744.введение в цифровую обработку сигналов и изображений математические модели изображений

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  • ..

    :

    -

    2006

    Copyright & A K-C

  • 004.932, 519.7 22.343 241

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

    : -p .-. , . . . , -p . , . . .

    241 : : . / [.. .]. : - . . . -, 2006. 180 . : .

    ISBN 5-7883-04-91-1

    , , -, , , . -. . .

    (-) 010500, 010501, - 010600, - 200401.

    004.932, 519.7 22.343

    ISBN 5-7883-04-91-1 .. , .. , .. , .. , .. , 2006

    , 2006

    2

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  • 3

    1. ........................................................... 5 1.1. ............................................................................... 5 1.2. ............................................................................ 7 1.3. ......................................................... 10

    2. . . ............... 16 2.1. ....................................................... 16 2.2. ................................................... 19 2.3. ......................................................................... 23 2.4. ........................................................ 30 2.5. ................................................... 33 2.6. ........................ 36

    3. ............................................. 37 3.1. ............................................................ 37 3.2. ............................................................ 38

    4. ....... 41 4.1. ........................................................................ 41 4.2. -............................................................... 44 4.3. -.................. 47 4.4. ...................................................................... 49 4.5. ....................................................... 52 4.6. - ............................................. 56 4.7. ................................. 59 4.8. ................................................... 63

    5. ............... 67 5.1. -

    ............................................................................................ 67 5.2. ........................... 70 5.3.

    ............................................................................................ 76 5.4.

    ............................................................................................. 80

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  • 4

    6. z-.................................................................................... 86 6.1. z-................................................................. 86 6.2. z- .............................................. 94 6.3. z-.............................................................. 98 6.4. - z-105 6.5. z- ......................................................... 113 6.6. z- ......................... 123 6.7. -

    z- ............................................................................ 126 7. ........................................... 133

    7.1. ................................................ 133 7.2. z-

    ........................................................................ 137 7.3.

    ............................................................................................ 139 7.4.

    ................................................................................... 140 7.5. ............................................................... 143 7.6. .......................... 146 7.7. ..................................................... 148

    8. ..................................................... 157 8.1. ..................................................................... 157 8.2. .................... 164 8.3.

    - .............................................................................. 168 8.4. ......................................... 170

    ................................................................................................ 178

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  • 1.

    1.1.

    . -, , . , , . - , - . , . .

    5

    1

    , , .1. , , - x , 2x -

    . . -

    .

    (C x )1 2, ,x

    ( )1 2 max0 , ,C x x C

    max

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    , (1)

    C - . -

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    -, ( )s . , -

    . min 0,35 = ma 8x 0,7 =

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  • - .

    , . -, , , - .

    .1. ,

    , - , - ( )1 2, ,C x x ( )s

    ( )max

    min

    1 2f x x

    ( ) ( )1 2, , , dC x x s=

    (

    . (3)

    )f 1 2,x x . - - - , -.

    6

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  • 1.2.

    -, . , . t ( )1 2 3, ,x x x=x , - ,

    ( ) ( ), i t

    7

    E t U e =x x , (4)

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    - , c ,

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    T

    T

    f E t tT

    = x x

    ( )1 2,

    . (7)

    f x x .

    , , - , .

    .

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  • 1.

    ( )2

    2

    1 iU e=

    xx

    x, 2 2 2 21 2 3x

    8

    x x= + +x . (8)

    . 2. , 3x ,

    ( )3

    1 2 3, , ,xi t cx x t e

    E x . (9)

    . ,

    , .2.

    .2.

    . - . .

    , .3.

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  • .3.

    - S,

    . - x, ,

    , ,

    S

    S

    ( ) ( ) ( )U t U tE t + . (10) = x

    ( ) ( ) ( )

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    d d .

    T T

    T TT

    T T

    t U t tT T

    U t U t t

    +

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    2

    2 2

    1 12

    T

    I E

    U t tT T

    = =

    +

    (11)

    9

    ( ) ( ) ( )dT

    T

    1lim2T

    R U t U t t

    T

    T = , (12)

    (11)

    ( ) ( ) ( )2 0 2I R R = + . (13) , -

    , , - . 3. .

    ( ) cosU t A t . (14) =

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  • ( ) ( )2

    d cos2 2

    At t =

    ( )

    21lim cos cosT

    TT

    R A tT

    = , (15)

    10

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    . (16)

    (16) .4.

    .4.

    - - . , .

    1.3.

    , , - .

    L, f g. (1-D) (2-D) .

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  • ( ) ( )g x f x

    11

    = L . (17)

    - ( ) ( )1 2 1 2, ,g x x f x x= L . (18)

    , .

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    L (19)

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    = L

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    L . (20)

    - . - - :

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    =

    (21)

    : - ,

    ( ) ( ){ }2 2 2 21 2exp x x1 2, limx x + = . (22) (22) -

    , - .5.

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  • .5. -

    -, , ( )1 2,

    1 1 2 2 , .

    x x

    ( )1 1 2 2,

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    =

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    = . (24)

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    ) 1 2 1 2d d ( , )x x f = , (25)

    ( )1 2,f - . - (24) (25) (22) .

    2-D , -. -

    12

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  • . 2-D . --, ( )1 2,x x ( )1 2, . , .6, , () - , .

    .6. -

    - ( ) ( )1 1h x 2 2 1 2, ,x h , (26)

    13

    1 1 1 2 2 2,x x = =

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    (

    . (27)

    , -, 2-D . )f 1 2,x x

    (

    (25) 2-D )1 2,h .

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  • ( ) ( )

    )

    1 2

    1 2 2 1 2

    , ,

    , , d d .

    x x

    x

    = ( ) (

    1 2

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    L

    L (28)

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    , ( ){ } ( )1 1 2 2x x 1 1 2 2, , ,h x x L ,

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    = x d d . (29)

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    14

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  • .7.

    15

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  • 2. . .

    2.1.

    , - .

    , ( ) ( )f x f x lL= + , (30)

    L ; l , - .

    ,

    ( ) 01k

    f x c

    =

    cos 2k kxc kL

    = +