1999 - a - . ) 2003 ( , - , , , . ) ( . , . " MATLAB . . . , . '
, . - b - [1] Anil. K. Jain, Fundamentals of Digital Image
Processing, Prentice Hall Englewood Cliffs, New-Jersy, 1989. [2]
Kenneth R. Castleman, Digital Image Processing, Prentice Hall
Englewood Cliffs, New-Jersy, 1996. [3] Brend Jahne, Digital Image
Processing Concepts, Algorithms, and Scientific Applications,
Springer Verlag, 1995. [4] Boaz Porat, A Course In Digital Signal
Processing, Wiley, New-York, 1997. [5] Dan E. Dudgeon and Russell
M. Mersereau, Multi-Dimensional Digital Signal Processing,
Prentice-Hall, Englewood-Cliffs, New Jersey, 1984. [6] George
Wolberg, Digital Image Warping, IEEE Computer Society Press,
Los-Alamitos California, 1990. [7] Nahum Kiriati, Doron Shaked, and
Nir Sochen, Lecture Notes in Digital Image Processing, The
Computer-Science Department, The Technion, Israel Institute of
Technology (Obtained by personal communication). [8] Alfred M.
Bruckstein, Image Processing Lecture Notes, the Computer Science
Department, The Technion, Israel Institute of Technology. [9]
Michael Lindenbaum, Lecture Notes in Digital Image Processing, The
Computer-Science Department, The Technion, Israel Institute of
Technology. Web-site: http://www.cs.technion.ac.il/~mic/isp.html
[10] Hagit Zabrodzki Hel-Or, Lecture Notes in Image Processing, The
Computer-Science Department, Haifa University. Web-site:
http://cs.haifa.ac.il/courses/image_p. . - c - 1 . 11.1 .......
21.2 \ .... 51.3 .... 81.4 ..101.5 ..11 2 - .... 152.1 - ..152.2 -
.....192.3 - ..232.4 .. ..252.5 ...292.6 (DFT) .39 3 . ... ..413.1
- .413.2 ........443 . 3 ...463.4 - .....51 4 . ... ..554.1 .554.2
- ......593 . 4 ......674.4 ...... 71 - d - 5 .. 755.1 .765.2
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1226.4 MAP .1256.5 1326.6 140 7 - . ... 1437.1 - 1437.2 - DFT -
1487.3 - DCT - ..1517.4 Hadamard - .1567.5 Haar - Wavelet ..1607.6
..1687.7 Over-Complete 171 8 ... ..1758.1 . 1758.2 . ..1818.3 - ..
1848.4 - ... 1888.5 - 191 9 ... .. ... ... 1959.1 ... .1969.2 - .
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25712.1 .25812.2 .26112.3 ..26512.4 27112.5 ..27612.6 ..283 : ..285
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- . . D - : ( ) ( ) [ ] n , m f nD , mD f y , x f nD y , mD x = ==
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] [ ] 1 , 01 N , 0 1 M , 0 n , m : f N M 0 1 . D , , . . . 1.1 ,
1.3 . , , . [0,1] , . , - L 7.7191 7.6989 7.6783 7.6573 7.6358
7.6138 7.7411 7.7209 7.7003 7.6793 7.6578 7.6358 7.7626 7.7424
7.7218 7.7007 7.6793 7.6573 7.7836 7.7634 7.7428 7.7218 7.7003
7.6783 7.8043 7.7841 7.7634 7.7424 7.7209 7.6989 7.8244 7.8043
7.7836 7.7626 7.7411 7.7191 1.3 1 - - 5 - " - ( ) { } ] n , m [ f 1
2 round L . [0,1] [0, 1 2L ] . ) - .( ! , , . " " NM ) Pixel -
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- " , , , . . 2 - - 15 - 2 - 2 - ... ... ... .. ..152.1 - - ..152.2
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, , , , . - - . - . 2.1 - - , f(x,y) , H , " { } ) y , x ( f H ) y
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- 16 - H (x,y) f (x,y) . - , . , - , . ) , ( , , . - , - . H ) Y ,
X ( 0 0 , { } { } ) Y y , X x ( g ) Y y , X x ( f H ) y , x ( g ) y
, x ( f H 0 0 0 0 = = 2.1 : , , . : . { } ) 5 y , 2 x ( f 3 ) y , x
( f ) y , x ( f H + + = . , . . { } ) 5 y , 2 x ( f ) y , x ( g ) y
, x ( f ) y , x ( f H + + = ) g(x,y) ( . , . . { } ) 5 y , 2 x ( f
) y , x ( f ) y , x ( f H + = . . . { } 1 ) y , x ( f ) y , x ( f H
+ = . . . { } { } ) y , x ( f Log ) y , x ( f H = . . . { } { } ) y
, x ( f Log ) y , x ( g ) y , x ( f H = . , . H - ) Y y , X x ( 0 0
( )0 0 Y , X , y , x h . , - - ) ( , - ) Y , X ( 0 0. " , h . , (
)0 0 Y , X , y , x h , H . f(x,y) " 2 - - 17 -( ) ( ) = d d y , x ,
f ) y , x ( f H , f(x,y) " { } ( ) ( )( ) ( ) { }( ) ( ) == ==)` =d
d , , y , x h , fd d y , x H , fd d y , x , f H ) y , x ( f H , H {
} ( ) ( ){ } ( ) ( )( ) ( ) = = = = = d d , , Y y , X x h , f ) Y y
, X x ( g . 2) Y y , X x ( g d d , , y , x h Y , X f ) Y y , X x (
f H . 1d d , , y , x h , f ) y , x ( g ) y , x ( f H0 0 0 00 0 0 0
0 0 ( ) ( )( ) ) y , x ( h , , y , x h Y , X , y , x h , , Y y , X
x h : Y & , X , , , y , x 0 0 0 0 0 0 = + + = . , , . " { } ( )
( )( ) ( ) ) y , x ( h ) y , x ( f d d y , x h , fd d , , y , x h ,
f ) y , x ( f H = == = . 2.2 : , : 2 - - 18 - . { } ) 5 y , 2 x ( f
3 ) y , x ( f ) y , x ( f H + + = . " ) 5 y , 2 x ( 3 ) y , x ( ) y
, x ( h + + = . . { } ) 5 y , 2 x ( f ) y , x ( g ) y , x ( f ) y ,
x ( f H + + = , . " ) 5 y , 2 x ( ) y , x ( g ) y , x ( ) , , y , x
( h + + = , , ) x ( - ) y ( . ? , ) y , x ( ) y , x ( h ) , , y , x
( h = , { } ( ) ( )( ) ( ) ) y , x ( g ) y , x ( h ) y , x ( f d d
y , x ( ) y , x h , fd d , , y , x h , f ) y , x ( f H= = == = , "
. h . ) ( - - ) y ( h ) x ( h ) y , x ( h 2 1= . , " { } ( ) ( )( )
( ) = == = d d ) y ( h , f ) x ( h d d ) y ( h ) x ( h , fd d y , x
h , f ) y , x ( f H2 1 2 1 - f(x,y) , - , . f { } ( ) = d ) y ( h f
d ) x ( h ) ( f ) y , x ( f H 2 2 1 1 - . . , . , , . 2 - - 19 -2.2
- - ( ) { } { }dxdy ) vy ux ( 2 j exp ) y , x ( f ) y , x ( f F v ,
u Fx y + = = u - v . " { } ( ) { }dudv ) vy ux ( 2 j exp v , u F )
