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38. no. 9. p. 1595­1606, 1990.


­ .

About the author
Elena A. Pavelyeva is an assistant of Chair of Mathematical Physics of Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University. E-mail: paveljeva@yandex.ru