y , x ( f F ) y , x ( fu v1 + + = = ) ( -2L , - , . ) ( - 0 , . 2.1
. - , . F(u,v) - . (u,v) F(u,v) . , , . F(u,v)= { } ) y , x ( f F
f(x,y)1 ( ) y , x ( ) { } v Y u X 2 j exp 0 0 + ( )0 0 Y y , X x (
)0 0 V v , U u ( ) { }0 0 yV xU 2 j exp + ( ) { }2 2 v u exp + ( )
{ }2 2 y x exp + Sinc(u,v)=( )uv) v sin( u sin 4 ( ) y , x rect =1
for 1 y , x 1 Sinc(u,v) ) y , x ( rect ) y , x ( rect ) y , x ( tri
=( ) k j j u , k u ( ) k j j y , k x 2.1 - 2 - - 20 - - . - . 1 . :
f(x,y) F(u,v) , , . . . 2 . : , { } { } { } ) y , x ( f F ) y , x (
f F ) y , x ( f ) y , x ( f F : f , f , , 2 1 2 1 2 1 + = + 3 . : ,
{ } { } ) v , u ( * F ) y , x ( * f F ) v , u ( F ) y , x ( f F = =
) v , u ( * F ) v , u ( F = . 4 . : { } { } ) v , u ( F ) y , x ( f
F ) v , u ( F ) y , x ( f F = = 5 . : - . f(x,y) . , ( ) { } { }dx
ux 2 j exp dy vy 2 j exp ) y , x ( f v , u Fx y (((
= " , , - ( ) { } { } ) v ( F ) u ( F dy vy 2 j exp ) y ( f dx
ux 2 j exp ) x ( f v , u F 2 1y 2y 1 =(((
(((
= 2 - - 21 -6 . : " h(x,y) , " H(u,v)=F{h(x,y)} . { } ) yV xU (
2 j exp ) y , x ( f 0 0 + = , { }{ }{ } { }{ } ) V , U ( H ) yV xU
( 2 j expd d ) , ( h V U ( 2 j exp ) yV xU ( 2 j expd d ) , ( h ) V
) y ( U ) x (( 2 j expd d ) y , x ( h ) V U ( 2 j exp ) y , x ( g0
0 0 00 0 0 00 00 0 + == + + == + == + = , . , . 7 . : a - b , , { }
{ } abbv,auF) by , ax ( f F ) v , u ( F ) y , x ( f F |.|
\|= = 8 . : , { }{ } ( ) { }( ) { } { } ) V v , U u ( F ) y , x
( f yV xU 2 j exp F ) v , u ( F vY uX 2 j exp ) Y y , X x ( f F ) y
, x ( f F ) v , u ( F0 0 0 00 0 0 0 = + + = = 9 . : , , { }{ } { }
) v , u ( F ) v , u ( F ) y , x ( f ) y , x ( f F) y , x ( f F ) v
, u ( F ) y , x ( f F ) v , u ( F2 1 2 12 21 1= )`== , - , { }{ } {
} ) v , u ( F ) v , u ( F ) y , x ( f ) y , x ( f F) y , x ( f F )
v , u ( F ) y , x ( f F ) v , u ( F2 1 2 12 21 1 =)`== 2 - - 22 -10
. : - , + + = d d ) y , x ( f ) , ( f ) y , x ( f * ) y , x ( f 2 1
2 1 { }{ } { } ) v , u ( F ) v , u ( F ) y , x ( f ) y , x ( f F) y
, x ( f F ) v , u ( F ) y , x ( f F ) v , u ( F2 1 2 12 21 1 = )`==
, - . 11 . : , { } { } = = == = =u v*2 1 2 1x y*2 1 2 12 2 1 1dudv
) v , u ( F ) v , u ( F ) v , u ( F ), v , u ( Fdxdy ) y , x ( f )
y , x ( f ) y , x ( f ), y , x ( f) y , x ( f F ) v , u ( F , ) y ,
x ( f F ) v , u ( F { } = =u v2x y2dudv ) v , u ( F dxdy ) y , x (
f ) y , x ( f F ) v , u ( F ? " , 6 . f(x,y) ) ( (x,y) . -2L . . .
, " " , . " . " " " , , . 2 - - 23 -2.3 - " f(x,y) f[n,m] . , . .
f[m,n] , H , " { } ] n , m [ f H ] n , m [ g = . " { } { } { } ] n
, m [ f H ] n , m [ f H ] n , m [ f ] n , m [ f H 2 1 2 1 + = + . H
- ] N n , M m [ 0 0 ] N , M , n , m [ h 0 0. , ' 1 ' . " . " =k j ]
j n , k m [ ] j , k [ f ] n , m [ f H , f[m,n] " { } =)` =k j k j ]
j , k , n , m [ h ] j , k [ f ] j n , k m [ ] j , k [ f H ] n , m [
f H H , ] j n , k m [ h ] j , k , n , m [ h = . " { } ] n , m [ h ]
n , m [ f ] j n , k m [ h ] j , k [ f ] n , m [ f Hk j = = . 2.3 :
- . : = =Otherwise 0 1 n , m 0 1] n , m [ f ,Otherwise 0 1 n , m 1
1] n , m [ f 2 1] n , m [ g ] n , m [ f ] n , m [ f ] j n , k m [ f
] j , k [ f 2 1k j 2 1 = = " " 1f , - 2f . . 2 - - 24 - " . ,
g[0,0] - g[0,2] 2.1 . 4 1 1 1 1 ] 1 , 1 [ f ] 1 , 1 [ f ] 0 , 1 [ f
] 0 , 1 [ f ] 1 , 1 [ f ] 1 , 1 [ f ] 1 , 0 [ f ] 1 , 0 [ f ] 0 , 0
[ f ] 0 , 0 [ f ] 1 , 0 [ f ] 1 , 0 [ f ] 1 , 1 [ f ] 1 , 1 [ f ] 0
, 1 [ f ] 0 , 1 [ f ] 1 , 1 [ f ] 1 , 1 [ f] j 0 , k 0 [ f ] j , k
[ f ] 0 , 0 [ g2 1 2 1 2 12 1 2 1 2 12 1 2 1 2 1k j 2 1= + + + = +
+ + + + + + + = = = , g[0,2]=2 . " g[m,n]=f[m,n]h[m,n] . . ] n [ h
] m [ h ] n , m [ h 2 1= 2.4 : . 2.1 . . { } ] 5 n , 2 m [ f 3 ] n
, m [ f ] n , m [ f H + + = . , . ] 5 n , 2 m [ 3 ] n , m [ ] n , m
[ h + + = . . { } ] 5 n , 2 m [ f ] n , m [ g ] n , m [ f ] n , m [
f H + + = ) g[m,n] ( . , . ] 5 n , 2 m [ ] n , m [ g ] n , m [ ] n
, m [ h + + = . . { } ] 5 n , 2 m [ f ] n , m [ f ] n , m [ f H + =
. . :] n , m [ f ] n , m [ f21 2.1 . g[0,0]=4 ) ( - g[0,2]=2 )
(nmnm 2 - - 25 - . { } 1 ] n , m [ f ] n , m [ f H + = . . . { } {
} ] n , m [ f Log ] n , m [ f H = . . . { } { } ] n , m [ f Log ] n
, m [ g ] n , m [ f H = . , . . { } ] 5 . 0 n , 5 . 0 m [ f ] n , m
[ f H + + = , . FIR ) Finite Impulse Response ( . . FIR IIR )
Infinite Impulse Response ( . IIR . " , - , . , FIR , IIR . 2.4
f(x,y) f[m,n] " . " - . ( ) =m n y n , x m ) y , x ( f ] n , m [ f~
, , - tilde . { } ( ) ( ) { }( ) ( ) { }( ) { } + = = + = = + =m nm
n y xy m nxvn um j exp ] n , m [ fdxdy vy ux j exp n y , x m ) n ,
m ( fdxdy vy ux j exp n y , x m ) y , x ( f ] n , m [ f~F , -
f[m,n] 2 - - 26 -( ) { } { } + = = m n 2 1 D 2 1 ) n m ( j exp ] n
, m [ f ] n , m [ f F , F 1 -2 , . ] , [ + , ] , [ + , , . " ( ) {
} ( ) { } + + = = 2 1 2 1 2 122 11D d d ) n m ( j exp , F41, F F ]
n , m [ f . . . \ , . 1 . : f[m,n] ) , ( F 2 1 , , . . ) y , x ( f1
- ) y , x ( f2 , . , - . 2 . : , { } { } { } ] n , m [ f F ] n , m
[ f F ] n , m [ f m [ f F 2 D 1 D 2 1 D + = + 3 . : , { } { } ) , (
* F ] n , m [ * f F ) , ( F ] n , m [ f F 2 1 D 2 1 D = = , ) , ( *
F ) , ( F 2 1 2 1 = . 4 . : { } { } ) , ( F ] n , m [ f F ) , ( F ]
n , m [ f F 2 1 2 1 = = 2 - - 27 -5 . : - . , f[m,n] . , ( ) { } {
} ((
= n 2m 1 2 1 n j exp m j exp ] n , m [ f , F " , , - ( ) { } {
}((
((
= n 2 2m 1 1 2 1 n j exp ] n [ f m j exp ] m [ f , F 6 . : "
h[m,n] , " ( ) { } ] n , m [ h F , H D 2 1 = . { } ) nV mU ( j exp
] n , m [ f 0 0 + = , { } { } ) V , U ( H ) mV mU ( j exp ) V ) i n
( U ) k m (( j exp ] i , k [ h ] n , m [ g 0 0 0 0k i 0 0 + = + = ,
. , . 7 . : , { }{ } ( ) { }( ) { } { } ) V , U ( F ] n , m [ f nV
mU 2 j exp F ) , ( F M M j exp ) N n , M m ( f F ] n , m [ f F ) ,
( F0 1 0 1 0 0 D2 1 0 2 0 1 0 0 DD 2 1 = + + = = 8 . : , , { }{ } {
} ) , ( F ) , ( F ] n , m [ f ] n , m [ f F] n , m [ f F ) , ( F ]
n , m [ f F ) , ( F2 1 2 2 1 1 2 12 2 1 21 2 1 1 = )`= = , - , 2 -
- 28 -{ }{ } { } ) , ( F ) , ( F41] n , m [ f ] n , m [ f F] n , m
[ f F ) , ( F ] n , m [ f F ) , ( F2 1 2 2 1 122 12 2 1 21 2 1 1
=)`= = 9 . : - + + =k j 2 1 2 1 ] j n , k m [ f ] j , k [ f ] n , m
[ f * ] n , m [ f { }{ } { } ) , ( F ) , ( F ] n , m [ f * ] n , m
[ f F] n , m [ f F ) , ( F ] n , m [ f F ) , ( F2 1 2 2 1 1 2 12 2
1 21 2 1 1 =)`= = , - . 10 . : , { } { }2 1 2 1*2 2 1 122 1 2 2 1
1m n 2 1 2 12 D 2 1 2 1 D 2 1 1d d ) , ( F ) , ( F41) , ( F ), , (
F] n , m [ f ] n , m [ f ] n , m [ f ], n , m [ f ] n , m [ f F ) ,
( F , ] n , m [ f F ) , ( F = = = = = = { } 2 122 1 12m n2D 2 1 d d
) , ( F41] n , m [ f ] n , m [ f F ) , ( F = = 11 . : , ) , ( F 2 1
- 2 , | | | | + + , , . 2 - - 29 -2.5 [m,n] , . - f[m,n] { } 1 N n
0 , 1 M m 0 | ] n , m [ = NM . H " h[m,n,k,j] . " { } = =k j] j , k
, n , m [ h ] j , k [ f ] n , m [ f H ] n , m [ g . f[m,n] , MN . "
. column/row stack (lexicographic ordering) " \ . 2.2 . 2.2 ) ( ) (
{ } 1 N n 0 , 1 M m 0 | ] n , m [ = 1 2 3 4 5 6 7 8 9 10 11 12 13
14 15 16 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16
12345678910111213141516mn 1 Mn m i + + = Nm 1 n i + + = i 2 - - 30
- , . : H ) " h[m,n,k,j] ( . 1 1N M , 1 1N M . 2 2N M , 2 2N M . 2
2N M -1 1N M . - " . " - . - . ! - f , - H , f H f g H = . , , . -
i g - i H f , ==1 1N M1 kk k , i if g H . H ? ? . 2.5 : f[m,n] -
g[m,n] { } 1 n 0 , 1 m 0 | ] n , m [ = ) , 2 2 .( { } = =k j] j , k
, n , m [ h ] j , k [ f ] n , m [ f H ] n , m [ g . . - [0,0]
g[m,n] . " 2 - - 31 -| |(((((
== + + + == =] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f ] 1 ,
1 , 0 , 0 [ h ] 1 , 0 , 0 , 0 [ h ] 0 , 1 , 0 , 0 [ h ] 0 , 0 , 0 ,
0 [ h] 1 , 1 , 0 , 0 [ h ] 1 , 1 [ f ] 1 , 0 , 0 , 0 [ h ] 1 , 0 [
f ] 0 , 1 , 0 , 0 [ h ] 0 , 1 [ f ] 0 , 0 , 0 , 0 [ h ] 0 , 0 [ f]
j , k , 0 , 0 [ h ] j , k [ f ] 0 , 0 [ gk j H (((((
(((((
=(((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 1 , 1 , 1 , 1 [ h
] 1 , 0 , 1 , 1 [ h ] 0 , 1 , 1 , 1 [ h ] 0 , 0 , 1 , 1 [ h] 1 , 1
, 1 , 0 [ h ] 1 , 0 , 1 , 0 [ h ] 0 , 1 , 1 , 0 [ h ] 0 , 0 , 1 , 0
[ h] 1 , 1 , 0 , 1 [ h ] 1 , 0 , 0 , 1 [ h ] 0 , 1 , 0 , 1 [ h ] 0
, 0 , 0 , 1 [ h] 1 , 1 , 0 , 0 [ h ] 1 , 0 , 0 , 0 [ h ] 0 , 1 , 0
, 0 [ h ] 0 , 0 , 0 , 0 [ h] 1 , 1 [ g] 1 , 0 [ g] 0 , 1 [ g] 0 , 0
[ g , , - { } 1 n 0 , 2 m 0 | ] n , m [g = . " (((((
(((((((((
=(((((((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 1 , 1 , 1 , 2 [ h
] 1 , 0 , 1 , 2 [ h ] 0 , 1 , 1 , 2 [ h ] 0 , 0 , 1 , 2 [ h] 1 , 1
, 1 , 1 [ h ] 1 , 0 , 1 , 1 [ h ] 0 , 1 , 1 , 1 [ h ] 0 , 0 , 1 , 1
[ h] 1 , 1 , 1 , 0 [ h ] 1 , 0 , 1 , 0 [ h ] 0 , 1 , 1 , 0 [ h ] 0
, 0 , 1 , 0 [ h] 1 , 1 , 0 , 2 [ h ] 1 , 0 , 0 , 2 [ h ] 0 , 1 , 0
, 2 [ h ] 0 , 0 , 0 , 2 [ h] 1 , 1 , 0 , 1 [ h ] 1 , 0 , 0 , 1 [ h
] 0 , 1 , 0 , 1 [ h ] 0 , 0 , 0 , 1 [ h] 1 , 1 , 0 , 0 [ h ] 1 , 0
, 0 , 0 [ h ] 0 , 1 , 0 , 0 [ h ] 0 , 0 , 0 , 0 [ h] 1 , 2 [ g] 1 ,
1 [ g] 1 , 0 [ g] 0 , 2 [ g] 0 , 1 [ g] 0 , 0 [ g . " . H[m,n,k,j]
[m,n] - [m,n] . Mn 1 m i + + = . . " . ) (1H -2H . | |f f f g g f g
, f g2 1 2 12 12211 H H H H H + = + = + = = 2 - - 32 - . . , , , ,
f g g , f g1 212211 H H H = = = . " , 1 2 2 1 H H H . . , . ? ,
h[m,n,k,j]=h[m-k,n-j] . . 2.6 : 2.5 , : h[m,n,k,j]=h[m-k,n-j] . ) (
(((((
(((((
==(((((
(((((
=(((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 , 0 [ h ] 0 , 1
[ h ] 1 , 0 [ h ] 1 , 1 [ h] 0 , 1 [ h ] 0 , 0 [ h ] 1 , 1 [ h ] 1
, 0 [ h] 1 , 0 [ h ] 1 , 1 [ h ] 0 , 0 [ h ] 0 , 1 [ h] 1 , 1 [ h ]
1 , 0 [ h ] 0 , 1 [ h ] 0 , 0 [ h] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f]
0 , 0 [ f] 1 , 1 , 1 , 1 [ h ] 1 , 0 , 1 , 1 [ h ] 0 , 1 , 1 , 1 [
h ] 0 , 0 , 1 , 1 [ h] 1 , 1 , 1 , 0 [ h ] 1 , 0 , 1 , 0 [ h ] 0 ,
1 , 1 , 0 [ h ] 0 , 0 , 1 , 0 [ h] 1 , 1 , 0 , 1 [ h ] 1 , 0 , 0 ,
1 [ h ] 0 , 1 , 0 , 1 [ h ] 0 , 0 , 0 , 1 [ h] 1 , 1 , 0 , 0 [ h ]
1 , 0 , 0 , 0 [ h ] 0 , 1 , 0 , 0 [ h ] 0 , 0 , 0 , 0 [ h] 1 , 1 [
g] 1 , 0 [ g] 0 , 1 [ g] 0 , 0 [ g 2.5 : (((((
(((((((((
=(((((((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 , 1 [ h ] 0 , 2
[ h ] 1 , 1 [ h ] 1 , 2 [ h] 0 , 0 [ h ] 0 , 1 [ h ] 1 , 0 [ h ] 1
, 1 [ h] 0 , 1 [ h ] 0 , 0 [ h ] 1 , 1 [ h ] 1 , 0 [ h] 1 , 1 [ h ]
1 , 2 [ h ] 0 , 1 [ h ] 0 , 2 [ h] 1 , 0 [ h ] 1 , 1 [ h ] 0 , 0 [
h ] 0 , 1 [ h] 1 , 1 [ h ] 1 , 0 [ h ] 0 , 1 [ h ] 0 , 0 [ h] 1 , 2
[ g] 1 , 1 [ g] 1 , 0 [ g] 0 , 2 [ g] 0 , 1 [ g] 0 , 0 [ g 2 - - 33
- " 2 2 , 3 ) ( 2 . - , , 2.3 . - . , , ) .( , 1 1N M 2 2N M 2 2N M
1 1N M . -1 2N N 1 2M M , . (((((((((
a f g h ib a f g hc b a f gd c b a fe d c b a : . . . 2.7 : .
2.3 5 5 . 9 25 . " , - .3.0 1.0 0.8 0.0 1.0 3.0 1.0 0.8 0.8 1.0 3.0
1.0 0.0 0.8 1.0 3.0 2.0 1.0 0.5 0.0 1.0 2.0 1.0 0.5 0.5 1.0 2.0 1.0
0.0 0.5 1.0 2.0 7.4 5.8 4.1 1.3 5.5 8.4 6.3 4.1 4.1 6.3 8.4 5.5 1.3
4.1 5.8 7.4 =3.0 1.0 0.8 0.0 1.0 3.0 1.0 0.8 0.8 1.0 3.0 1.0 0.0
0.8 1.0 3.0 2.0 1.0 0.5 0.0 1.0 2.0 1.0 0.5 0.5 1.0 2.0 1.0 0.0 0.5
1.0 2.0 7.4 5.5 4.1 1.3 5.8 8.4 6.3 4.1 4.1 6.3 8.4 5.8 1.3 4.1 5.5
7.4 = 2 - - 34 - , . , . , . ] n [ h ] m [ h ] n , m [ h2 1= . .
2.8 : 2.6 ) ( , . (((((
(((((
=(((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 [ h ] 0 [ h ] 0
[ h ] 1 [ h ] 1 [ h ] 0 [ h ] 1 [ h ] 1 [ h] 0 [ h ] 1 [ h ] 0 [ h
] 0 [ h ] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h] 1 [ h ] 0 [ h ] 1 [ h ] 1
[ h ] 0 [ h ] 0 [ h ] 0 [ h ] 1 [ h] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h
] 0 [ h ] 1 [ h ] 0 [ h ] 0 [ h] 1 , 1 [ g] 1 , 0 [ g] 0 , 1 [ g] 0
, 0 [ g2 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 1
" ? (Kronecker) 2 2 (((((
((
((
((
((
==((
((
==(((((
] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h] 0 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0
[ h] 1 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h] 1 [ h] 0 [ h ] 1 [ h] 1 [
h ] 0 [ h] 0 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h] 0 [ h ] 1 [ h] 1 [
h ] 0 [ h] 0 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 0 [ h ] 1 [ h ]
1 [ h] 0 [ h ] 1 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 1 [ h ] 0 [
h] 1 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 0 [ h ] 0 [ h ] 0 [ h ] 1 [ h] 1
[ h ] 1 [ h ] 1 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 0 [ h ] 0 [ h1 11 121
11 121 11 121 11 121 11 12 22 22 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2
1 2 1 2 12 1 2 1 2 1 2 1 , =(((((((((
] 0 [ h ] 1 [ h ] 0 [ h ] 2 [ h ] 1 [ h ] 1 [ h ] 1 [ h ] 2 [ h]
0 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 0 [ h ] 1 [ h ] 1 [ h] 0 [
h ] 1 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h] 1 [ h ]
1 [ h ] 1 [ h ] 2 [ h ] 0 [ h ] 1 [ h ] 0 [ h ] 2 [ h] 1 [ h ] 0 [
h ] 1 [ h ] 1 [ h ] 0 [ h ] 0 [ h ] 0 [ h ] 1 [ h] 1 [ h ] 1 [ h ]
1 [ h ] 0 [ h ] 0 [ h ] 1 [ h ] 0 [ h ] 0 [ h2 1 2 1 2 1 2 12 1 2 1
2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 1
2 - - 35 -((((
((
=] 1 [ h ] 2 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h] 0 [ h ] 1 [ h] 1
[ h ] 0 [ h1 11 11 12 22 2 ) .( , 1 1N M 2 2N M 2 2N M 1 1N M . 1
2N N -1 2M M . , . " . , { } = = =k2j1k j] j n [ h ] j , k [ f ] k
m [ h ] j n , k m [ h ] j , k [ f ] n , m [ f H ] n , m [ g . ? , ,
. 2.9 : , f[m,n] , 2 2 , ((
=] 1 , 1 [ f ] 0 , 1 [ f] 1 , 0 [ f ] 0 , 0 [ ff , 3 2 . , , "
((((
=((
((
((((
] 1 , 2 [ g ] 0 , 2 [ g] 1 , 1 [ g ] 0 , 1 [ g] 1 , 0 [ g ] 0 ,
0 [ g] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h] 1 , 1 [ f ] 0 , 1 [ f] 1 , 0 [
f ] 0 , 0 [ f] 1 [ h ] 2 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h2 22 21
11 11 1 ) 2 2 ( " , . , . 2 - - 36 - . , , . . { } 1 N n 0 , 1 M m
0 | ] n , m [ = , : | | =otherwise N mod n , M mod m f1 N n 0 , 1 M
m 0 ] n , m [ f] n , m [ f 2.4 3 4 . ) ( ) ( , " = ==1 M0 k1 N0 jc]
N mod ) j n ( , M mod ) k m [( h ] j , k [ f ] n , m [ g . mod M M
/ m m M mod m = , - * . , m 0 M-1 , . , (M+1) mod M=1, M mod M=0 .
, -1 mod M=M , -2 mod M=M-1 , ' . , . , 2.4 . , 3 4 . 2 - - 37 -
2.10 : f[m,n] { } 1 n 0 , 1 m 0 | ] n , m [ = , g[m,n] { } 1 n 0 ,
2 m 0 | ] n , m [g = . . . - [0,0] g[m,n] . " | |(((((
== + + + == =] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f ] 1 ,
1 [ h ] 1 , 0 [ h ] 0 , 1 [ h ] 0 , 0 [ h] 1 , 1 [ h ] 1 , 1 [ f ]
1 , 0 [ h ] 1 , 0 [ f ] 0 , 1 [ h ] 0 , 1 [ f ] 0 , 0 [ h ] 0 , 0 [
f] 2 mod j , 2 mod k [ h ] j , k [ f ] 0 , 0 [ gk j H (((((
(((((((((
=(((((((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 , 1 [ h ] 0 , 0
[ h ] 1 , 1 [ h ] 1 , 0 [ h] 0 , 0 [ h ] 0 , 1 [ h ] 1 , 0 [ h ] 1
, 1 [ h] 0 , 1 [ h ] 0 , 0 [ h ] 1 , 1 [ h ] 1 , 0 [ h] 1 , 1 [ h ]
1 , 0 [ h ] 0 , 1 [ h ] 0 , 0 [ h] 1 , 0 [ h ] 1 , 1 [ h ] 0 , 0 [
h ] 0 , 1 [ h] 1 , 1 [ h ] 1 , 0 [ h ] 0 , 1 [ h ] 0 , 0 [ h] 1 , 2
[ g] 1 , 1 [ g] 1 , 0 [ g] 0 , 2 [ g] 0 , 1 [ g] 0 , 0 [ g , , . ,
(Block-Circulant) . , , " . . 2.5 . , - " - , - . , . =(((((
(((((((((
=(((((((((
] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 [ h ] 1 [ h ] 0
[ h ] 0 [ h ] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h] 0 [ h ] 0 [ h ] 0 [ h
] 1 [ h ] 1 [ h ] 0 [ h ] 1 [ h ] 1 [ h] 0 [ h ] 1 [ h ] 0 [ h ] 0
[ h ] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h
] 0 [ h ] 1 [ h ] 0 [ h ] 0 [ h] 1 [ h ] 0 [ h ] 1 [ h ] 1 [ h ] 0
[ h ] 0 [ h ] 0 [ h ] 1 [ h] 1 [ h ] 1 [ h ] 1 [ h ] 0 [ h ] 0 [ h
] 1 [ h ] 0 [ h ] 0 [ h] 1 , 2 [ g] 1 , 1 [ g] 1 , 0 [ g] 0 , 2 [
g] 0 , 1 [ g] 0 , 0 [ g2 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2
12 1 2 1 2 1 2 12 1 2 1 2 1 2 12 1 2 1 2 1 2 1 2 - - 38 -(((((
((
((((
=] 1 , 1 [ f] 1 , 0 [ f] 0 , 1 [ f] 0 , 0 [ f] 0 [ h ] 1 [ h] 1
[ h ] 0 [ h] 1 [ h ] 0 [ h] 0 [ h ] 1 [ h] 1 [ h ] 0 [ h1 11 12 22
22 2 - . - . . 2.11 : . , . , . . 2.5 5 5 . ) ( 9 , ) ( 5 . " - , -
.(((((((((
a e d c bb a e d cc b a e dd c b a ee d c b a (((((((((
a f g h ib a f g hc b a f gd c b a fe d c b a 3.0 1.0 0.8 0.0
0.0 3.0 1.0 0.8 0.8 0.0 3.0 1.0 1.0 0.8 0.0 3.0 2.0 1.0 0.5 0.0 0.0
2.0 1.0 0.5 0.5 0.0 2.0 1.0 1.0 0.5 0.0 2.0 6.4 5.0 4.1 1.3 1.3 6.4
5.0 4.1 4.1 6.3 6.4 5.0 5.0 4.1 1.3 6.4 =3.0 1.0 0.8 0.0 0.0 3.0
1.0 0.8 0.8 0.0 3.0 1.0 1.0 0.8 0.0 3.0 2.0 1.0 0.5 0.0 0.0 2.0 1.0
0.5 0.5 0.0 2.0 1.0 1.0 0.5 0.0 2.0 6.4 5.0 4.1 1.3 1.3 6.4 5.0 4.1
4.1 6.3 6.4 5.0 5.0 4.1 1.3 6.4 = 2 - - 39 -2.6 ) DFT ( , , .
f[m,n] { } 1 N n 0 , 1 M m 0 | ] n , m [ = . , , ( ) { } ( ) { } +
= = ==1 M0 m1 N0 n 2 1 D 2 1 n m j exp ] n , m [ f ] n , m [ f F ,
F " ( ) { } ( ) ( ) { } 2 1 2 1 2 122 11D d d n m j exp , F41, F F
] n , m [ f + = = , . , : , . , . , , | | | | + + , , . , , . , | |
| | + + , , , . MN , . , (Discrete Fourier Transform DFT) { }
)`|.|
\| + = = ==1 M0 m1 N0 nDFTNnMmk2 j exp ] n , m [ f ] n , m [ f F
] , k [ F ll " ) , ( F 2 1 | | N 2 , M k 2 1 1 l = = . , ] , k [ l
, , MN . " { } )`|.|
\| + = = == 1 M0 k1 N01DFTNnMmk2 j exp ] , k [ FNM1] , k [ F F ]
n , m [ flll l 2 - - 40 - - DFT )` =Nk 2j exp WkN. " { }{ } = = =
===== 1 M0 k1 N0 nNkmM1DFT1 M0 m1 N0 n nNkmM DFTW W ] , k [ FNM1] ,
k [ F F ] n , m [ fW W ] n , m [ f ] n , m [ f F ] , k [ Fllll ll
MN ? ) ( , , f F] 1 N , 1 M [ f] 0 , 1 [ f ] 0 , 0 [ fW W WW W W W
W W] 1 N , 1 M [ F] 0 , 1 [ F ] 0 , 0 [ F) 1 N )( 1 M (MN1 MMN0MN1
NMN1MN0MN0MN0MN0MNW = (((((
((((((
=(((((
MLM O M MLLM ) .( , ) " .( , MN MN . MN MN , , H , * WHW . ? , H
. , f " f g H = . H - , | || | G F g f f g H = = = W W * WHW H H .
, BIN " . W , - . . , . . - DFT , , . - 4 . 3 - 41 - 3 3 ... .. ..
..413.1 - ..413.2 ..............443.3 .........463.4 - ...51 - . 1
, " , . ) " ( . . 3.1 - f(x,y) . xD -yD ( )y xyx nD , mD fnD y mD
x) y , x ( f ] n , m [ f ==== xD -yD f(x,y) f[m,n] ? , " . " 3 - 42
-( ) =m n y x y nD , x mD ) y , x ( f ] n , m [ f~ ) 1 ( . , . { }
( ){ } ( ) ||.|
\| == ||.|
\| ==)` ==)` =m n y x y xm n y x y xm n y xm n y xDnv ,Dmu FD D
1Dnv ,Dmu ) v , u ( FD D 1y nD , x mD F ) y , x ( f Fy nD , x mD )
y , x ( f F ] n , m [ f~F - . - - " : ( ){ } ) D , D v, Comb(u,D D
1) D , D y, Comb(x, F) D Comb(y, ) D Comb(x, y nD , x mD ) D , D y,
Comb(x,1 -y1 -xy xy xy xm n y x y x= = = F(u,v) - ( )y x D / 1 , D
/ 1 . 3.1 . F(u,v) , . F(u,v) =otherwise 0 V v , U u ) v , u ( F) v
, u ( F max max , 3 - 43 -maxyymaxmaxxxmaxV 2 1DD 21VU 2 1DD
21U< 1 2 . - . . " 0 - 1 . . . 8 - - 186 - 8.9 : 6 -
{A,B,C,D,E,F} 16 1 } F { P , 16 1 } E { P , 8 1 } D { P , 8 1 } C {
P , 8 1 } B { P , 2 1 } A { P = = = = = = . 8.4 . . E - F . E+F . -
D ) E+F .( 1 , . . , ) ( E " 1 , 1 , 1 , 0 - . - . A,1/2} {B,1/8}
{C,1/8} {D,1/8} {E+F,1/8} {A,1/2} {B+C,1/4} {D+E+F,1/4} { A,1/2}
{B,1/8} {C,1/8} {D,1/8} {E,1/16} {F,1/6} {A,1/2} {B,1/8} {C,1/8}
{D+E+F,1/4} {A,1/2} {B+C+D+E+F,1/2} { {A+B+C+D+E+F,1/2} 8.4 - 0 10
11 01 01 0 8 - - 187 - 2 ) " ( , , . , : 1 ) X ( H L ) X ( HAverage
+ < , " . , - " - " , - " - " . , . , N 1/N . - . - 100 , 100 .
10,000 , \ . . , 5.14 . -6.14 - , . , \ . 8.5 . . , . , . 8.5 - 8 -
- 188 -8.4 - - . . , , 4 . - ) ( , . - , . , \ , . . . - " , - . -
, ) - ( . 8.6 . " , . . 8.5 . ) , ( , - . . , " " , . " " , , . 8.6
- " . ) ( , Non-Symetric Half Plane ) NSHP ( . 8 - - 189 - 8.10 :
X[k,j] ( ) ] 1 j , k [ X ] 1 j , 1 k [ X ] j , 1 k [ X ] 1 j , 1 k
[ X41] j , k [ X + + + + = , . " 8 , - 255 + 255 0.25 . , 2041 . -
2041 . , , 255 . { } + =2 1 E2 E Q [-1,+1) 0 , [+1,+3) - 2 . Lenna
. ; . , . 4.86 , 2.78 . , ) .( , . - " , " , . , . . , . , - , - -
. 8.7 . X[k,j] . - ] j , k [ X~ . , " . - ] j , k [ X. : 8 - - 190
-{ } { } ] 1 j , k [ X], 1 j , 1 k [ X], j , 1 k [ X], 1 j , 1 k [
Xf ] j , k [ X~] j , k [ X P + = = ] j , k [ X~] j , k [ X ] j , k
[ E = Q . . , , . { } ] k [ E Q ] k [ E = , . ) ( , . ] k [ E ] j ,
k [ X~ . : ( ) ( )( ) ] j , k [ E] j , k [ E ] j , k [ X ] j , k [
E] j , k [ E ] j , k [ X~] j , k [ E ] j , k [ X~] j , k [ E] j , k
[ X = = + = = + = , . ] j , k [ X. X QPP 8.7 - - DPCM . . " " .E E
^X~X^X^ 8 - - 191 - 8.11 : 8.9 , " - . , : +=4 2 E4 } E { Q 0
[-2,2) , 4 [2,6) , ' . 2.1 , 2 . . , , " - . . , . , . , :1 . - .2
. ) . ( , . 8.5 - - . " . - M N - . . , , , . , . 8.8 . 8.8 - . .X
QZTZ^ TX^1 - 8 - - 192 - - . 7 - KLT . - KLT , . . - - KLT - , ) (
. - KLT - . - KLT . - DCT - KLT , ) 16 16 .( , - KLT , ) 8 8 ( ,
DCT - . " - FFT . , . 64 ) 8 8 ( , . ) .( , . - , . - . - JPEG . "
DCT - . 8.12 : Lena " . 8 8 " DCT - . 8 8 - 8 - (0,0) , - 3 (0,*) -
(*,0) , ) " 14 ( , - 2 (1,1) , (1,2) , (2,1) - (2,2) . , " 8*64=512
- 68 , 1 - 8 . " " . , 8.9 . ) " ( 13.14 ) .( - . - 8 - - 193 - , .
1 - 10 . 6 . , - JPEG - Matlab . " ) imwrite ( - - Matlab A) -
uint8 ( , imwrite(A,'temp.jpg','quality',70) temp.jpg ) - JPEG .( -
JPEG , . 100% , . . 8.10 - 8.11 - JPEG . 8.10 ) quality ( , . 0 ,
0.7 - 0.3 . - - 0.5 , . , , . - 0.1 5.4 - . 8.9 - ) ( 1 - 8 " , 8 -
- 194 - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1024681012141618 8.10
- , . JPEG - Matlab . 8.11 - - JPEG : - , - 7.12 4.5 , - 11.65 5.84
. - 52.27 16.8 9 - - 195 - 9 9 1959.1 .. ...1969.2 - .2019.3 - ..
.2059.4 ...2109.5 - MPEG 215 , , . . - 30 . , . ) ( , . " . . ? , -
, , , . " . " : 1 . " . . , , . 2 . " . , . . 9 - - 196 - - . , . ,
. ) ( . 9.1 : - X[k,j,t] - X[k,j,t-1] . - ? , - . 9.1 . , , , - . .
: ] 1 t ), t , j , k ( dy j ), t , j , k ( dx k [ X ] t , j , k [ X
= dx(k,j,t) - dy(k,j,t) - ) k,j ( t . t , . , , \ \ . 9.2 - . . t ?
. " ." - . - , . , . . , . : 1 . - ) x,y ( : 9 - - 197 - =+=
feyxyxfeyxyx1 t t t 1 t , ] -e,-f .[ 2 . ) ( - " : ==+ =feyx) cos(
1 ) sin( ) sin( ) cos( 1yxyx) t , y , x ( dy ) t , y , x ( dxfeyx)
cos( ) sin( ) sin( ) cos(yxt 1 t tt 1 t 9.1 - , ) 9 - - 198 - . . ,
3 . - " : + = feyx) cos( ) sin( ) sin( ) cos(b 0 0 ayxt 1 t . , \ ,
" 5 . . 4 . - " :+ ==+=feyxd 1 c b a 1yxyx) t , y , x ( dy ) t , y
, x ( dxfeyxd c b ayxt 1 t tt 1 t . shear - - .X[k,t]X[k,t-1]kk 9.2
- " , 9 - - 199 - 5 . - " : [ ] 1yx h g feyxd c b ayxtt1 t ++= . ,
. 6 . - , - , . : LL+ + + + + = + + + + + = 22 2 2 2 221 1 1 1 1) t
( x e ) t ( y ) t ( x d ) t ( y c ) t ( x b a ) 1 t ( y) t ( x e )
t ( y ) t ( x d ) t ( y c ) t ( x b a ) 1 t ( x 9.3 . ) ( [2.1,4.2]
, ) ( [-15,15] 10 . , [-5,5] 0.7 - 1.5 . [-45,-15] [1, 0.7, -0.1,
1.3] . [0.01, 0.0062] . , , " . , . , " , . - , . - . - , ) , ( , .
. - . 9 - - 200 - 9.3 - ) ( : ) ( , ) ( , ) ( , ) ( , ) ( . 9 - -
201 - . ] t ), t , j , k ( dy j ), t , j , k ( dx k [ X ] 1 t , j ,
k [ X + + = X[k,j,t] X[k,j,t-1] . . F[t,1] , t t-1 . , F[t,k] t t-k
. : ) t ( X ) 1 , t ( F ) 1 t ( X = N . F . : ) t ( X ] 1 , t [ F ]
1 t , j , k [ X ) 1 t ( X nN1 n ] n , n [ 0 0 n 0 0 = = = - n0 ) ,
- [k0,j0] - ( . - 1 . , - n0 - n0+3 , [ ] ] 1 , t [ F 3 n , n 0 0 +
1 . , , . , . , ) Nearest Neighbor ( , - F 1 . - 4 - 1 , . , , , ,
. 9 - - 202 -9.2 - 512 512 . : 1 . . , .2 . , . , . , , - - . , .3
. . X[k,j,t] , . , . ? . , , . , - , ) 8 8 ( , . ) - 64 .( , , , .
- - . 512 512 , - 64 64 8 8 . , . - X[k,j,t] X[j,k,t-1] . " , . . -
B , ] n , m [ 0 0 X[k,j,t] , : 8 j , k 1 ] t , j n , k m [ X ] j ,
k [ B 0 0 + + = : 9 - - 203 -[ ] ( ) + + + + == =81 k81 j 20 0 1 t
, j n n , k m m X ] j , k [ B ] n , m [ E [m+m0,n+n0] , B . , [m,n]
- , . , - 6 , ] n , m [ 0 0 13 13 . , E[m,n] m - n - 6 + 6 . 9.4 4
4 . - ) p (2p+1)2 ( , E , . , . E : [ ] + + + + == =81 k81 j 0 0 1
t , j n n , k m m X ] j , k [ B ] n , m [ E B [m0,n0] t (t-1) 9.4 -
4 4 6 . , [m0,n0] 9 - - 204 - - . , E[m,n] ) - ( , . , E[m,n] . 9.5
, 9.6 - 9.7 9.1 16 16 10 . , . . 9.5 - " 9 - - 205 - 9.6 - " 9.7 -
" 9 - - 206 -9.3 - . - , . , . : ) 1 t , y , x ( I ) t ), t , y , x
( dy y ), t , y , x ( dx x ( I = + + ) , .( : 1 . .2 . - . , . -
[dx(x,y,t),dy(x,y,t)] ) , [-1,+1] .( , (x,y,t) - 1 . : ) t , y , x
( dy ) t , y , x ( I ) t , y , x ( dx ) t , y , x ( I ) t , y , x (
I) t , y , x ( dyy ) t , y , x ( I) t , y , x ( dxx ) t , y , x (
I) t , y , x ( I) t ), t , y , x ( dy y ), t , y , x ( dx x ( I ) 1
t , y , x ( Iy x + + ==++ == + + = [dx(x,y,t),dy(x,y,t)] , .
I(x,y,t) . , . . " " - (Brightness Constrained Equation - BCE) . 5
. , , - BCE . , . 9 - - 207 - - BCE . " Lucas - Kanade , . [k0,j0]
) .( 5 5 , [dx[k0,j0,t],dy[k0,j0,t]] . - 25 LS , , : B AVt , 2 j ,
2 k [ I ] 1 t , 2 j , 2 k [ I] t , j , k [ I ] 1 t , j , k [ I] t ,
2 j , 2 k [ I ] 1 t , 2 j , 2 k [ IB] t , j , k [ dy ] t , j , k [
dxV] t , 2 j , 2 k [ I ] t , 2 j , 2 k [ I] t , j , k [ I ] t , j ,
k [ I] t , 2 j , 2 k [ I ] t , 2 j , 2 k [ IA0 0 0 00 0 0 00 0 0 00
00 00 0 y 0 0 x0 0 y 0 0 x0 0 y 0 0 x= + + + + ==+ + + + =MMM MM M
V : ( ) B A A A B AV ArgMin V T1T2Vopt = = , - . 2 2 , . . , . , ,
, I(x,y,t-1) I(x,y,t) . . - . ATA , . - A - - . " " (Aperture
Problem) . 9.8 9 - - 208 - , " " , . . , , . - Condition Number - .
. 9.10 . , . 9.11 Lukas & Kanade . . 9.8 - - " . , , " - BCE -
. 9.10 - : [-1,1] . : ) ( , ) ( ) ( 9 - - 209 - [-1,+1] ,
[-0.919,0.937] . " , , , . 9.11 - " Lukas & Kanade . - . - 9 -
- - 210 - , Horn -Schunck . . U - x , - V - y . , . - BCE : | | YVU
H , H] t , N , M [ I] t , 1 , 1 [ IVU] t , N , M [ I 00 ] t , 1 , 1
[ I] t , N , M [ I 00 ] t , 1 , 1 [ Iy xxtyyxx=((
((((
=((
((((
M O O N M . " . MN MN 2 . . " " U , . U V , . , : { }((
(((
+ +=(((
=((
+ + + =Y H Y HD D H H H H H H D D H HVUV D U D Y V H U H ArgMin
V, Uyx1Ty y x yy xTx xoptopt2 22y xV , Uopt opt - , . , , - SD , )
( , : )`((
((
(((
+ + ((
=((
+ Y H Y HVUD D H H H H H H D D H HVUVUyxkTy y x yy xTx xk 1 k ,
. U - V - , U - V - . 9 - - - 211 - 9.12 9.10 - 9.11 . 100 = .
[0.9921,-0.9952] . 9.13 . 9.12 - " Horn & Schunck , 9.10 .0 10
20 30 40 50 60 70 80 90 1000.40.60.811.21.41.61.822.2 x 105 9.13 -
9 - - - 212 -9.4 . . , . . ) - ) t ( X , M N . ) t ( Y , M N , : )
t ( N )+ t ( X )= t ( Y , ) t ( Y ) t ( X . , ) ( . Y(t) , ) t ( X.
, ) t ( X - " . ) ( . , } ) k - t ( X , ) t ( X { } ) k - t ( Y , )
t ( Y { . - ) t,k ( G - ) k - t ( X ) t ( X , F . : ) k t ( X ) k ,
t ( G ) t ( X = - k , k . , 6 - - : 2 2) t ( XIntra ) t ( X D ) t (
X ) t ( Y ArgMin ) t ( X + = - Y , " . Intra ) Inter-frame ( )
Intra-frame .( . . : 9 - - - 213 -2 2 2) t ( XIn ) t ( X D ) t ( X
) 1 t ( Y ) 1 , t ( G ) t ( X ) t ( Y ArgMin ) t ( X + + = ) t ( X
, , ) 1 - t ( Y . - 1 . t=0 . : 2t0 k2k) t ( X ) t ( X D ) t ( X )
k t ( Y ) k , t ( G ArgMin ) t ( X + == k , . . : | | =(((
+ =((
+ = + =+==t0 k k T1 tTt0 k kTt0 k k) k t ( Y ) k , t ( G ) t (
XD D I11) t ( XD D I0 ) t ( X D D 2 ) k t ( Y ) k , t ( G ) t ( X 2
, 0 t , . ) 1 , 1 k t ( G ) 1 , 2 k t ( G ) 1 , 1 t ( G ) 1 , t ( G
) k , t ( G + + = L) 1 t ( P ) 1 , t ( G ) t ( Y) 1 j t ( Y ) 1 , j
t ( G ) 1 , 1 t ( G ) 1 , t ( G ) t ( Y) k t ( Y ) 1 , 1 k t ( G )
1 , 1 t ( G ) 1 , t ( G ) t ( Y) k t ( Y ) 1 , 1 k t ( G ) 1 , t (
G ) k t ( Y ) k , t ( G ) t ( P1 t0 j T kt1 k T kt0 k kt0 k k + ==
+ + == + + == + = ==== =LLL , ) t ( X ) 1 t ( P ) ( , " , ) t ( P )
t ( XD D I1 1 T ((
+ 9 - - - 214 - t 0t . " - SD : ) t ( P ) t ( XD D ) t ( X1) t (
X) t ( X kTk k 1 k + =+ , - , . ) t ( P , - (I) , - ) II ( . . 0 =
, , : ( ) ( ) ( )( ) ) 1 t ( X) 1 , t ( G ) t ( Y 1 ) t ( X ) 1 t (
P ) 1 , t ( G 1 ) t ( Y 1 ) t ( P 1 ) t ( X + + = = ) t ( X " - . .
G - , . ) 1 t ( X - ) t ( Y , ) 1 - t ( Y - ) t ( Y . 9.14 . ) t (
YG(t,1)) 1 - t ( P ) t ( P) t ( X 9.14 - . 9 - - 215 -9.5 - MPEG
On-Line , , . - . , . , , - , . . . , -MPEG . - JPEG , . , . 9.15 .
Prediction 9.15 - MPEG . DPCM , " JPEG . JPEGPrediction 9 - - 216 -
, DPCM . X(t) , - ) t ( X~ . " , ) t ( X, . , . , . , : 1 . X(t) 16
16 .2 . ) t ( X~ - X(t) .3 . " ) 1 t ( X . , ) 1 t ( X - ) t ( X~ .
) 1 t ( X ) 1 t ( X ) ( .4 . ) t ( X~ . X(t) - . ) t ( X~ , : ) t (
X~) t ( X ) t ( E = . - DPCM , , - E(t) , . " -JPEG - E(t) , DCT -
, . ) t ( E- E(t) . ) t ( E ) t ( X~ - , " " ) 1 t ( X . : )] t (
E) t ( E [ ) t ( X )] t ( E) t ( E [ ) t ( X~) t ( E ) t ( X~) t (
E) t ( X = + = + = - DPCM " - JPEG . 9.16 , , . 9 - - 217 - , )
1172 , 235 - - 4 . . . , 1265 65 - - 20 . ' . , . 9.16 , . 9.17 , .
, , . - . . . 30 500 500 , 7.5 MB . - MPEG 10-200 ) .( . 9.16 - : )
( ) .( : ) ( , " 8 8 ) ( , ) .( 9 - - 218 - 9.17 - 8 8 10 - - 219 -
10 0 1 . 21910.1 .22010.2 ..22110.3 ..22310.4 " .. 22610.5 "
22810.6 " 229 6 ) Restoration ( , . , 6 ) Inverse Problems .( , ) (
, . , , ) ( . ) Reconstruction ( . , , " " , . ) Computerized
Tomography - CT .( , , , . , - . Restoration Reconstruction . 10 -
- 220 - , , , . , , , . , . 10.1 - f(x,y) . . - (x,y) . 0I f(x,y) ,
L , . dL { } dL ) y , x ( f exp ) f(x,y) .( , . ,)` = L0 dL ) y , x
( f exp I I . , . 10.1 . f(x,y)sg(s,) 10.1 10 - - 221 - L " s . , (
))` + = x y0 dxdy s sin y cos x ) y , x ( f exp I ) , s ( I . I(s,)
< 0 < < s , f(x,y) . g(s,) :( ) + =)` = x y 0 dxdy s sin y
cos x ) y , x ( fI ) , s ( Ilog ) , s ( g . - . " : f(x,y) , ,
X-Ray CT . , . , , ) " " ( , " . , PET ) Positron Emission
Tomography ( . , \ . . - MRI ) ( , . , , " . 10.2 . , f(x,y) , { }
) y , x ( f " { } ( ) + = = x ydxdy s sin y cos x ) y , x ( f ) y ,
x ( f ) , s ( g . g < 0 - < < s . g(s,) f(x,y) . f f(r,) =
= sin r y cos r x , 10 - - 222 -{ } ( )( )( ) == == == + == + = = 0
r200 r20x ydxdy s ) cos( r ) , r ( rfdxdy s sin sin r cos cos r ) ,
r ( rfdxdy s sin y cos x ) y , x ( f ) y , x ( f ) , s ( g - f(r,)
f(s,) } r, { - ) cos( r s = . (x,y) . { } ) y , x ( f ) , s ( g = :
, , ) y , x ( f1 - ) y , x ( f2 { } { } { } ) y , x ( f ) y , x ( f
) y , x ( f ) y , x ( f 2 1 2 1 + = + . f(x,y) , , 0 ) y , x ( f ,
D y x | ) y , x ( 2 2 + , - D s D . -) k 2 , s ( g ) , s ( g + = ,
- ) , s ( g ) , s ( g + = . [0,] . f(x,y) (x0,y0) s . " :{ } ( )(
)). , sin y cos x s ( gdxdy s sin y cos x sin y cos x ) y , x (
fdxdy s sin y cos x ) y y , x x ( f ) y y , x x ( f0 0x y 0 0x y 0
0 0 0 == + + + == + = - { } a / ) , as ( g ) ay , ax ( f = . = s x
yds ) , s ( g dxdy ) y , x ( f , . . , 10.1 , ) " s .( " , f(x,y) .
, , , g(s,) < 0 - < < s f(x,y) . , . 10 - - 223 -10.3 . -
g(s,) s { } { } { } ) , u ( G ) y , x ( f ) , s ( g 1 1 = = . { } {
}{ } { } ( ) { }( ) { }( ) { }dxdy sin uy cos ux 2 j exp ) y , x (
fdxdy ds su 2 j exp s sin y cos x ) y , x ( fdxdy ds su 2 j exp s
sin y cos x ) y , x ( f ) y , x ( fds su 2 j exp ) , s ( g ) , s (
g ) , u ( Gx ys x ys x y1s1 + ==((
+ == + = == = = . - f(x,y) " ( ) ( ) { }dxdy y x 2 j exp ) y , x
( f , F y xx yy x + = . = = sin u , cos u y x - f(x,y) - ( ) ( ) =
, u F~sin u , cos u F :( ) ( ) { }dxdy sin yu cos xu 2 j exp ) y ,
x ( f , u F~x y + = , G(u,) - . " ) " Projection Slice Theorem .(
f(x,y) - g(s,) , " 10.2 :1 . \ - - g(s,) s . - G(u,) . ( ) , u F~.2
. \ {u,} = = sin u , cos u y x. ) .( ( )y x, F .3 . \ - ( )y x, F
f(x,y) . 10 - - 224 - , . - - . . . g(s,) : + =02 dsds sin y cos x)
, s ( gs21) y , x ( f , . " g(s,) s . " ." . . . , . " ." " + =0d )
, sin y cos x ( g ) y , x ( b g(s,) - (x,y) . (x,y) , - g(s,) - - s
. ? . { } ) y , x ( f f(x,y) g(s,) 1D{ } , s ( g1) , u ( F~ ' ) , (
F y x 2D 10.2 . 10 - - 225 - - Adjoint . , R f ) ( , TR ) Transpose
.( . . f(x,y) , g(s,) , b(x,y) , :2 2y x 1) y , x ( f ) y , x ( b+
= , - " . . . , - 1 N , , 1 , 0 n , N / nn = = K2 / M m 2 / M , M /
mS sm < = . N , M [-S,+S] . S/M f[k,j] . - 02 , . , -02 / 1 . M
. N -02 , . , MN , f[k,j] , . 02 , 02 / 1 D = . f S) s [-S,+S] . (
, , 2S 2S ( )202 / S 2 . ( )02 / S 2 , ( )02 / S 2 10 - - 226 - . ,
. . . - f(x,y) . 10.4 " . - . , . g[m,n] N n 0 , 2 / M m 2 / M <
< . ) m - g[m,:] Matlab ( , ) n - g[:,n] Matlab ( . 1D-FFT . M ,
- FFT - M . " . , - M N , N M(N+N) , FFT - . M(N+N) , , 10.3 . .
10.3 f[k,j] . , , . . , 2D-FFT . " . 10.4 . , . . 10 - - 227 - N N
, 2D-FFT . - , . xy 10.4 .xy 10.3 FFT . 10 - - 228 - 10.5 " . , .
g[m,n] N n 0 , 2 / M m 2 / M < < . ) m ( , ) n ( . , g[m,n] )
(= ((
|.|
\| +|.|
\| = 1 N0 n n ,Nnsin yNncos x g ) y , x ( b - . " x=kd, y=jd - d
= ((
|.|
\| +|.|
\| = = 1 N0 n n ,Nnsin jdNncos kd g ] j , k [ b ) jd , kd ( b .
m g . . :( ) ( )( ) ( ) )`+ = )`+ = + =2 21y x y x2 2y x y x2 2y x
1, B , Fy x 1, F , By x 1) y , x ( f ) y , x ( b F , . , , . , . ,
. . , , , , . 10 - - 229 - 10.6 " , . f[k,j] f . R f g , { } 1 N0
nnv f R g nn= + = , , , , , . " 6 , - Maximum Likelihood { } = = 1
N0 n22ff R g f nn. Min " ((
((
= = = 1 N0 nT11 N0 nToptnn n n g R R R f . " :v f RvvvfRRRgggg1
N101 N101 N10+ =(((((
+((((((
=((((((
= M M M " ( ) g R R R f T1Topt = . g RT . R RT . ML . ,
Condition-Number ) , .( , MAP . , { } = + = 1 N0 n2222ff D f R g f
nn. Min 10 - - 230 - " | | g R D D R R g R D D R R f T1T T1 N0
nT1T1 N0 nToptnn n n= = + =((
((
+ = . " " R RT , . 6 , . - . , . R N ) N ( . , . . f . , - . .
ML :{ } 2222 f D f R g f + = . " { } ( ) f D D 2 g f R R 2ff T T +
= ) Steepest Descent ( " ( ) ( )kTkTk 1 k f D D 2 g f R R f f + =+.
, f - D ) ( , DT . . R . RT . ) R - RT ( . . , . 10 - - 231 - - LMS
. . :{ } ( )= = = L1 j2j j22 f r g f R g f - L L , L ) ( . - SD ( )
( )j k jTjL1 jk kTk 1 k g f r r f g f R R f f = = =+. L . " , L " ,
. - LMS f . ( )( )( )( ) = = = = + + + + Lk1 L LTLk1 LkL1 jkj 1 jT1
jkjk1 j2k1 2T2k1k211 kL 1T11 kLk1g f r r f fg f r r f fg f r r f f
g f r r f fMM. , . " L - SD . , " . - SD ) ( - LMS . - LMS , . -
LMS . , . - 100 100 10.5 . 10 - - 232 -20 40 60 80
100102030405060708090100 10.5 100 100 . 100 [0,) , 100 s -50 49 . [
] 4 / , 4 / [ ] 4 / 3 , 4 / . , s , x [-50,49] ) ( y 0 s sin y cos
x = + . (x,y) 100 , . . y ) ( g(s,) . 100 s - 100 . 10.6 . Angle in
the range -/4 to 3*/4Shift s in the range -50 to 50-40 -20 0 20
400102030405060708090 10.6 g(s,) . 10 - - 233 - y 100 [-50,49] -x 0
s sin y cos x = + . ) Nearest-Neighbor ( , " , , , . 200 = ) - 100
[0,255] , 20 = . 10.7 - LMS . , R - RT , " " . . " " - ML .20 40 60
80 100102030405060708090100 20 40 60 80 100102030405060708090100
10.7 - LMS . 10 - - 234 - - LMS jr . , , . , , . . jr , , R 10000
10000 100 ' 1 ' ) .( . 10.8 {1,5,10,15} - SD . 20 40 60 80
10010203040506070809010020 40 60 80 10010203040506070809010020 40
60 80 10010203040506070809010020 40 60 80 100102030405060708090100
10.8 - ML ) ( , 5 ) ( , 10 ) ( - 15 ) ( - SD . 11 - - 235 - 11 1 1
. 23511.1 .23611.2 24011.3 Wavelet " - Lifting Scheme 249 - " ." ,
. . , , . - . , . - , ? , , . , . - Wavelet , " " . , - . . 11 - -
236 -.1 1 1 , ) ( . X(m,n) N N . PG - PG(0) . LPF . , PG(1) , .
PG(1) PG(2) . , . - LPF - 2 / ) .( 2:1 . , . 11.1 . ? . , - . Burt
- Adelson , 2N+1 { }k kwconst w , k . 4 , w w , 0 k . 3w w , 0 k .
2 , 1 w . 1jj 2 k 1 k kk kNN kk= > = > = = + = 11.1 . ,
.PG(0)PG(1)PG(2)PG(3) 11 - - 237 - . . . . 11.2 . , N=2 {c b a b c}
, 1 a b 2 c 2 = + + . , a b c . - b 2 a c 2 = + . b=0.25 ) ( , a -
0.25 ) ( , - c c=0.5(a-0.25) . a=0.4 " ." 11.3 - , - . ? . . , - .
, 11.1 , . . . ) 9 .( X 11.2 . - k , - 3 a+2c . , 2b . k - PG(k+1)
k - PG(k) 11 - - 238 - " H 2:1 " H 2:1 " H 2:1 11.3 - . 11 - - 239
-N N , Y L L ) L
